In this work, a novel finite element model using the mechanical homogenization techniques of the human annulus fibrosus (AF) is proposed to accurately predict relevant moduli of the AF lamella for tissue engineering application. A general formulation for AF homogenization was laid out with appropriate boundary conditions. The geometry of the fibre and matrix were laid out in such a way as to properly mimic the native annulus fibrosus tissue’s various, location-dependent geometrical and histological states. The mechanical properties of the annulus fibrosus calculated with this model were then compared with the results obtained from the literature for native tissue. Circumferential, axial, radial, and shear moduli were all in agreement with the values found in literature. This study helps to better understand the anisotropic nature of the annulus fibrosus tissue, and possibly could be used to predict the structure-function relationship of a tissue-engineered AF.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
ATEAS V1(1):: American Transactions on Engineering & Applied Sciencesdrboon
Research from American Transactions on Engineering & Applied Sciences::
A Novel Finite Element Model for Annulus Fibrosus Tissue Engineering Using Homogenization Techniques
Relevance Vector Machines for Earthquake Response Spectra
Influence of Carbon in Iron on Characteristics of Surface Modification by EDM in Liquid Nitrogen
Establishing empirical relations to predict grain size and hardness of pulsed current micro plasma arc welded SS 304L sheets
Cyclic Elastoplastic Large Displacement Analysis and Stability Evaluation of Steel Tubular Braces
SAFARILAB: A Rugged and Reliable Optical Imaging System Characterization Set-up for Industrial Environment
Modal Analysis of Fibre Reinforced Composite Beams with a Transverse Crack U...IJMER
In many structures like high speed machineries, aircrafts and light weight structures
composite beams and beam like structures are main constituent elements. Cracks induced in these
structural elements cause serious failure and monitoring of these cracks is essential. The presence of
these cracks influences the dynamic characteristics of the structural elements. Hence the changes in
natural frequencies and mode shapes have been the subject of interest of many investigations. In the
present work two Fiber- Reinforced Plastic (FRP) materials, Graphite Fibre Reinforced Polyamide
and E-Glass Fibre Reinforced Polymer have been selected as beam materials for modal analysis using
ANSYS 13.0. The analysis is carried out for these two beams in different ways. Initially the analysis is
carried out for different orientation of fibres for two beams. Later the effect of dimensions is analyzed
by varying one dimension of the beam at a time by keeping the other two constant. In the next step the
analysis is performed for constant dimensions of each beam for same layer orientation and constant
volume fraction of fibre by introducing transverse cracks of different depths at various positions along
the length of the beam. The results obtained are analyzed.
Stiffness Characteristics of Joshi’s External Stabilization System under Axia...IJERA Editor
A finite element model of fractured tibia with Joshi’s External Stabilizing System (JESS) mounted on it was developed using 3D beam elements in the ANSYS software. The model was loaded in axial compression and the average axial stiffness of the model was calculated. The analytical value of axial stiffness was compared with reported experimental value to validate the finite element model. The validated model was used to carry out parametric studies on the model to determine the axial properties of JESS. It was observed that axial stiffness of JESS increased by 58% when k-wire diameter was varied from 2 mm to 4 mm while keeping other geometric configurations of the device constant; however, the axial stiffness of the device does not show any significant improvement when the diameter of medio-lateral pins in diaphyseal hold were increased. The findings should help in understanding the axial properties of JESS so that it can be used judiciously in clinical applications.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
ATEAS V1(1):: American Transactions on Engineering & Applied Sciencesdrboon
Research from American Transactions on Engineering & Applied Sciences::
A Novel Finite Element Model for Annulus Fibrosus Tissue Engineering Using Homogenization Techniques
Relevance Vector Machines for Earthquake Response Spectra
Influence of Carbon in Iron on Characteristics of Surface Modification by EDM in Liquid Nitrogen
Establishing empirical relations to predict grain size and hardness of pulsed current micro plasma arc welded SS 304L sheets
Cyclic Elastoplastic Large Displacement Analysis and Stability Evaluation of Steel Tubular Braces
SAFARILAB: A Rugged and Reliable Optical Imaging System Characterization Set-up for Industrial Environment
Modal Analysis of Fibre Reinforced Composite Beams with a Transverse Crack U...IJMER
In many structures like high speed machineries, aircrafts and light weight structures
composite beams and beam like structures are main constituent elements. Cracks induced in these
structural elements cause serious failure and monitoring of these cracks is essential. The presence of
these cracks influences the dynamic characteristics of the structural elements. Hence the changes in
natural frequencies and mode shapes have been the subject of interest of many investigations. In the
present work two Fiber- Reinforced Plastic (FRP) materials, Graphite Fibre Reinforced Polyamide
and E-Glass Fibre Reinforced Polymer have been selected as beam materials for modal analysis using
ANSYS 13.0. The analysis is carried out for these two beams in different ways. Initially the analysis is
carried out for different orientation of fibres for two beams. Later the effect of dimensions is analyzed
by varying one dimension of the beam at a time by keeping the other two constant. In the next step the
analysis is performed for constant dimensions of each beam for same layer orientation and constant
volume fraction of fibre by introducing transverse cracks of different depths at various positions along
the length of the beam. The results obtained are analyzed.
Stiffness Characteristics of Joshi’s External Stabilization System under Axia...IJERA Editor
A finite element model of fractured tibia with Joshi’s External Stabilizing System (JESS) mounted on it was developed using 3D beam elements in the ANSYS software. The model was loaded in axial compression and the average axial stiffness of the model was calculated. The analytical value of axial stiffness was compared with reported experimental value to validate the finite element model. The validated model was used to carry out parametric studies on the model to determine the axial properties of JESS. It was observed that axial stiffness of JESS increased by 58% when k-wire diameter was varied from 2 mm to 4 mm while keeping other geometric configurations of the device constant; however, the axial stiffness of the device does not show any significant improvement when the diameter of medio-lateral pins in diaphyseal hold were increased. The findings should help in understanding the axial properties of JESS so that it can be used judiciously in clinical applications.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Characterization of Mechanical, Thermal, and Electrical Properties of Carbon ...drboon
In this paper, the mechanical, thermal and electrical properties of carbon fiber modified thermoplastic polyimide were numerically analyzed by finite element analysis. A three-dimensional model was created, in which continuous carbon fibers are aligning and paralleling to each other and uniformly distributing in the polymer matrix. The behaviors of the composites in two extreme situations, i.e., parallel or perpendicular to carbon fiber direction, were simulated. The effects of the volume fraction of carbon fiber content on the physical properties were investigated. It shows clearly that carbon fibers significantly improve the mechanical strength, and thermal and electrical conductivities. The future work includes investigation of the physical properties of the conductive network of the composites with random carbon fiber orientation, and different fillers, such as graphite, and carbon nanotubes.
Linear And Nonlinear Analytical Modeling of Laminated Composite Beams In Thre...researchinventy
The large current development of aerospace and automotive technologies is based on the use of composite materials which provide significant weight savings compared to their mechanical characteristics. Correct dimensioning of composite structures requires a thorough knowledge of their behavior in small as in large deflection.This work aims to simulate linear and nonlinear behavior of laminates composites under threepoint bending test. The used modelization is based on first-order shear deformation theory (FSDT), classical plate theory (CPT) and Von-Karman’s equations for large deflection. A differential equation of Riccati, describing the variation of the deflection depending on the load, was obtained. Hence, the results deduced show a good correlation with experimental curves
Recent joint surgery studies reveal increased
revisions and resurfacing of the metal on metal hip joints. Metal
on metal hip implants were developed more than thirty years ago
and their application has been refined because of availability of
advanced manufacturing techniques and partly by advancements
in material science and engineering. Development of composite
materials may provide greater durability to metal-on-metal hip
implants .This review article is a study of the latest literature of
metal-on-metal hip implants and its various modeling techniques.
Numbers of methods are used for convergence and numerical
solution to investigate the performance of metal-on-metal hip
implant for accurate stable solution. This paper presents analysis
done by various researchers on metal-on-metal hip implants for
wear, lubrication, fatigue, bio-tribo-corrosion, design, toxicity
and resurfacing. After in vivo and in vitro studies, it is found that
all these methods have limitations. There is a need of more
insight for lubrication analysis, geometry of bearings, materials
and input parameters. The information provided in this work is
intended as an aid in the assessment of metal-on-metal hip joints.
Micromechanical Modeling of the Macroscopic Behavior of Soft Ferromagnetic Co...IJMERJOURNAL
ABSTRACT: Soft ferromagnetic composites consist of ferromagnetic particles embedded within nonmagnetic electrically insulating matrix. The aims of this article are twofold. In the first one, multiaxial nonlinear isothermal constitutive equations that govern the behavior of soft ferromagnetic materials are generalized to include the temperature and hysteretic effects. The second aim consists of developing a micromechanical analysis which takes into account the detailed interaction between the phases, and establishes the instantaneous concentration tensors which relate between the local magneto-thermo-elastic field and the externally applied loading. The ferromagnetic particles constituents employed in the micromechanical analysis are governed by the developed magneto-thermo-elastic coupled hysteretic constitutive relations. With the established concentration tensors, the macroscopic (global) re- sponse of the composite can be readily determined at any instant of loading. The offered micromechanical modeling is capable of predicting the response of soft ferromagnetic composites that are subjected to various types of magneto-thermo-elastic loadings, and it can be employed by the designerto easily determine the composite response for a particular desired application.
Dr jehad al sukhun gives modelling of orbital deformationjehadsukhun
The purpose of this study was to develop a three-dimensional finite-element model (FEM) of the human orbit, containing the globe, to predict orbital deformation in subjects following a blunt injury
Modelling of orbital deformation - Jehad Al Sukhun and othersDr Jehad Al Sukhun
The purpose of this study was to develop a three-dimensional finite-element model (FEM) of the human orbit, containing the globe, to predict orbital deformation in subjects following a blunt injury. This study investigated the hypothesis that such deformation could be modelled using finite-element techniques. To know more about modelling of orbital deformation contact to Jehad Al Sukhun at http://drjehadalsukhun.com.
Dynamic Relaxation (DR) method is presented for the analysis of
geometrically linear laterally loaded, rectangular laminated plates. The
analysis uses the Mindlin plate theory which accounts for transverse shear
deformations. A computer program has been compiled. The convergence
and accuracy of the DR solutions of isotropic, orthotropic, and laminated
plates for elastic small deflection response are established by comparison
with different exact and approximate solutions. The present Dynamic
Relaxation (DR) method shows a good agreement with other analytical and
numerical methods used in the verification scheme.
It was found that: The convergence and accuracy of the DR solution is
dependent on several factors which include boundary conditions, mesh size
and type, fictitious densities, damping coefficients, time increment and
applied load. Also, the DR small deflection program using uniform meshes
can be employed in the analysis of different thicknesses for isotropic,
orthotropic or laminated plates under uniform loads in a fairly good
accuracy.
Dynamic Homogenisation of randomly irregular viscoelastic metamaterialsUniversity of Glasgow
An analytical framework is developed for investigating the effect of viscoelasticity on irregular hexagonal lattices. At room temperature, many polymers are found to be near their glass temperature. Elastic moduli of honeycombs made of such materials are not constant, but changes in the time or frequency domain. Thus consideration of viscoelastic properties is essential for such honeycombs. Irregularity in lattice structures being inevitable from a practical point of view, analysis of the compound effect considering both irregularity and viscoelasticity is crucial for such structural forms. On the basis of a mechanics-based bottom-up approach, computationally efficient closed-form formulae are derived in the frequency domain. The spatially correlated structural and material attributes are obtained based on Karhunen-Lo\`{e}ve expansion, which is integrated with the developed analytical approach to quantify the viscoelastic effect for irregular lattices. Consideration of such spatially correlated behaviour can simulate the practical stochastic system more closely. Two Young's moduli and shear modulus are found to be dependent on the viscoelastic parameters, while the two in-plane Poisson's ratios are found to be independent of viscoelastic parameters. Results are presented in both deterministic and stochastic regime, wherein it is observed that the elastic moduli are significantly amplified in the frequency domain. The response bounds are quantified considering two different forms of irregularity, randomly inhomogeneous irregularity and randomly homogeneous irregularity. The computationally efficient analytical approach presented in this study can be quite attractive for practical purposes to analyse and design lattices with predominantly viscoelastic behaviour along with consideration of structural and material irregularity.
Homogeneous dynamic characteristics of damped 2 d elastic latticesUniversity of Glasgow
Lattice materials are characterised by their equivalent elastic moduli for analysing mechanical properties of the microstructures. The values of the elastic moduli under static forcing condition are primarily dependent on the geometric properties of the constituent unit cell and the mechanical properties of the intrinsic material. Under a static forcing condition, the equivalent elastic moduli (such as Young's modulus) are always positive. Poisson’s ratio can be positive or negative, depending only on the geometry of the lattice (e.g., re-entrant lattices have negative Poisson’s ratio). When dynamic forcing is considered, the equivalent elastic moduli become functions of the applied frequency and can become negative at certain frequency values. This paper, for the first time, explicitly demonstrates the occurrence of negative equivalent Young's modulus in lattice materials. In addition, we show the reversal of Poisson’s ratio. Above certain frequency values, a regular lattice can have negative Poisson’s ratio, while a re-entrant lattice can have a positive Poisson’s ratio. Using a titanium-alloy hexagonal lattice metastructure, it is shown that the real part of experimentally measured in-plane Young's modulus becomes negative under a dynamic environment as well as the reversal of the real part of the Poisson’s ratio. In fact, we show that the onset of negative Young's modulus and Poisson’s ratio reversal in lattice materials can be precisely determined by capturing the sub-wavelength scale dynamics of the system. Experimental confirmation of the negative Young's moduli and Poisson’s ratio reversal together with the onset of the same as a function of frequency provide the necessary physical insights and confidence for its potential exploitation in various multi-functional structural systems and devices across different length scales.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Characterization of Mechanical, Thermal, and Electrical Properties of Carbon ...drboon
In this paper, the mechanical, thermal and electrical properties of carbon fiber modified thermoplastic polyimide were numerically analyzed by finite element analysis. A three-dimensional model was created, in which continuous carbon fibers are aligning and paralleling to each other and uniformly distributing in the polymer matrix. The behaviors of the composites in two extreme situations, i.e., parallel or perpendicular to carbon fiber direction, were simulated. The effects of the volume fraction of carbon fiber content on the physical properties were investigated. It shows clearly that carbon fibers significantly improve the mechanical strength, and thermal and electrical conductivities. The future work includes investigation of the physical properties of the conductive network of the composites with random carbon fiber orientation, and different fillers, such as graphite, and carbon nanotubes.
Linear And Nonlinear Analytical Modeling of Laminated Composite Beams In Thre...researchinventy
The large current development of aerospace and automotive technologies is based on the use of composite materials which provide significant weight savings compared to their mechanical characteristics. Correct dimensioning of composite structures requires a thorough knowledge of their behavior in small as in large deflection.This work aims to simulate linear and nonlinear behavior of laminates composites under threepoint bending test. The used modelization is based on first-order shear deformation theory (FSDT), classical plate theory (CPT) and Von-Karman’s equations for large deflection. A differential equation of Riccati, describing the variation of the deflection depending on the load, was obtained. Hence, the results deduced show a good correlation with experimental curves
Recent joint surgery studies reveal increased
revisions and resurfacing of the metal on metal hip joints. Metal
on metal hip implants were developed more than thirty years ago
and their application has been refined because of availability of
advanced manufacturing techniques and partly by advancements
in material science and engineering. Development of composite
materials may provide greater durability to metal-on-metal hip
implants .This review article is a study of the latest literature of
metal-on-metal hip implants and its various modeling techniques.
Numbers of methods are used for convergence and numerical
solution to investigate the performance of metal-on-metal hip
implant for accurate stable solution. This paper presents analysis
done by various researchers on metal-on-metal hip implants for
wear, lubrication, fatigue, bio-tribo-corrosion, design, toxicity
and resurfacing. After in vivo and in vitro studies, it is found that
all these methods have limitations. There is a need of more
insight for lubrication analysis, geometry of bearings, materials
and input parameters. The information provided in this work is
intended as an aid in the assessment of metal-on-metal hip joints.
Micromechanical Modeling of the Macroscopic Behavior of Soft Ferromagnetic Co...IJMERJOURNAL
ABSTRACT: Soft ferromagnetic composites consist of ferromagnetic particles embedded within nonmagnetic electrically insulating matrix. The aims of this article are twofold. In the first one, multiaxial nonlinear isothermal constitutive equations that govern the behavior of soft ferromagnetic materials are generalized to include the temperature and hysteretic effects. The second aim consists of developing a micromechanical analysis which takes into account the detailed interaction between the phases, and establishes the instantaneous concentration tensors which relate between the local magneto-thermo-elastic field and the externally applied loading. The ferromagnetic particles constituents employed in the micromechanical analysis are governed by the developed magneto-thermo-elastic coupled hysteretic constitutive relations. With the established concentration tensors, the macroscopic (global) re- sponse of the composite can be readily determined at any instant of loading. The offered micromechanical modeling is capable of predicting the response of soft ferromagnetic composites that are subjected to various types of magneto-thermo-elastic loadings, and it can be employed by the designerto easily determine the composite response for a particular desired application.
Dr jehad al sukhun gives modelling of orbital deformationjehadsukhun
The purpose of this study was to develop a three-dimensional finite-element model (FEM) of the human orbit, containing the globe, to predict orbital deformation in subjects following a blunt injury
Modelling of orbital deformation - Jehad Al Sukhun and othersDr Jehad Al Sukhun
The purpose of this study was to develop a three-dimensional finite-element model (FEM) of the human orbit, containing the globe, to predict orbital deformation in subjects following a blunt injury. This study investigated the hypothesis that such deformation could be modelled using finite-element techniques. To know more about modelling of orbital deformation contact to Jehad Al Sukhun at http://drjehadalsukhun.com.
Dynamic Relaxation (DR) method is presented for the analysis of
geometrically linear laterally loaded, rectangular laminated plates. The
analysis uses the Mindlin plate theory which accounts for transverse shear
deformations. A computer program has been compiled. The convergence
and accuracy of the DR solutions of isotropic, orthotropic, and laminated
plates for elastic small deflection response are established by comparison
with different exact and approximate solutions. The present Dynamic
Relaxation (DR) method shows a good agreement with other analytical and
numerical methods used in the verification scheme.
It was found that: The convergence and accuracy of the DR solution is
dependent on several factors which include boundary conditions, mesh size
and type, fictitious densities, damping coefficients, time increment and
applied load. Also, the DR small deflection program using uniform meshes
can be employed in the analysis of different thicknesses for isotropic,
orthotropic or laminated plates under uniform loads in a fairly good
accuracy.
Dynamic Homogenisation of randomly irregular viscoelastic metamaterialsUniversity of Glasgow
An analytical framework is developed for investigating the effect of viscoelasticity on irregular hexagonal lattices. At room temperature, many polymers are found to be near their glass temperature. Elastic moduli of honeycombs made of such materials are not constant, but changes in the time or frequency domain. Thus consideration of viscoelastic properties is essential for such honeycombs. Irregularity in lattice structures being inevitable from a practical point of view, analysis of the compound effect considering both irregularity and viscoelasticity is crucial for such structural forms. On the basis of a mechanics-based bottom-up approach, computationally efficient closed-form formulae are derived in the frequency domain. The spatially correlated structural and material attributes are obtained based on Karhunen-Lo\`{e}ve expansion, which is integrated with the developed analytical approach to quantify the viscoelastic effect for irregular lattices. Consideration of such spatially correlated behaviour can simulate the practical stochastic system more closely. Two Young's moduli and shear modulus are found to be dependent on the viscoelastic parameters, while the two in-plane Poisson's ratios are found to be independent of viscoelastic parameters. Results are presented in both deterministic and stochastic regime, wherein it is observed that the elastic moduli are significantly amplified in the frequency domain. The response bounds are quantified considering two different forms of irregularity, randomly inhomogeneous irregularity and randomly homogeneous irregularity. The computationally efficient analytical approach presented in this study can be quite attractive for practical purposes to analyse and design lattices with predominantly viscoelastic behaviour along with consideration of structural and material irregularity.
Homogeneous dynamic characteristics of damped 2 d elastic latticesUniversity of Glasgow
Lattice materials are characterised by their equivalent elastic moduli for analysing mechanical properties of the microstructures. The values of the elastic moduli under static forcing condition are primarily dependent on the geometric properties of the constituent unit cell and the mechanical properties of the intrinsic material. Under a static forcing condition, the equivalent elastic moduli (such as Young's modulus) are always positive. Poisson’s ratio can be positive or negative, depending only on the geometry of the lattice (e.g., re-entrant lattices have negative Poisson’s ratio). When dynamic forcing is considered, the equivalent elastic moduli become functions of the applied frequency and can become negative at certain frequency values. This paper, for the first time, explicitly demonstrates the occurrence of negative equivalent Young's modulus in lattice materials. In addition, we show the reversal of Poisson’s ratio. Above certain frequency values, a regular lattice can have negative Poisson’s ratio, while a re-entrant lattice can have a positive Poisson’s ratio. Using a titanium-alloy hexagonal lattice metastructure, it is shown that the real part of experimentally measured in-plane Young's modulus becomes negative under a dynamic environment as well as the reversal of the real part of the Poisson’s ratio. In fact, we show that the onset of negative Young's modulus and Poisson’s ratio reversal in lattice materials can be precisely determined by capturing the sub-wavelength scale dynamics of the system. Experimental confirmation of the negative Young's moduli and Poisson’s ratio reversal together with the onset of the same as a function of frequency provide the necessary physical insights and confidence for its potential exploitation in various multi-functional structural systems and devices across different length scales.
TRANSIENT ANALYSIS OF PIEZOLAMINATED COMPOSITE PLATES USING HSDTP singh
Piezoelectric materials have excellent sensing and actuating capabilities have made them the most practical smart materials to integrate with laminated structures. Integrated structure system can be called a smart structure because of its ability to perform self-diagnosis and quick adaption to environment changes. An analytical procedure has been developed in the work based on higher order shear deformation theory subjected to electromechanical loading for investigating transient characteristics of smart material plates. For analysis two displacement models are to be considered i.e., model-1 accounts for strain in thickness direction is zero whereas in model-2 in-plane displacements are expanded as cubic functions of the thickness coordinate. Navier’s technique has been adopted for obtaining solutions of anti-symmetric cross–ply and angle-ply laminates of both model-1 and model-2 with simply supported boundary conditions. For obtaining transient response of a laminated composite plate attached with piezoelectric layer Newmark’s method has been used. Effect of thickness coordinate of composite laminated plates attached with piezoelectric layer subjected to electromechanical loadings is studied.
Size dependent and tunable elastic properties of hierarchical honeycombs with...Libo Yan
Simple closed-form results for all the independent elastic constants of macro-, micro- and nanosized first-order regular honeycombs
with square and equilateral triangular cells and for the self-similar hierarchical honeycombs were obtained. It is found that, if the cell wall
thickness of the first-order honeycomb is at the micrometer scale, the elastic properties of a hierarchical honeycomb are size dependent,
owing to the strain gradient effects. Further, if the first-order cell wall thickness is at the nanometer scale, the elastic properties of a hierarchical
honeycomb are not only size dependent owing to the effects of surface elasticity and initial stresses, but are also tunable. In addition,
the cell size and volume of hierarchical nanostructured cellular materials can be varied, and hierarchical nanostructured cellular
materials could also possibly be controlled to collapse.
11(4) 2020 ITJEMAST Multidisciplinary Research Articlesdrboon
Research papers 2020 Behavioral finance; Personality traits; Behavioral factors; Overconfidence bias; Locus of control; Decision-making; Biased behavior Carbon (CO2) emissions; Economic Growth; Energy consumption; Trade; ARDL Approach; Granger Causality; Energy use Pedestrian start-up time; Street crosswalk, Pedestrian traffic signals; Pedestrians traffic lights; zebra crossings; Intersection crossings Service Attributes; Relationship quality; Relationship outcomes; Banking services; Electronic Customer Relationship Management; Virtual relationships; eBanking; eCRM College town landscape; College town character; Campus community; Urban identity; College town space; Sense of a place; Public Space; University gardens; Cultural identity; Campus identity; Businesses in college towns Emotional quotient; Self-emotional appraisal; Workplace Advice Network (WAN) Centrality; Service Sector Organizations; Sociometric matrix; Interconnectivity of nodes
11(3) 2020 ITJEMAST Multidisciplinary Research Articles drboon
Non-destructive testing method Heat loss Thermal conductivity Specific heat Know-how Psychological contract breach Employees' Workplace behaviour Workplace spirituality Human resource management (HRM) Power sector Positive classroom Male teachers Classroom management system Public primary schools Private primary school Positive motivation students Quality primary education Grout rheology Construction workings High-precision lining Tunneling complex Cement slurry Reinforcement solutions Smart building systems Green architecture Green roof Green design Sustainable environmental architecture Smart energy management Architecture technology Neo-Functionalism Trade integration CPEC agreement Economic integration Regional cooperation Pak-China relations Pak-Iran relations Central Asia Republics Sino-Pakistan Agreement
11(2)2020 International Transaction Journal of Engineering, Management, & Ap...drboon
Multidisciplinary Management, Journalism and Mass Communication Science (Information and Media Sciences), Political Sciences (International Affairs), Global Studies), Animal Sciences, Feeding Technology, Healthcare Management.
V8(3) 2017:: International Transaction Journal of Engineering, Management, & ...drboon
Research articles published in V8(3) 2017:: International Transaction Journal of Engineering, Management, & Applied Sciences & Technologies ==>
Awareness of Passive Design on Apartment Façade Designs in Putrajaya, Malaysia
127
Comparative Analysis of Low-Cost Housing Policies in Malaysia and Nigeria
139
A Study on Kevin Lynch’s Urban Design Elements: Precinct 9 East Putrajaya
153
Investigating Urban Design Elements of Bandar Baru Sentul, Kuala Lumpur
169
A Study on Sharing Home Ownership Schemes in Malaysia
183
The Impact of Window to Wall Ratio (WWR) and Glazing Type on Energy Consumption in Air-Conditioned Office Buildings
197
Competitiveness Factors of Thai Construction Industry within the AEC Context: A Qualitative Approach
209
Application of Confirmatory Factor Analysis in Government Construction Procurement Problems in Thailand
221
In a world of rapidly increasing urbanization, striving to develop more livable cities, the city’s streets designing and planning should be high on the agenda for policymakers, city planners and other practitioners, as well as researchers. Designing streets is not as easy as it might originally seem, however, done correctly it means that one third of the city was designed successfully with an immense impact on the rest of the city. The key challenge in developing sustainable and fulfilling streets is to develop an integrated approach in planning them, where it is necessary to consider all aspects involved. Meanwhile, efforts devoted to this topic vary considerably from place to place. Thus, this paper aims at discussing the main elements involved in designing streets for a livable city, in a comprehensive approach including pedestrians, vehicles, and parking areas.
Impact of Building Envelope Modification on Energy Performance of High-Rise A...drboon
In residential buildings, providing comfortable living environment for building occupants is a major challenge for architects, engineers and those who involved in the building industry. It is reported that considerable energy is consumed to provide and maintain acceptable indoor conditions for thermal comfort in residential buildings in hot-humid climate. The observable increase in energy consumption is chiefly resulting from the growing use of air conditioning system. There are various energy conservation measures which can be applied to reduce energy consumption and among these measures are passive envelope design measures. This paper addresses the energy performance of selected high-rise apartments in Kuala Lumpur. Energy Plus software is utilized in measuring the performance because of its availability, validity and accuracy. Possible energy savings due to passive envelope design measures integration are investigated. This includes investigating the effect of thermal insulation and glazing type on potential energy savings.
Enhancement of Space Environment Via Healing Gardendrboon
Green nature, sunlight and fresh air have been known as important component of healing in healthcare facilities. This paper presents the finding of an exploratory study on healing garden elements in healthcare facilities. The purpose of the paper is to find the elements of healing gardens and its healing factors in the existing garden design. In conducting this research study, site observation and informal interview at selected healthcare facilities have been performed. The study reveals the elements of existing garden design, the interactivity and the end users expectation on a garden. The finding shows that lacking some of the elements of garden design lead to less user friendliness and interactivity in the garden. It also shows that the visibility, accessibility, quietness and comfortable condition in the garden give impact to the utilization of the garden.
Design of Quadruped Walking Robot with Spherical Shelldrboon
We propose a new quadruped walking robot with a spherical shell, called "QRoSS." QRoSS is a transformable robot that can store its legs in the spherical shell. The shell not only absorbs external forces from all directions, but also improves mobile performance because of its round shape. In rescue operations at a disaster site, carrying robots into a site is dangerous for operators because doing so may result in a second accident. If QRoSS is used, instead of carrying robots in, they are thrown in, making the operation safe and easy. This paper reports details of the design concept and development of the prototype model. Basic experiments were conducted to verify performance, which includes landing, rising and walking through a series of movements.
Motion Analysis of Pitch Rotation Mechanism for Posture Control of Butterfly-...drboon
We developed a small flapping robot on the basis of movements made by a butterfly with a low flapping frequency of approximately 10 Hz, a few degrees of freedom of the wings, and a large flapping angle. In this study, we clarify the pitch rotation mechanism that is used to control its posture during takeoff for different initial pitch and flapping angles by the experiments of both manufactured robots and simulation models. The results indicate that the pitch angle can be controlled by altering the initial pitch angle at takeoff and the flapping angles. Furthermore, it is suggested that the initial pitch angle generates a proportional increase in the pitch angle during takeoff, and that certain flapping angles are conducive to increasing the tendency for pitch angle transition. Thus, it is shown that the direction of the flight led by periodic changing in the pitch angle can be controlled by optimizing control parameters such as initial pitch and flapping angles.
Analysis of Roll Rotation Mechanism of a Butterfly for Development of a Small...drboon
In this paper, we investigated the aerodynamic characteristics during roll rotation of a butterfly based on computational fluid dynamics using a three-dimensional high-speed camera information. This method allows to create a numerical model of a butterfly from the camera images and to analyze the flow field corresponding to the captured behavior. We photographed two behaviors different in rotational axis and analyzed the roll rotational mechanism. In a typical pitch rotational flight, the differential pressure was concentrated on the tip of fore wings. The magnitudes of reaction forces on left and right wings were roughly matched each other. On the other hands, the differential pressure of the roll rotational flight was distributed in the whole of wings. The magnitude of the right reaction force was twice greater than that of left at the first down stroke. The roll angle changed largely at the same time. These results show that a butterfly rotates about roll by changing the reaction forces on each side.
Effect of Oryzalin on Growth of Anthurium andraeanum In Vitrodrboon
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A Novel Finite Element Model for Annulus Fibrosus Tissue Engineering Using Homogenization Techniques
1. 2012 American Transactions on Engineering & Applied Sciences
American Transactions on Engineering
& Applied Sciences
http://TuEngr.com/ATEAS, http://Get.to/Research
A Novel Finite Element Model for Annulus Fibrosus
Tissue Engineering Using Homogenization Techniques
a b b
Tyler S. Remund , Trevor J. Layh , Todd M. Rosenboom ,
a a* b*
Laura A. Koepsell , Ying Deng , and Zhong Hu
a
Department of Biomedical Engineering Faculty of Engineering, University of South Dakota, USA
b
Department of Mechanical Engineering Faculty of Engineering, South Dakota State University, USA
ARTICLEINFO A B S T RA C T
Article history: In this work, a novel finite element model using the
Received September 06, 2011
Received in revised form - mechanical homogenization techniques of the human annulus
Accepted September 24, 2011 fibrosus (AF) is proposed to accurately predict relevant moduli of
Available online: September 25, the AF lamella for tissue engineering application. A general
2011
formulation for AF homogenization was laid out with appropriate
Keywords:
boundary conditions. The geometry of the fibre and matrix were
Finite Element Method
Annulus Fibrosus
laid out in such a way as to properly mimic the native annulus
Tissue Engineering fibrosus tissue’s various, location-dependent geometrical and
Homogenization histological states. The mechanical properties of the annulus
fibrosus calculated with this model were then compared with the
results obtained from the literature for native tissue.
Circumferential, axial, radial, and shear moduli were all in
agreement with the values found in literature. This study helps to
better understand the anisotropic nature of the annulus fibrosus
tissue, and possibly could be used to predict the structure-function
relationship of a tissue-engineered AF.
2012 American Transactions on Engineering and Applied Sciences.
*Corresponding authors (Y.Deng). Tel/Fax: +1-605-367-7775/+1-605-367-7836. E-mail
addresses: ying.deng@usd.edu. (Z.Hu). Tel/Fax: +1-605-688-4817/+1-605-688-5878.
E-mail address: Zhong.hu@sdstate.edu. 2012. American Transactions on Engineering 1
& Applied Sciences. Volume 1 No.1 ISSN 2229-1652 eISSN 2229-1660
Online Available at http://TUENGR.COM/ATEAS/V01/01-23.pdf
2. 1. Introduction
The annulus fibrosus (AF) is an annular cartilage in the intervertebral disc (IVD) that aids in
supporting the structure of the spinal column. It experiences complex, multi-directional loads
during normal physiological functioning. To compensate for the complex loading experienced,
the AF exhibits anisotropic behavior, in which fibrous collagen bundles that are strong in tension,
run in various angles in an intersecting, crossing pattern which helps to absorb the loadings. (Wu
and Yao 1976) The layers of the AF are composed of fibrous collagen fibrils that are oriented in
such a way that the angles rotate from ± 28 degrees relative to the transverse axis of the spine in
the outer AF (OAF) to ± 44 degrees relative to the transverse axis of the spine in the inner AF
(IAF). (Hickey and Hukins 1980; Cassidy, Hiltner et al. 1989; Marchand and Ahmed 1990).
The approach that homogenization offers to deal with anisotropic materials includes
averaging the directionally-dependent mechanical properties in what is called a representative
volume elements (RVE). These RVE are averages of the directionally- and spatially-dependent
material properties. When summed over the volume of the material, they can be very useful in
describing the macroscopic mechanical properties of materials with complex microstructures.
(Bensoussan A 1978; Sanchez-Palencia E 1987; Jones RM 1999) Homogenization has been
applied to address some of the shortcomings of structural finite element analysis (FEA) models
that utilized truss and cable elements (Shirazi-Adl 1989; Shirazi-Adl 1994; Gilbertson, Goel et al.
1995; Goel, Monroe et al. 1995; Lu, Hutton et al. 1998; Lee, Kim et al. 2000; Natarajan,
Andersson et al. 2002) and fiber-reinforced strain energy models (Wu and Yao 1976; Klisch and
Lotz 1999; Eberlein R 2000; Elliott and Setton 2000; Elliott and Setton 2001) for modeling the
AF. Homogenization has also been used to describe biological tissues such as trabecular bone
(Hollister, Fyhrie et al. 1991), articular cartilage (Schwartz, Leo et al. 1994; Wu and Herzog
2002) and AF. (Yin and Elliott 2005).
The mechanical complexity of the AF has posed substantial problems for engineers
attempting to model the system. To date, the circumferential modulus and axial modulus have
been predicted accurately, but the predicted shear modulus has been consistently two orders of
magnitude high. An explanation proposed in a recent paper (Yin and Elliott 2005), which offered
a novel homogenization model for the AF, is that the high magnitude prediction for shear
2 Tyler S. Remund, Trevor J. Layh, Todd M. Rosenboom, L. A. Koepsell, Y. Deng, Z. Hu
3. modulus can be explained by the fact that the models assume the tissue to be firmly anchored in
surrounding tissue, whereas the experimentally measured tissue is removed from its surrounding
tissue. This removal of the sample from surrounding tissue releases the fibers near the edge,
which prevents a portion of the fiber stretch component from being included as a part of the
overall shear measurement.
The purpose of this paper was to establish a novel method for modeling the AF using FEA
and homogenization theory that predicts the circumferential-, axial-, and radial- modulus
accurately while also predicting a shear modulus that accurately represents that of the
experimentally measured tissue. A general formulation for annulus fibrosus lamellar
homogenization was laid out. Appropriate changes to the boundary conditions as well as the
geometry of the structural fibres was made to accommodate the measurements of the mechanical
properties under various annulus fibrosus volume fractions and orientations. The specific
changes in the three dimensional location and orientation of the cylindrical, crossing fibers within
the matrix was taken into account. And the mechanical properties of the human AF by modeling
were compared with the results obtained in the literatures for the native tissues.
2. Mathematical Model
The general homogenization formulation used here was applied to the AF before. (Yin and
Elliott 2005) In the homogenization approach volumetric averaging is used to arrive at the
general formulation. (Sanchez-Palencia 1987; Bendsoe 1995; Jones RM 1999) The
homogenization formula is created by averaging material properties for a material that is assumed
to be linear elastic over discrete, volumetric segments. The overall material is assumed to have
inhomogeneous properties throughout the entire volume. So, the average material properties can
be calculated by multiplying the inhomogeneous, localized material properties c by the
independent strain rates u, in independent strain states α , β , over the volume of the tissue Ω like
in Eq. (1).
1 α β
Cα , β = ∫ ui, juk ,l dΩ
ΩΩ
(1)
*Corresponding authors (Y.Deng). Tel/Fax: +1-605-367-7775/+1-605-367-7836. E-mail
addresses: ying.deng@usd.edu. (Z.Hu). Tel/Fax: +1-605-688-4817/+1-605-688-5878.
E-mail address: Zhong.hu@sdstate.edu. 2012. American Transactions on Engineering 3
& Applied Sciences. Volume 1 No.1 ISSN 2229-1652 eISSN 2229-1660
Online Available at http://TUENGR.COM/ATEAS/V01/01-23.pdf
4. Cα , β : overall average material properties
ci , j ,k ,l : non-homogeneous material properties
ui, j : independent strain rates
α , β : independent strain rates
Ω: volume
The stiffness tensor Eq. (2) rotates around a certain angle, α , in both the positive and
negative direction. This tensor thus rotates the average material properties to simulate the
direction of the AF collagenous fibers. This angle, α , is measured from the midline, θ , and it
changes with spatial location.
C α = RT C ⋅ R (2)
C∞: average elasticity tensor for two lamellae
R: rotation tensor
The elasticity tensor of two, combined lamella Eq. (3) rotated at the same angle, α , in
opposite directions .
C + α + C −α
C + / −α = (3)
2
There are four in-plane material properties: C11 , C22 , C12 , and C66 that are calculated for a
single lamella. They are arranged in matrix notation, like in Eq. (4).
⎡C11 C12 0 ⎤
C = ⎢C12 C22
⎢ 0 ⎥⎥ (4)
⎢0
⎣ 0 C66 ⎥
⎦
And the values for C11 , C22 , C12 , and C66 can be calculated from the system of equations
shown in Eq. (5) using the height of the fiber portion of the segment ρ , the elastic modulus of
the fiber and matrix E f , E m respectively and the Poisson ratio of the fiber and matrix υ f , υ m
respectively:
4 Tyler S. Remund, Trevor J. Layh, Todd M. Rosenboom, L. A. Koepsell, Y. Deng, Z. Hu
5. C11 =
ρE f
+
(1 − ρ )Em − ρE fν f 2 − (1 − ρ )Emν 2 + (ρν + (1 − ρ ) m ) Em E f
ν 2
( ) ( )
f
1 −ν f
2
1 −ν m
2
1 −ν f
2
1 −ν m
2
ρEm 1 − ν f 2 + (1 − ρ ) 1 − ν m 2 E f
(ρν + (1 − ρ ) m )E m E f
ν
C12 =
f
(
ρE m 1 − ν f
2
)+ (1 − ρ )(1 −ν )E
2
m f
Em E f
C 22 =
(
ρE m 1 − ν f 2
)+ (1 − ρ )(1 −ν )E
m
2
f
1 Em E f
C66 =
2 ρEm (1 + ν f ) + (1 − ρ )(1 + ν m )E f
(5)
ρ: height of the fiber
Ef : elastic modulus of the fiber
Em : elastic modulus of the matrix
vf : Poisson ratio of the fiber
vm : Poisson ratio of the matrix
Taken together, this system of equations accurately modeled the AF in the existing model.
(Yin and Elliott 2005) It addressed many of the shortcomings of structural truss and cable
models and of strain energy models. However it did predict a shear modulus that was two orders
of magnitude higher than native tissue.
2.1 Model from the literature
The homogenization model for the AF created by Yin et al. accurately predicted most of the
important mechanical properties of the AF tissue. But it did not make accurate shear modulus
predictions. As a matter of fact, the predictions from this model were two orders of magnitude
higher than the measurements reported in the literature. In this section we will detail some
aspects of the published model that may contribute to the unnaturally high modulus prediction.
*Corresponding authors (Y.Deng). Tel/Fax: +1-605-367-7775/+1-605-367-7836. E-mail
addresses: ying.deng@usd.edu. (Z.Hu). Tel/Fax: +1-605-688-4817/+1-605-688-5878.
E-mail address: Zhong.hu@sdstate.edu. 2012. American Transactions on Engineering 5
& Applied Sciences. Volume 1 No.1 ISSN 2229-1652 eISSN 2229-1660
Online Available at http://TUENGR.COM/ATEAS/V01/01-23.pdf
6. 2.1.1 Fiber angle and fiber volume fraction
The first two important geometric considerations are the volumetric ratio of fiber to matrix
fiber volume fraction (FVF) within the RVE and the fiber angle. (Table 1) (Ohshima, Tsuji et al.
1989; Lu, Hutton et al. 1998) These ratios are used extensively in the calculations. Both the
FVF and the fiber angle vary by which lamina they are located in. But the finite element method
is a great tool for taking these variabilities into account. The original model used fiber angles in
the range of 15 to 45 degrees. It also used FVFs in the range of 0 to 0.3. These ranges were used
first in parametric studies in order to better understand how the fiber angle and FVF affect the
various relevant moduli. Also, beings fiber angle, and to a lesser extent FVF, can be determined
experimentally, the parametric studies helped in determining some of the more difficult to
elucidate material properties of the collagen fibers and the proteoglycan matrix.
2.1.2 Fiber configuration
The second important geometric consideration is the 3D arrangement of the fibers and matrix
within the composite RVE. In the original formulation, (Yin and Elliott 2005) they assumed the
two fiber populations to be within a single continuous material and not layered as in native tissue
structure. (Sanchez-Palencia 1987)
2.1.3 Boundary conditions
The final important consideration is the boundary conditions applied to the RVE. The
boundary condition for the tensile case can be seen in Figure 1. A similar boundary condition for
the tensile case was applied to the proposed model. But when they set the boundary conditions
for the shear case, they fixed the edges along both the θ - and z- axis when they applied a shear
along z = 1 and θ = 1 . (Sanchez-Palencia 1987) The proposed model has adopted a boundary
condition from (K. Sivaji Babu 2008), It constrains the rz-surface at θ = 0 and applies a shear to
the rz surface at θ = 1 . (K. Sivaji Babu 2008) This boundary condition can be visualized in
Figure 2. Taken together, these geometric considerations allow the proposed model of the AF
tissue’s mechanical behavior to be accurate.
2.2 Proposed model changes
Changes to the original model are proposed here. They include changes to the fiber angle
and FVF in order to bring them closer to the physiological range. Changes in the fiber
configuration were proposed in order to more closely mimic the native state of the tissue where
6 Tyler S. Remund, Trevor J. Layh, Todd M. Rosenboom, L. A. Koepsell, Y. Deng, Z. Hu
7. the crossing collagen fibers are separated by a section of proteoglycan matrix, whereas in the
original model they were welded together in the shape of an ‘X’. The final change made to the
original model was in the applied boundary conditions.
2.2.1 Fiber angle and fiber volume fraction
The ranges for this study were based loosely on the values used for the original study. In this
simulation graphs of circumferential-, axial-, and radial- modulus as well as shear modulus
against fiber volume fraction at fiber angles of 20, 25, 30, and 35 degrees were generated.
Graphs were also generated for axial- and circumferential- modulus as well as shear modulus
against varying fiber angle at fiber volume fractions of 0.05, 0.1, 0.15, 0.2, 0.25, and 0.3. The
angles of collagen in native tissue range from 24.5-36.3 degrees to the transverse plane with an
average of 29.6 degrees.
2.2.2 Fiber configuration
In this paper it is assumed that the fiber populations are layered and separated by matrix
material. The three dimensional geometric arrangement for this fiber and matrix composite is
shown in Figure 1 as a RVE along with the tensile case’s boundary conditions. The
corresponding RVE for the shear case is shown in Figure 2. With the material being a
composite, it is important to assign dimensions to repeating components within the RVE. The
width of the segment, which is denoted by c in Eq. (6) was set to be equal to 13 times the radius,
r, of the fiber when the number of fibers, n, within the RVE is 4. This means that the distance
between fibers is the equivalent of one radius. The length of b is dependent on the fiber angle α
and the length of a. Eq. (7) The length of a was derived from looking at the ratio of total fiber
volume to total segment volume. A number of new variables are introduced in the derivation of a
Eq. (8). So a can be derived from Eq. (9) by substitution of Eq. (10) and then rearranging.
c = 13 ⋅ r (6)
b = a ⋅ tan(α ) (7)
4π ⋅ r 2
a= (8)
ρ ⋅ c ⋅ sin (α )
*Corresponding authors (Y.Deng). Tel/Fax: +1-605-367-7775/+1-605-367-7836. E-mail
addresses: ying.deng@usd.edu. (Z.Hu). Tel/Fax: +1-605-688-4817/+1-605-688-5878.
E-mail address: Zhong.hu@sdstate.edu. 2012. American Transactions on Engineering 7
& Applied Sciences. Volume 1 No.1 ISSN 2229-1652 eISSN 2229-1660
Online Available at http://TUENGR.COM/ATEAS/V01/01-23.pdf
8. Figure 1: Meshed 3D geometric representation of matrix and fiber orientation along with
coordinate system, dimensions, and tensile boundary conditions.
8 Tyler S. Remund, Trevor J. Layh, Todd M. Rosenboom, L. A. Koepsell, Y. Deng, Z. Hu
9. Figure 2: Meshed 3D geometric representation of composite RVE along with corresponding
axes, dimensions, and shear boundary conditions.
V fiber π ⋅n⋅lf ⋅r2
ρ= = (9)
VRVE a ⋅b⋅c
l f = a 1 + tan 2 (α ) (10)
After substituting, making use of a trigonometric identity, and rearranging, the simplified
formula for a, becomes clear.
So to equally space the four fibers along the c edge from each other and also the edge of the
matrix, the length d was derived as given by Eq. (11). It makes use of the idea that when there
*Corresponding authors (Y.Deng). Tel/Fax: +1-605-367-7775/+1-605-367-7836. E-mail
addresses: ying.deng@usd.edu. (Z.Hu). Tel/Fax: +1-605-688-4817/+1-605-688-5878.
E-mail address: Zhong.hu@sdstate.edu. 2012. American Transactions on Engineering 9
& Applied Sciences. Volume 1 No.1 ISSN 2229-1652 eISSN 2229-1660
Online Available at http://TUENGR.COM/ATEAS/V01/01-23.pdf
10. are four fibers within the RVE, that there are five equal divisions of width.
2⋅n⋅c⋅r
d= +r (11)
5
a : width of the representative volume element
b : height of the representative volume element
c : length of the representative volume element
d : distance between fibers
n : number of fibers in the representative volume element
r : radius of the fibers
α : angle between fibers.
So by putting the above equations into the prototype code, a master program code was
developed that is useful for predicting the various moduli at each variation of fiber angle and
FVF.
2.2.3 Boundary conditions
The original paper had fixed boundary conditions along two adjoining faces of the RVE and
applied shear on the two opposite faces of the RVE. In the proposed model one face has fixed
boundary conditions, and the opposite face has an applied shear. These changes taken together
make for a model that predicts all moduli, including the shear modulus, accurately.
3. Material Properties
It is also important to assign material properties to the parameters that remain constant
regardless of where they are measured throughout the AF. The elastic modulus and Poisson ratio
for the collagen fibers and proteoglycan matrix can be assigned specific values. For modeling the
varying conditions of the AF tissue, laminae, and IVD, the parameters were chosen based on the
literature of past numerical models of the AF, and in some cases, direct measurements of the
10 Tyler S. Remund, Trevor J. Layh, Todd M. Rosenboom, L. A. Koepsell, Y. Deng, Z. Hu
11. tissues. An elastic modulus of 500 MPa and a Poisson’s Ratio of 0.35 were adopted for the
collagen fibers (Goel, Monroe et al. 1995; Lu, Hutton et al. 1998), while an elastic modulus of
0.8 Mpa (Lee, Kim et al. 2000; Elliott and Setton 2001) and a Poisson’s Ratio of 0.45 (Shirazi-
Adl, Shrivastava et al. 1984; Goel, Monroe et al. 1995; Tohgo and Kawaguchi 2005) were
assigned to the proteoglycan matrix. Fiber volume fractions and fiber angles were varied over
ranges found in previous homogenization.
4. Results
The first input parameter from the lamina that is varied in order to investigate the effect on
the various moduli is the FVF. The FVF is varied from 0.05 to 0.3, which are normal
physiological ranges. (Table 1) Table 1 gives estimates for the cross-sectional area of the AF,
FVF of the AF, and fiber angle. Each are estimated for the corresponding lamella. Of course
these parameters are variable throughout the AF. But this list was compiled for the original
model, so it was used here for ease of comparison. There are also more than six lamellar layers
in the AF, but six is a reasonable approximation.
Table 1: Annulus fibrosus cross-sectional area for each of the lamina layers, collagen fiber
volume fraction for each of the lamina layers, and fiber orientation angle as reported in the
literatures. These values were inserted into the proposed formulation.
Lamina Layer Inner 2nd 3rd 4th 5th Outer References
Annulus fibrosus (Lu, Hutton et al.
0.06 0.11 0.163 0.22 0.2662 0.195
cross sectional area 1998)
Collagen fiber (Yin and Elliott
0.05 0.09 0.13 0.17 0.2 0.23
volume fraction 2005)
(Lu, Hutton et al.
Fiber angle Annulus Fiber orientation average: 29.6 (range 24.5‐36.3)
1998)
*Corresponding authors (Y.Deng). Tel/Fax: +1-605-367-7775/+1-605-367-7836. E-mail
addresses: ying.deng@usd.edu. (Z.Hu). Tel/Fax: +1-605-688-4817/+1-605-688-5878.
E-mail address: Zhong.hu@sdstate.edu. 2012. American Transactions on Engineering 11
& Applied Sciences. Volume 1 No.1 ISSN 2229-1652 eISSN 2229-1660
Online Available at http://TUENGR.COM/ATEAS/V01/01-23.pdf
12. Figure 3 looks at how the circumferential modulus varies with varying FVF and fiber angle.
At a fiber angle of 20 degrees the circumferential modulus varies from 7 Mpa at a FVF of 0.05 to
26 Mpa at a FVF of 0.3. At a fiber angle of 35 degrees the circumferential modulus varies from 2
Mpa at a FVF of 0.05 to 17 Mpa at a FVF of 0.3.
Figure 3: Circumferential modulus vs. fiber volume fraction at various fiber angles.
Figure 4 takes a look at how the axial modulus varies with FVF and fiber angle. The axial
modulus at a fiber angle of 20 degrees varies from 1 Mpa at a FVF of 0.05 to 4 Mpa at a FVF of
0.3. It also varies from 1 Mpa at a FVF of 0.05 to 9 Mpa at a FVF of 0.3 when the fiber angle is
35 degrees.
12 Tyler S. Remund, Trevor J. Layh, Todd M. Rosenboom, L. A. Koepsell, Y. Deng, Z. Hu
13. Figure 4: Axial modulus vs. fiber volume fraction at various fiber angles.
Figure 5: Shear modulus vs. fiber volume fraction at various fiber angles.
*Corresponding authors (Y.Deng). Tel/Fax: +1-605-367-7775/+1-605-367-7836. E-mail
addresses: ying.deng@usd.edu. (Z.Hu). Tel/Fax: +1-605-688-4817/+1-605-688-5878.
E-mail address: Zhong.hu@sdstate.edu. 2012. American Transactions on Engineering 13
& Applied Sciences. Volume 1 No.1 ISSN 2229-1652 eISSN 2229-1660
Online Available at http://TUENGR.COM/ATEAS/V01/01-23.pdf
14. In Figure 5 the shear modulus is evaluated against fiber volume fraction at various fiber
angles. The shear modulus, at a fiber angle of 20 degrees, was 0.1 Mpa at a FVF of 0.05 and was
0.6 Mpa at a FVF of 0.3. The shear modulus, at a fiber angle of 35 degrees, was 0.3 Mpa at a
FVF of 0.05 and was 1.2 Mpa at a FVF of 0.3.
Figure 6 shows that the radial modulus seemed to depend very little on fiber angle. But it
also shows that radial modulus increases linearly with increasing FVF from 0 Mpa at a FVF of
0.05 to 1.6 Mpa at a FVF of 0.3.
Figure 6: Radial modulus vs. fiber volume fraction at various fiber angles.
The next input parameter from the lamina that is varied in order to investigate the effect on
the various moduli is the fiber angle. The physiologically-relevant range of fiber angles is
roughly 20 to 35 degrees (Table 1).
In Figure 7 the circumferential modulus at a FVF of 0.05 varies from 7 Mpa at a fiber angle
of 20 degrees to 2 Mpa at a fiber angle of 35 degrees, and at a FVF of 0.3 it varies from 25 Mpa
at a fiber angle of 20 degrees to 16 Mpa at a fiber angle of 35 degrees.
14 Tyler S. Remund, Trevor J. Layh, Todd M. Rosenboom, L. A. Koepsell, Y. Deng, Z. Hu
15. Figure 7: Circumferential modulus vs. fiber angle at various fiber volume fractions.
Figure 8: Axial modulus vs. fiber angle at various fiber volume fractions.
In Figure 8 the axial modulus at a FVF of 0.05 is 1 Mpa, and at a FVF of 0.3 it varies from
*Corresponding authors (Y.Deng). Tel/Fax: +1-605-367-7775/+1-605-367-7836. E-mail
addresses: ying.deng@usd.edu. (Z.Hu). Tel/Fax: +1-605-688-4817/+1-605-688-5878.
E-mail address: Zhong.hu@sdstate.edu. 2012. American Transactions on Engineering 15
& Applied Sciences. Volume 1 No.1 ISSN 2229-1652 eISSN 2229-1660
Online Available at http://TUENGR.COM/ATEAS/V01/01-23.pdf
16. 3.5 Mpa at a fiber angle of 20 degrees to 9 Mpa at a fiber angle of 35 degrees.
In Figure 9 the shear modulus at a FVF of 0.05 varies from 0.6 Mpa at a fiber angle of 20
degrees to 1.2 Mpa at a fiber angle of 35 degrees, and at a FVF of 0.3 it varies from 0.1 Mpa at a
fiber angle of 20 degrees to 0.2 Mpa at a fiber angle of 35 degrees.
Figure 9: Shear modulus vs. fiber angle at various fiber volume fractions.
Table 2: Values predicted by the model in both range form and real case calculations as
compared to the corresponding values of circumferential-, axial-, radial-, and shear- modulus
measured experimentally as found in the literature.
Modeling Ranges
Real
Modulus (Mpa) Fα[20‐30] FVF Experimental
Case
[0.05‐0.30]
Circumferential 18±14
1.92≤E≤25.35 7.09
Modulus (Elliott and Setton 2001)
0.7±0.8
(Acaroglu, Iatridis et al. 1995)
Axial Modulus 0.91≤E≤9.09 2.12
(Ebara, Iatridis et al. 1996)
(Elliott and Setton 2001)
Radial Modulus 1.10≤E≤1.57 1.34
0.1
Shear Modulus 0.08≤G≤1.20 0.16
(Iatridis, Kumar et al. 1999)
16 Tyler S. Remund, Trevor J. Layh, Todd M. Rosenboom, L. A. Koepsell, Y. Deng, Z. Hu
17. The changes to the moduli are mostly linear. But while the axial- and shear- moduli (Figures
8-9) increase with increasing fiber angle, the circumferential modulus (Figure 7) decreases with
increasing fiber angle (Table 2).
While modeling ranges allow us to evaluate the effect of changing the input parameters such
as fiber angle and fiber volume fraction on the various mechanical characteristics of the tissue,
they don’t allow us to compare our model to the real case. Table 2 shows the ranges of the
moduli predicted by the model accompanied by the modulus predicted when the input parameters
used were what was assumed to be found in the human body. These values were then compared
to experimentally measured values found in literature.
5. Discussion
Here comparisons between the proposed model and existing homogenization model, as well
as the experimentally measured data from the literature, will be made. It is worth repeating that
in the 3D homogenization models, the fibres of the AF are modelled as truss or cable elements
that are strong in tension but not capable of resisting compression or bending moment. This
holds true for both the proposed as well as the existing homogenization model. Also, the surfaces
of the fiber and matrix that come into contact with each other are ‘glued’ as if the surfaces that
those two features share are actually one in the same. So the interface is a blend and there is no
slippage between the components at their respective interfaces.
An explanation would be in order for how the ‘real case’ moduli (Table 2) were calculated.
The fiber angle in the native tissue varies not only from lamella-to-lamella, but also within each
lamella. So an average fiber angle of 29.6 degrees was taken from the literature (Lu, Hutton et al.
1998). Fiber volume fraction is also variable, so a weighted FVF was used. To arrive at this
weighted FVF, an approximate FVF from each lamella was considered (Yin and Elliott 2005)
along with the cross sectional area of the corresponding lamella (Lu, Hutton et al. 1998). Using
these parameters, calculations were made for the moduli for each of the lamella. Then the moduli
were weighted based on the cross-sectional areas (Table 1) of the various lamellas relative to the
overall cross sectional area. Once the weighting factors were multiplied by the modulus for that
specific lamella, the various weighted moduli were summed to come to an actual modulus.
*Corresponding authors (Y.Deng). Tel/Fax: +1-605-367-7775/+1-605-367-7836. E-mail
addresses: ying.deng@usd.edu. (Z.Hu). Tel/Fax: +1-605-688-4817/+1-605-688-5878.
E-mail address: Zhong.hu@sdstate.edu. 2012. American Transactions on Engineering 17
& Applied Sciences. Volume 1 No.1 ISSN 2229-1652 eISSN 2229-1660
Online Available at http://TUENGR.COM/ATEAS/V01/01-23.pdf
18. The existing model has a circumferential modulus in the 11 MPa range, an axial modulus of
around 2 MPa, and a shear modulus of around 18 MPa. Conversely, the proposed model had a
circumferential modulus of about 7 MPa, an axial modulus of about 2 MPa, and a shear modulus
of around 0.5 MPa. The experimentally measured values for these parameters are a
circumferential modulus in the range of 4-32 MPa, an axial modulus in the range of 0.1-1.5 MPa,
and a shear modulus of 0.1 MPa. (Table 2).
While there is agreement between the various models and the experimentally-measured
values from literature when it comes to tensile moduli, the models uniformly disagree with the
experimentally measured data from the literature when it comes to the shear modulus. The shear
modulus is over two orders of magnitude higher in the models than in the experimentally
measured data from the literature. The author suggested that this is because the tissue has to be
removed from its surroundings to be measured experimentally. (Yin and Elliott 2005) This frees
up the ends of the fibers so there is fiber sliding but not fiber stretching contributing to overall
shear measurements. Whereas the nature of the models can have more realistic in vivo boundary
conditions, so the tissue can experience both fiber stretch and fiber sliding in its shear
measurement. Conversely, the proposed model will more accurately emulate the former.
In this study, a homogenization model of the AF was revised to address the discrepancy
between the shear modulus prediction in the previously proposed model and the experimental
data of human AF tissue. The original model had a shear modulus two orders of magnitude
higher than that of the experimental values for native AF tissue. It was suggested that the shear
was lower in the experimental values, because the pieces of AF tissue were removed from their
native surroundings. This causes the fibers of the tissue near the edges to not be anchored into
the surrounding tissue. So the stretch of the tissue’s fibers may not have been contributing to
shear measurements. Here is suggested a model that gives accurate accounts of the shear
modulus in the AF tissue while not sacrificing modulus predictions in the circumferential-, axial-,
and radial-directions.
Several significant changes have been made to the reported model (Yin and Elliott 2005) to
address the discrepancy between the shear modulus in the model and that experimentally
measured in the native tissue. The first change made to the model was the arrangement of the
18 Tyler S. Remund, Trevor J. Layh, Todd M. Rosenboom, L. A. Koepsell, Y. Deng, Z. Hu
19. fibers and matrix within the RVE. In both this model and the original, there are four fibers. In
the original model there are two fibers on each opposing face. The two crossing fibers are in the
same plane, so they are in effect welded together. One of the changes made to this model is in
the geometrical layout of the fibers. The alternating fibers are separated in space and by matrix
material. This separation of the fibers allows them to slide against each other. Once the
arrangement of the fibers and the matrix were changed, the shear modulus prediction was
decreased. But it had decreased to a level much smaller than that of the native tissue value. The
value the model had predicted was actually 10 −12 MPa. This is much, much smaller than the
value tested in native tissue of roughly 0.1 MPa. So a literature search was performed to try to
find alternative approaches to improving shear predictions in homogenization models. The paper
that was found called for changing the boundary conditions. In the original model, two adjoining
sides of the RVE are constrained, and the opposing two sides of the RVE have the shear loadings
applied. This model has one side constrained at a time. The opposing side of the RVE has the
shear loading applied. This has brought the shear modulus prediction much closer to that tested
in the native AF tissue. And while the original model is likely more accurate for 3D predictions
as the tissue is in the IVD in vivo, if the aim is to develop a model that more accurately predicts
the mechanical properties of a resected piece of AF tissue as is measured in the literature, then
boundary conditions used in the proposed model are more applicable. This is because the
boundary conditions in the proposed model allow for the fibres to slide more freely, avoiding
incorporating fiber stretch, and resulting in significantly lower shear measurements.
This model is important in understanding the mechanics of the AF, especially when tissue
samples are resected from the greater IVD. It can be useful for better understanding disc
degeneration and for improving approaches to designing functional tissue engineered constructs.
It can help in understanding disc degeneration as the process is usually characterized by a
degradation of the proteoglycan matrix. Through the alteration of the matrix, disc degradation
can be modeled accurately. Also, more appropriate benchmarks for the design of functional
tissue engineered constructs can be set through the better understanding of the interaction of the
AF subcomponents that this model provides.
*Corresponding authors (Y.Deng). Tel/Fax: +1-605-367-7775/+1-605-367-7836. E-mail
addresses: ying.deng@usd.edu. (Z.Hu). Tel/Fax: +1-605-688-4817/+1-605-688-5878.
E-mail address: Zhong.hu@sdstate.edu. 2012. American Transactions on Engineering 19
& Applied Sciences. Volume 1 No.1 ISSN 2229-1652 eISSN 2229-1660
Online Available at http://TUENGR.COM/ATEAS/V01/01-23.pdf
20. It should be noted that this model, like those proposed in the past, does not take interlamellar
interactions into account. To this point, it has not been determined if the interlamellar
interactions and interweaving, that have been observed in the literature, are of mechanical
significance.
6. Conclusion
In summary, this study established a novel approach to an existing homogenization model. It
more closely models the anisotropic AF tissue’s in-plane shear modulus as if it were excised
from the IVD. It did this while still making accurate predictions of circumferential-, axial-, and
radial- moduli. The lower shear stress predictions were more in line with experimental
measurements than past models. The model also elucidates the relationship between FVF, fiber
angle, and composite mechanical properties. The proposed model will also help to better
understand the structure-function relationship for future work with disc degeneration and
functional tissue engineering.
7. Acknowledgements
This research was partially supported by the joint Biomedical Engineering (BME) Program
between the University of South Dakota and the South Dakota School of Mines and Technology.
The authors would also acknowledge the South Dakota Board of Regents Competitive Research
Grant Award (No. SDBOR/USD 2011-10-07) for the financial support.
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*Corresponding authors (Y.Deng). Tel/Fax: +1-605-367-7775/+1-605-367-7836. E-mail
addresses: ying.deng@usd.edu. (Z.Hu). Tel/Fax: +1-605-688-4817/+1-605-688-5878.
E-mail address: Zhong.hu@sdstate.edu. 2012. American Transactions on Engineering 21
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Tyler S. Remund is a PhD candidate in the Biomedical Engineering Department at the
University of South Dakota. He holds a BS in Mechanical Engineering from South Dakota State
University. He is interested in tissue engineering of the annulus fibrosus.
Trevor J. Layh holds a BS in Mechanical Engineering from South Dakota State University. After
graduation he was accepted into the Department of Defense SMART Scholarship for Service
Program in August 2010, Trevor is now employed by the Naval Surface Warfare Center
Dahlgren Division in Dahlgren, VA as a Test Engineer.
22 Tyler S. Remund, Trevor J. Layh, Todd M. Rosenboom, L. A. Koepsell, Y. Deng, Z. Hu
23. Todd M. Rosenboom holds a BS in Mechanical Engineering from South Dakota State
University. He currently works as an application engineer for Malloy Electric in Sioux Falls,
SD.
Laura A. Koepsell holds a PhD in Biomedical Engineering and a BS in Chemistry, both from the
University of South Dakota. She is a Postdoctoral Research Associate at the University of
Nebraska Medical Center Department of Orthopedics and Nano-Biotechnology. She is
interested in cellular adhesion, growth, and differentiation of mesenchymal stem cells on
titanium dioxide nanocrystalline surfaces. She is trying to better understand any inflammatory
responses evoked by these surfaces and to evaluate the expression patterns and levels of
adhesion and extracellular matrix-related molecules present (particularly fibronectin).
Dr. Ying Deng received her Ph.D. from Huazhong University of Science and Technology in 2001.
She then completed a post-doctoral fellowship at Tsinghua University and a second post-
doctoral fellowship at Rice University. In 2008, Dr. Deng joined the faculty of the University of
South Dakota at Sioux Falls where she is currently assistant Professor of Biomedical
Engineering. She has authored over 15 scientific publications in the biomedical engineering area.
Dr. Zhong Hu is an Associate Professor of Mechanical Engineering at South Dakota State
University, Brookings, South Dakota, USA. He has about 70 publications in the journals and
conferences in the areas of Nanotechnology and nanoscale modeling by quantum
mechanical/molecular dynamics (QM/MD); Development of renewable energy (including
photovoltaics, wind energy and energy storage material); Mechanical strength evaluation and
failure prediction by finite element analysis (FEA) and nondestructive engineering (NDE);
Design and optimization of advanced materials (such as biomaterials, carbon nanotube, polymer
and composites). He has been worked on many projects funded by DoD, NSF RII/EPSCoR,
NSF/IGERT, NASA EPSCoR, etc.
Peer Review: This article has been internationally peer-reviewed and accepted for publication
according to the guidelines given at the journal’s website.
*Corresponding authors (Y.Deng). Tel/Fax: +1-605-367-7775/+1-605-367-7836. E-mail
addresses: ying.deng@usd.edu. (Z.Hu). Tel/Fax: +1-605-688-4817/+1-605-688-5878.
E-mail address: Zhong.hu@sdstate.edu. 2012. American Transactions on Engineering 23
& Applied Sciences. Volume 1 No.1 ISSN 2229-1652 eISSN 2229-1660
Online Available at http://TUENGR.COM/ATEAS/V01/01-23.pdf