1. The document analytically describes Feigen's experimental results on plastic straining under combined loading using the synthetic theory of irrecoverable deformation.
2. Feigen observed the unexpected phenomenon of plastic "untwisting" where the accumulated torsional plastic strain decreased during torsional unloading, which cannot be explained by classical plasticity theories.
3. The synthetic theory, which models plastic deformation through the displacement of tangent planes on the yield surface, can readily model Feigen's experiment without additional assumptions. It represents both loading and deformation as vectors, making the analysis simpler than using tensors.
Peculiarities of irrecoverable straining in stress-drop testIJERA Editor
The paper concerns with analytical description of the phenomena observed in stress drop tests, namely, negative increment in plastic and creep deformation due to the sudden decrease in the acting stresses while the net stress remains positive. The model is developed in terms of the synthetic theory of irrecoverable deformation which has been generalized by introducing interplay between the deformation properties of material in the direction of acting load and opposite to it.
Research on Contact Characteristics between Bump End Effector and WaferIJRES Journal
In the IC industry, commonly used methods are wafer clamping friction transmission type and vacuum suction. Combining science and theological contact theory,the contact friction transmission characteristics when using the bump and transmission actuator wafer, the wafer and the end actuators. Starting from the material properties of the wafer by ANSYS simulation analysis in contact with the wafer bump deformation due to its own gravity, and verify that it meets the requirements of small deformation wafer transfer. Compute and solve the friction contact with the wafer bump bristles between.
Prediction of joint strength and effect of the surface treatment on the singl...Filipe Giesteira
A two-component high-ductility adhesive (acrylic and catalyst based), SikaFast® - 5211 NT, was used to bond single overlap joints with mild steel adherends and 25 mm of overlap. One joint configuration used treated bonding surfaces while the other was did not employ treatment of the adherend surfaces, with the aim of studying the influence of the material surface treatment. The specimens were tensile tested in a INSTRON® universal testing machine and the non-treated surface have shown a strength four times lower than the treated surface. Several analytical methods were used to predict joint strength, with two methods achieving reasonably accurate failure load predictions.
EFFECT OF SURFACE ROUGHNESS ON CHARACTERISTICS OF SQUEEZE FILM BETWEEN POROUS...IAEME Publication
In investigation aims to analyse the effect of transverse surface roughness on the squeeze film performance between porous rectangular plates. The associated differential equation is stochastically averaged making use of stochastic averaging method of Christensen and Tonder for transverse surface roughness. The equation is solved with appropriate boundary conditions to obtain the pressure and consequentlythe load bearing. The graphical results suggest that the bearing suffers because of transverse surface roughness. However the situation is slightly better in the case of
negatively skew roughness. Further variance (-ve) makes the situation furtherimproved even if moderate values of porosity are involved
Expositions on the Variation of Torsional-Distortional Stresses and Deformati...IJERD Editor
- In this work a single cell and a double cell mono symmetric box girder study profile with the same
cross sectional (enclosed) area and same material thickness were used to obtain the effect of sectorial properties
on the distortional bending stresses and deformation of mono-symmetric box girders. The principles of Vlasov’s
theory of thin walled plates were used to obtain the torsional-distortional equilibrium equation for the analysis
of the study profiles. The distortional bending stresses for the profiles were obtained by numerical
differentiation of the warping function to obtain the distortion diagrasm which formed the base system for
evaluation of the distortional bending moments. By solving the fourth order differential equations for torsionaldistortional
equilibrium the deformations of the study profiles were obtained. The warping functions, the
distortion diagrams, the distortional bending moments and the torsional and distortional deformations of the
study profiles were critically examined and conclusions were made.
Literature Review of Experimental Study on Load Bearing Masonry WallIOSRJMCE
Masonry load bearing wall subjected to vertical concentric and eccentric loading may collapse through instability. In this Paper the buckling behavior of masonry load bearing wall of different slenderness ratio were investigated by many researcher has been reviewed via testing a series of scale masonry wall subjected to concentric and eccentric vertical loading. The influence of nonlinear behavior of interface element, slenderness ratio and various end conditions have been investigated together with the effect of different end eccentricity of vertical load.
Examples of Homogenization Techniques in the Material Modeling Under the Effe...Sardasht S. Weli
Explosions become a very attractive research area in the last decades.
This is due to the increase of accidental and intentional explosions.
Historical structure were not designed and built against the extreme loading events.
Homogenization Techniques were developed to assess the masonry response.
Peculiarities of irrecoverable straining in stress-drop testIJERA Editor
The paper concerns with analytical description of the phenomena observed in stress drop tests, namely, negative increment in plastic and creep deformation due to the sudden decrease in the acting stresses while the net stress remains positive. The model is developed in terms of the synthetic theory of irrecoverable deformation which has been generalized by introducing interplay between the deformation properties of material in the direction of acting load and opposite to it.
Research on Contact Characteristics between Bump End Effector and WaferIJRES Journal
In the IC industry, commonly used methods are wafer clamping friction transmission type and vacuum suction. Combining science and theological contact theory,the contact friction transmission characteristics when using the bump and transmission actuator wafer, the wafer and the end actuators. Starting from the material properties of the wafer by ANSYS simulation analysis in contact with the wafer bump deformation due to its own gravity, and verify that it meets the requirements of small deformation wafer transfer. Compute and solve the friction contact with the wafer bump bristles between.
Prediction of joint strength and effect of the surface treatment on the singl...Filipe Giesteira
A two-component high-ductility adhesive (acrylic and catalyst based), SikaFast® - 5211 NT, was used to bond single overlap joints with mild steel adherends and 25 mm of overlap. One joint configuration used treated bonding surfaces while the other was did not employ treatment of the adherend surfaces, with the aim of studying the influence of the material surface treatment. The specimens were tensile tested in a INSTRON® universal testing machine and the non-treated surface have shown a strength four times lower than the treated surface. Several analytical methods were used to predict joint strength, with two methods achieving reasonably accurate failure load predictions.
EFFECT OF SURFACE ROUGHNESS ON CHARACTERISTICS OF SQUEEZE FILM BETWEEN POROUS...IAEME Publication
In investigation aims to analyse the effect of transverse surface roughness on the squeeze film performance between porous rectangular plates. The associated differential equation is stochastically averaged making use of stochastic averaging method of Christensen and Tonder for transverse surface roughness. The equation is solved with appropriate boundary conditions to obtain the pressure and consequentlythe load bearing. The graphical results suggest that the bearing suffers because of transverse surface roughness. However the situation is slightly better in the case of
negatively skew roughness. Further variance (-ve) makes the situation furtherimproved even if moderate values of porosity are involved
Expositions on the Variation of Torsional-Distortional Stresses and Deformati...IJERD Editor
- In this work a single cell and a double cell mono symmetric box girder study profile with the same
cross sectional (enclosed) area and same material thickness were used to obtain the effect of sectorial properties
on the distortional bending stresses and deformation of mono-symmetric box girders. The principles of Vlasov’s
theory of thin walled plates were used to obtain the torsional-distortional equilibrium equation for the analysis
of the study profiles. The distortional bending stresses for the profiles were obtained by numerical
differentiation of the warping function to obtain the distortion diagrasm which formed the base system for
evaluation of the distortional bending moments. By solving the fourth order differential equations for torsionaldistortional
equilibrium the deformations of the study profiles were obtained. The warping functions, the
distortion diagrams, the distortional bending moments and the torsional and distortional deformations of the
study profiles were critically examined and conclusions were made.
Literature Review of Experimental Study on Load Bearing Masonry WallIOSRJMCE
Masonry load bearing wall subjected to vertical concentric and eccentric loading may collapse through instability. In this Paper the buckling behavior of masonry load bearing wall of different slenderness ratio were investigated by many researcher has been reviewed via testing a series of scale masonry wall subjected to concentric and eccentric vertical loading. The influence of nonlinear behavior of interface element, slenderness ratio and various end conditions have been investigated together with the effect of different end eccentricity of vertical load.
Examples of Homogenization Techniques in the Material Modeling Under the Effe...Sardasht S. Weli
Explosions become a very attractive research area in the last decades.
This is due to the increase of accidental and intentional explosions.
Historical structure were not designed and built against the extreme loading events.
Homogenization Techniques were developed to assess the masonry response.
Torsional-Distortional Performance of Multi-Cell Trapezoidal Box Girder with ...IJERA Editor
In this study, the torsional and distortional performance of a three triangular cell trapezoidal box girder section was studied using Vlasov’s theory of thin walled structures. The potential energy of a system under equilibrium was used to obtain the governing differential equations of equilibrium for torsionl-distortional analysis of the box structure. The strain modes diagrams representing torsional and distortional interactions of the box girder structure were obtained as well as the distortional bending moment diagram for the box girder structure. These were used to compute Vlasov’s coefficients contained in the differential equations of equilibrium. The fourth order differential equations obtained were solved using method of trigonometric series with accelerated convergence to obtain the distortional and torsional deformations which were compared with torsional and distortional deformations of a single cell mono symmetric box girder section of similar overall dimensions and plates thicknesses. The maximum distortional deformation was found to be 168% lower than that of a single cell mono-symmetric box girder section of the same size and dimensions. The inclined internal web members, which also act as diaphragms, brought about increase in the pure torsional and distortional components of the applied torsional load, resulting to marginal increase in the torsional deformation but major decrease in the distortional deformation.
Implementation of a tension-stiffening model for the cracking nonlinear analy...Luis Claudio Pérez Tato
The development of a smeared-crack model offers a general crack-modeling method that is independent of the structural configuration. It treats cracking as a constitutive material behaviour rather than a geometric discontinuity and lends itself well to implementation in large finite element codes. This paper deals with the implementation in XC of a constitutive model for reinforced concrete elements that takes into account the increase in stiffness of a cracked member due to the development of tensile stresses in the concrete between the cracks, effect known as tension-stiffening. The nonlinear analysis in XC of fiber-like sections with this constitutive model allows for a more general, direct and intuitive evaluation of the crack amplitude than applying the mostly specific formulae developed in the standards. The numerical results obtained by the program compare extremely well with existing designing results issued by other applied methods.
ANALYTICAL BENDING ANALYSIS OF A CIRCULAR SANDWICH PLATE UNDER DISTRIBUTED LOADijmech
In this paper, bending analysis of a circular sandwich plate under distributed load with simply supported and clamped boundary conditions is investigated. First, the governing equations of the circular sandwich plate are obtained and they are solved using the Bessel functions. Then in order to validate the correctness of analytical results, numerical finite element method is used and its results are presented in the forms of
contours and graphs. The results indicate that under distributed load, maximum deflection happens at 0.3
of outside radius, away from centre, and minimum deflection occurs at the outer edge of the circular sandwich plate. The results from analytical and numerical methods are compared and it shows that analytical method provides an acceptable accuracy.
A Review of Masonry Buckling CharacteristicsIJERA Editor
Masonry load bearing wall subjected to vertical concentric and eccentric loading may collapse through instability. In this Paper the buckling behaviour of masonry load bearing wall of different slenderness ratio were investigated by many researcher has been reviewed via testing a series of scale masonry wall subjected to concentric and eccentric vertical loading. It is also observed that buckling behaviour is greatly influenced by the material properties of units, mortar and units-mortar interface. The influence of nonlinear behaviour of interface element, slenderness ratio and various end conditions have been investigated together with the effect of different end eccentricity of vertical load
During the last decades, several studies on suspension bridges under wind actions have been developed in civil engineering and many techniques have been used to approach this structural problem both in time and frequency domain. In this paper, four types of time domain techniques to evaluate the response and the stability of a long span suspension bridge are implemented: nonaeroelastic, steady, quasi steady, modified quasi steady. These techniques are compared considering both nonturbulent and turbulent flow wind modelling. The results show consistent differences both in the amplitude of the response and in the value of critical wind velocity.
The convergence and accuracy of the Dynamic Relaxation (DR) solutions for elastic
large deflection response are established by comparison with various exact and approximate
solutions. New numerical results are generated for uniformly loaded square laminated plates
which serve to quantify the effects of shear deformation, length to thickness ratio, number of
layers, material anisotropy and fiber orientation.
It was found that linear analysis seriously over predicts deflection of plates. The shear
deflection depends greatly on a number of factors such as length to thickness ratio, degree of
anisotropy and number of layers. As the degree of anisotropy increases, the plate becomes
stiffer and when it is greater than a critical value, the deflection becomes virtually
independent on the degree of anisotropy. It was also found that deflection of plates depends
on the angle of orientation of individual plies and the size of load applied.
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
call for paper 2012, hard copy of journal, research paper publishing, where to publish research paper,
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
A comprehensive literature review on different theories of laminated plates have been
reviewed and discussed thoroughly. It has been found that there are two main theories of
laminated plates which are known as linear and nonlinear theories. The two theories are
depending on the magnitude of deformation resulting from loading the given plates. The
difference between the two theories is that the deformations are small in the linear theory,
whereas they are finite or large in the nonlinear theory.
In comparisons between FEM and different numerical methods it has been found that
FEM can be considered of acceptable accuracy, and can also be applied to different
complicated geometries and shapes.
Steady State Thermoelastic Problem in an Infinite Elastic Layer Weakened by a...inventionjournals
The paper is concerned with a thermoelastic behavior in an infinite elastic layer of finite thickness with a crack in it lying in the middle of the layer and parallel to the faces of the layer. The faces of the layer are maintained at constant temperature of different magnitude. The problem is a steady state thermoelastic problem. The layer surfaces are supposed to be acted on by symmetrically applied concentrated forces of magnitude with respect to the centre of the crack. The applied concentrated force may be compressive or tensile in nature. The problem is solved by using integral transform technique .The solution of the problem has been reduced to the solution of a Cauchy type singular integral equation, which requires numerical treatment. The stress-intensity factor and the crack opening displacement are determined and thermal effects on various subjects of physical interest are shown graphically
Non- Newtonian behavior of blood in very narrow vesselsIOSR Journals
The purpose of the study is to get some qualitative and quantitative insight into the problem of flow in vessels under consideration where the concentration of lubrication film of plasma is present between each red cells and tube wall. This film is potentially important in region to mass transfer and to hydraulic resistance, as well as to the relative resistance times of red cells and plasma in the vessels network.
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
Torsional-Distortional Performance of Multi-Cell Trapezoidal Box Girder with ...IJERA Editor
In this study, the torsional and distortional performance of a three triangular cell trapezoidal box girder section was studied using Vlasov’s theory of thin walled structures. The potential energy of a system under equilibrium was used to obtain the governing differential equations of equilibrium for torsionl-distortional analysis of the box structure. The strain modes diagrams representing torsional and distortional interactions of the box girder structure were obtained as well as the distortional bending moment diagram for the box girder structure. These were used to compute Vlasov’s coefficients contained in the differential equations of equilibrium. The fourth order differential equations obtained were solved using method of trigonometric series with accelerated convergence to obtain the distortional and torsional deformations which were compared with torsional and distortional deformations of a single cell mono symmetric box girder section of similar overall dimensions and plates thicknesses. The maximum distortional deformation was found to be 168% lower than that of a single cell mono-symmetric box girder section of the same size and dimensions. The inclined internal web members, which also act as diaphragms, brought about increase in the pure torsional and distortional components of the applied torsional load, resulting to marginal increase in the torsional deformation but major decrease in the distortional deformation.
Implementation of a tension-stiffening model for the cracking nonlinear analy...Luis Claudio Pérez Tato
The development of a smeared-crack model offers a general crack-modeling method that is independent of the structural configuration. It treats cracking as a constitutive material behaviour rather than a geometric discontinuity and lends itself well to implementation in large finite element codes. This paper deals with the implementation in XC of a constitutive model for reinforced concrete elements that takes into account the increase in stiffness of a cracked member due to the development of tensile stresses in the concrete between the cracks, effect known as tension-stiffening. The nonlinear analysis in XC of fiber-like sections with this constitutive model allows for a more general, direct and intuitive evaluation of the crack amplitude than applying the mostly specific formulae developed in the standards. The numerical results obtained by the program compare extremely well with existing designing results issued by other applied methods.
ANALYTICAL BENDING ANALYSIS OF A CIRCULAR SANDWICH PLATE UNDER DISTRIBUTED LOADijmech
In this paper, bending analysis of a circular sandwich plate under distributed load with simply supported and clamped boundary conditions is investigated. First, the governing equations of the circular sandwich plate are obtained and they are solved using the Bessel functions. Then in order to validate the correctness of analytical results, numerical finite element method is used and its results are presented in the forms of
contours and graphs. The results indicate that under distributed load, maximum deflection happens at 0.3
of outside radius, away from centre, and minimum deflection occurs at the outer edge of the circular sandwich plate. The results from analytical and numerical methods are compared and it shows that analytical method provides an acceptable accuracy.
A Review of Masonry Buckling CharacteristicsIJERA Editor
Masonry load bearing wall subjected to vertical concentric and eccentric loading may collapse through instability. In this Paper the buckling behaviour of masonry load bearing wall of different slenderness ratio were investigated by many researcher has been reviewed via testing a series of scale masonry wall subjected to concentric and eccentric vertical loading. It is also observed that buckling behaviour is greatly influenced by the material properties of units, mortar and units-mortar interface. The influence of nonlinear behaviour of interface element, slenderness ratio and various end conditions have been investigated together with the effect of different end eccentricity of vertical load
During the last decades, several studies on suspension bridges under wind actions have been developed in civil engineering and many techniques have been used to approach this structural problem both in time and frequency domain. In this paper, four types of time domain techniques to evaluate the response and the stability of a long span suspension bridge are implemented: nonaeroelastic, steady, quasi steady, modified quasi steady. These techniques are compared considering both nonturbulent and turbulent flow wind modelling. The results show consistent differences both in the amplitude of the response and in the value of critical wind velocity.
The convergence and accuracy of the Dynamic Relaxation (DR) solutions for elastic
large deflection response are established by comparison with various exact and approximate
solutions. New numerical results are generated for uniformly loaded square laminated plates
which serve to quantify the effects of shear deformation, length to thickness ratio, number of
layers, material anisotropy and fiber orientation.
It was found that linear analysis seriously over predicts deflection of plates. The shear
deflection depends greatly on a number of factors such as length to thickness ratio, degree of
anisotropy and number of layers. As the degree of anisotropy increases, the plate becomes
stiffer and when it is greater than a critical value, the deflection becomes virtually
independent on the degree of anisotropy. It was also found that deflection of plates depends
on the angle of orientation of individual plies and the size of load applied.
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
call for paper 2012, hard copy of journal, research paper publishing, where to publish research paper,
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
A comprehensive literature review on different theories of laminated plates have been
reviewed and discussed thoroughly. It has been found that there are two main theories of
laminated plates which are known as linear and nonlinear theories. The two theories are
depending on the magnitude of deformation resulting from loading the given plates. The
difference between the two theories is that the deformations are small in the linear theory,
whereas they are finite or large in the nonlinear theory.
In comparisons between FEM and different numerical methods it has been found that
FEM can be considered of acceptable accuracy, and can also be applied to different
complicated geometries and shapes.
Steady State Thermoelastic Problem in an Infinite Elastic Layer Weakened by a...inventionjournals
The paper is concerned with a thermoelastic behavior in an infinite elastic layer of finite thickness with a crack in it lying in the middle of the layer and parallel to the faces of the layer. The faces of the layer are maintained at constant temperature of different magnitude. The problem is a steady state thermoelastic problem. The layer surfaces are supposed to be acted on by symmetrically applied concentrated forces of magnitude with respect to the centre of the crack. The applied concentrated force may be compressive or tensile in nature. The problem is solved by using integral transform technique .The solution of the problem has been reduced to the solution of a Cauchy type singular integral equation, which requires numerical treatment. The stress-intensity factor and the crack opening displacement are determined and thermal effects on various subjects of physical interest are shown graphically
Non- Newtonian behavior of blood in very narrow vesselsIOSR Journals
The purpose of the study is to get some qualitative and quantitative insight into the problem of flow in vessels under consideration where the concentration of lubrication film of plasma is present between each red cells and tube wall. This film is potentially important in region to mass transfer and to hydraulic resistance, as well as to the relative resistance times of red cells and plasma in the vessels network.
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
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.
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.
International Journal of Engineering Research and Applications (IJERA) aims to cover the latest outstanding developments in the field of all Engineering Technologies & science.
International Journal of Engineering Research and Applications (IJERA) is a team of researchers not publication services or private publications running the journals for monetary benefits, we are association of scientists and academia who focus only on supporting authors who want to publish their work. The articles published in our journal can be accessed online, all the articles will be archived for real time access.
Our journal system primarily aims to bring out the research talent and the works done by sciaentists, academia, engineers, practitioners, scholars, post graduate students of engineering and science. This journal aims to cover the scientific research in a broader sense and not publishing a niche area of research facilitating researchers from various verticals to publish their papers. It is also aimed to provide a platform for the researchers to publish in a shorter of time, enabling them to continue further All articles published are freely available to scientific researchers in the Government agencies,educators and the general public. We are taking serious efforts to promote our journal across the globe in various ways, we are sure that our journal will act as a scientific platform for all researchers to publish their works online.
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.
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.
On the Rheological Model of Asphalt Concreteijtsrd
Since asphalt concrete exhibits elastic, plastic, and viscous properties in response to changes in temperature and external influences, establishing a relation ship between stress and deformation is an important issue. The study of the elastic and viscosity properties of physical bodies began in 1868 with the introduction of the con cept of relaxation by Maxwell. In 1890, Kelvin introduced the concept of retardation subsequent effect . Different models have been proposed to establish the above men tioned relationship. Models such as Maxwell, Kelvin, Jeffries, Lesersich, Bingham, Burgers, Shvedov, Hutchek, and Crassus have been proposed. Despite the large num ber of models offered, they are based on and are a combination of Hooke, Newton, and Saint Venan models for elastic, viscous, and plastic bodies. H. Jumaev "On the Rheological Model of Asphalt Concrete" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-6 | Issue-3 , April 2022, URL: https://www.ijtsrd.com/papers/ijtsrd49553.pdf Paper URL: https://www.ijtsrd.com/other-scientific-research-area/other/49553/on-the-rheological-model-of-asphalt-concrete/h-jumaev
vertical response of a hereditary deformable systemIJAEMSJORNAL
An investigation of a viscoelastic material damping effect is studied on an example of plenum air-cushion craft model. A numerical investigation was conducted to determine the vertical response characteristic of an open plenum air-cushion structure. The pure vertical motion of an air-cushion structure is investigated using a non-linear mathematical model; this incorporates a simple model to account hereditary deformable characteristic of the material.
A COMPARATIVE STUDY OF VARIOUS METHODS TO EVALUATE IMPEDANCE FUNCTION FOR SHA...Samirsinh Parmar
Impedance function, Foundation Vibration, dynamic soil-structure interaction, Barkan, Dominguez, Dobry and Gazetas for evaluation of impedance functions for various modes of vibration of shallow foundation
First order shear deformation (FSDT) theory for laminated composite beams is used to study free vibration of
laminated composite beams, and finite element method (FEM) is employed to obtain numerical solution of the
governing differential equations. Free vibration analysis of laminated beams with rectangular cross – section for
various combinations of end conditions is studied. To verify the accuracy of the present method, the frequency
parameters are evaluated and compared with previous work available in the literature. The good agreement with
other available data demonstrates the capability and reliability of the finite element method and the adopted beam
model used.
techDynamic characteristics and stability of cylindrical textured journal bea...ijmech
The dynamic characteristics of cylindrical textured hydrodynamic journal bearing are presented in this paper. The Reynolds equation is solved numerically in a finite difference grid in an iterative scheme satisfying the appropriate boundary conditions. Stiffness and damping coefficients of fluid film and stability parameter are found using the first-order perturbation method for different eccentricity ratios and various texture parameters like texture depth and texture density.. From the present analysis, it has been found that stability is enhanced with increase in texture depth, whereas there is an optimum texture density corresponding to the maximum stability of the bearing
Analysis and Design of One Dimensional Periodic Foundations for Seismic Base ...IJERA Editor
Periodic foundationis a new type of seismic base isolation system. It is inspired by the periodic material crystal
lattice in the solid state physics. This kind of material has a unique property, which is termed as frequency band
gap that is capable of blocking incoming waves having frequencies falling within the band gap. Consequently,
seismic waves having frequencies falling within the frequency band gap are blocked by the periodic foundation.
The ability to block the seismic waveshas put this kind of foundation as a prosperous next generation of seismic
base isolators. This paper provides analytical study on the one dimensional (1D) type periodic foundations to
investigate their seismic performance. The general idea of basic theory of one dimensional (1D) periodic
foundations is first presented.Then, the parametric studies considering infinite and finite boundary conditions are
discussed. The effect of superstructure on the frequency band gap is investigated as well. Based on the analytical
study, a set of equations is proposed for the design guidelines of 1D periodic foundations for seismic base
isolation of structures.
Analysis and Design of One Dimensional Periodic Foundations for Seismic Base ...IJERA Editor
Periodic foundationis a new type of seismic base isolation system. It is inspired by the periodic material crystal
lattice in the solid state physics. This kind of material has a unique property, which is termed as frequency band
gap that is capable of blocking incoming waves having frequencies falling within the band gap. Consequently,
seismic waves having frequencies falling within the frequency band gap are blocked by the periodic foundation.
The ability to block the seismic waveshas put this kind of foundation as a prosperous next generation of seismic
base isolators. This paper provides analytical study on the one dimensional (1D) type periodic foundations to
investigate their seismic performance. The general idea of basic theory of one dimensional (1D) periodic
foundations is first presented.Then, the parametric studies considering infinite and finite boundary conditions are
discussed. The effect of superstructure on the frequency band gap is investigated as well. Based on the analytical
study, a set of equations is proposed for the design guidelines of 1D periodic foundations for seismic base
isolation of structures.
Dynamic Relaxation (DR) method is presented for the geometrically nonlinear laterally loaded,
rectangular laminated plates. The analysis uses the Mindlin plate theory which accounts for transverse
shear deformation. A computer program has been compiled. The convergence and accuracy of the DR
solutions for elastic large deflection response are established by comparison with various exact and
approximate solutions. New numerical results are generated for uniformly loaded square laminated
plates which serve to quantify the effects of shear deformation, length to thickness ratio, number of
layers, material anisotropy and fiber orientation.
It was found that linear analysis seriously over predicts deflection of plates. The shear
deflection depends greatly on a number of factors such as length to thickness ratio, degree of
anisotropy and number of layers. As the degree of anisotropy increases, the plate becomes stiffer and
when it is greater than a critical value, the deflection becomes virtually independent on the degree of
anisotropy. It was also found that deflection of plates depends on the angle of orientation of individual
plies and the size of load applied.
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.
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Af4301172180
1. Andrew Rusinko Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 4, Issue 3( Version 1), March 2014, pp.172-180
www.ijera.com 172 | P a g e
Feigen’s Phenomenon in Terms of the Synthetic Theory
Andrew Rusinko
Obuda University, Népszínház St. 8, Budapest, Hungary, H-1081
Abstract The paper concerns with the analytic description of Feigen’s results on plastic straining under
combined loading. The model is developed in terms of the synthetic theory of irrecoverable deformation.
Criterion to establish when Feigen’s phenomenon can be observed is proposed. It is worthwhile to note that the
synthetic theory requires no special additional assumptions, or generalizations to model Feigen’s experiment.
Keywords: Feigen’s phenomenon, plastic deformation, combined loading, synthetic theory of irrecoverable
deformation
I. Introduction
Feigen’s experimental results (Feigen, M., 1954) are of crucial importance to obtain further insight into
mechanisms of plastic deforming. Despite the fact that this phenomenon dates back to the 1950s of the twentieth
century, its modeling has not been completely solved yet.
Consider Feigen’s experiment consisting in the following loading regime:
(i) a specimen plastically deforms in a complex stress state, tension and torsion (Fig. 1a);
(ii) the torsional component decreases and the tension increases, (Fig. 1b). The loading path (ABC, >AC AB) is
shown in Fig. 2.
Feigen reports an unexpected phenomenon is observed. The torsional plastic deformation ( S
)
accumulated in the initial combined loading decreases during the torsional unloading, 0S
along BC
portion: the specimen is plastically “untwisting”. According to classical ideas, a plastic strain developed in
active loading remains unchangeable during the succeeding unloading.
This phenomenon can be explained by the fact that, along portion BC, plastic shifts develop within such slip
systems that give negative increment in torsional strain thereby resulting in the plastic untwisting of specimen.
At the same time, the fraction of grains, which produced positive torsional strains along portion AB, remains
hardened along BC.
The aim of the paper is to model Feigen’s experiments in terms of the synthetic theory of recoverable
deformation. Another goal of the study is to establish a criterion for predicting the condition when the
phenomenon is manifested. It is worth noting that the synthetic theory needs no additional assumptions or
generalizations; its classical statement is readily applicable to the analytical description of Feigen’s results. In
contrast, for example, Mazilu, P. (1985) tried to explain this phenomenon by assuming the existence of certain
hypoelastic deformations (Lehmann, Th., 1962) accompanying the elasto-plastic one.
The research presented here may be of interest for the studies dealing with a wide variety of engineering
mechanics (Mirsalimov and Veliyev (2013); Szekeres (2012); Kharchenko and Sobkowski (2005); Zabłocka et
al. (2012); Malinin, V. (2011)).
It is clear that Feigen’s phenomenon can not be modeled in terms of classical flow plasticity theories
(for an extensive review, see Rees, 1987). If we take, for example, flow plasticity theory with isotropic
hardening rule, it will relate plastic strain tensor components increment ( S
ijd ) to stress deviator tensor
components ( ij ) as
0 0
S
ij ijd C d , (1.1)
where 0 is the second invariant of stress tensor and 0C is
0
0
1 1 1
2 t
C
G G
, (1.2)
where G is elastic shear modulus and 0 03tG d d ( 0 is the second invariant of strain tensor). Condition
tG G implies that 0 0C .
RESEARCH ARTICLE OPEN ACCESS
2. Andrew Rusinko Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 4, Issue 3( Version 1), March 2014, pp.172-180
www.ijera.com 173 | P a g e
For the case of biaxial loading (tension + torsion), Eq. (1.1) give
0 0
S
d C d , 0 0
S
d C d . (1.3)
In terms of the flow theory with isotropic hardening, plastic deformation is assumed to develop if 0 0d . If to
suggest that 0 0d along portion BC ( 0 and 0 ), then Eq. (1.3) gives positive increments in both S
and S
components. For the case 0 0d , we have 0S S
d d . Both results contradict Feigen’s
experiment reporting that 0S
d .
II. Mathematical apparatus: the synthetic theory of irrecoverable deformation.
The synthetic theory, which concerns with small strains of work-hardening metals, incorporates the
elements of flow plasticity theory (Sanders, 1954) and slip concept (Budiansky, 1949). The fundamentals of the
synthetic theory are put forth in details in Rusinko’s works (2009, 2011).
(i) The synthetic theory belongs to two-level models. Similarly to the Budiansky slip concept, the synthetic
theory has a micro- and a macro-level. For the macrolevel we take as the elementary volume of the body, ,
which is considered as point in the mathematical sense. The given volume, , consists of a large quantity of
volumes, 0 (the micro-level), each being an element of the continuous, capable of deforming under the applied
forces. Accordingly to Budiansky, it is assumed that the stress state in every volume 0 is the same as that in the
volume . Plastic deformation in the microvolume 0 (grain) is assumed as slip of one part of 0 in relation to
another. Therefore, in contrast to the even distribution of the stress above microvolumes 0, the plastic
deformation (or plastic slip) depends on the orientation of the slip system relative to the direction of the acting
forces. It is assumed that the quantity of 0 is so great (theoretically it tends to infinity) that every possible
orientation of slip systems exists in volume . The total deformation of is determined as the sum of the
components of deformations generated within volumes 0. Lichatchev et al. (1993) give the substantiation of
the sizes of microvolumes 0.
(ii) The establishment of stress~strain relationships on microlevel takes place in the three-dimensional
subspace, R3
, of the Ilyushin five-dimensional stress deviator space, R5
, where a loading is presented by stress
vector, 3
S R
, whose components are
1 3 2 xxS S , 2 2 2xx yyS S S , 3 2 xzS S , (2.1)
where ijS are the stress deviator tensor components. The length of the vector S
is related to the second
invariant of stress deviator tensor ( 2J ) as 22 3JS
.
(iii) New yield criterion is introduced, which coincides with nor Tresca’s, no von-Mises’s one in R5
. At the
same time, its trace in 3
R gives the von-Mises yield criterion:
2 2 2 2
1 2 3 SS S S S , 2 3S SS (2.2)
where S is the yield strength of material in uniaxial tension. Through each point on the sphere we draw a
tangent plane. So, the yield surface can be thought of the inner envelope of equidistant planes. The position of
plane in 3
R is defined by the following two quantities (Fig. 3):
a) Unit vector 1 2 3( , , )m m mm
normal to the plane:
1 cos cosm , 2 sin cosm , 3 sinm , (2.3)
where α and β are spherical angles giving the orientation of m
in 3
R (Rusinko, 2009). For simplicity, we
consider only planes tangential to yield/loading surface in 3
R and those tangential to the yield/loading surface
in 5
R are ignored.
b) The distance from the origin of coordinates to the plane, mh .
The condition that a plane is located on the endpoint of stress vector is expressed as
mh S m
. (2.4)
(iv) According to Sanders, to establish a hardening rule, we extend the provision that a surface is constructed as
an inner envelope of planes to the case of loading as well. During loading, the vector S
displaces on its
endpoint a set of planes from their initial position, i.e. from sphere (2.2). Each plane moves without changing its
3. Andrew Rusinko Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 4, Issue 3( Version 1), March 2014, pp.172-180
www.ijera.com 174 | P a g e
orientation. As a result, the loading surface – an inner envelope of planes – has a form as shown in Fig. 4. It
consists of
- a cone whose lateral surface is formed by the boundary planes reached by the S
and
- the part of sphere (2.2), which is the inner envelope of stationary planes.
(v) Each tangent plane corresponds to an appropriate slip system, and the displacement of the plane on the
endpoint of stress vector symbolizes the development of plastic microdeformation within the slip system. Plastic
microstrain modeled by the displacement of one plane is assumed to be a vector normal to the plane (see Fig. 3).
It is easy to see that the distance to a plane gives the degree of the hardening of material. Indeed, the greater mh ,
the greater stress vector is needed to reach the plane, i.e. to induce plastic shift within the corresponding slip
system. Further, we introduce an average measure of plastic strain developed within a slip system (i.e. for one
plane), termed as plastic strain intensity ( m ), as follows
2 2
if (plane is reached by )1
0 if (plane is not reached by )
m S m
m
m
h S h
r h
S m S
S m S
(2.5)
where r is the constant of material, 2
MPar . It must be noted that the product S m
is the resolve stress
acting within a slip system. Further, it is easy to see that the greater mh , the greater distance is traveled by the
plane on the endpoint of stress vector, i.e. the greater plastic deformation develops within the corresponding slip
system.
(vi) The macroplastic deformation, expressed via plastic strain vector components ( S
ke ), is calculated as the sum
of non-zero m (Rusinko, 2009, 2011):
S S
md dV
e e m
, or S
k m ke m dV
, cosdV d d , 1,2,3k . (2.6)
The components ke from Eq. (2.6) can be converted to the strain deviator tensor components ( ije ) as
1 3 2 xxe e , 2 2 2xx yye e e , 3 2 xze e (2.7)
It must be noted that, in terms of the synthetic theory, both loading and deformation are expressed via vectors:
S
and S
e
, respectively. It is clear that vector algebra is much easier than tensor analysis. One more point that
deserves attention is that vector components iS have the same rights in the criterion (2.2); it is not the case if the
von-Mises yield criterion is expressed via, e.g., stress deviator tensor components:
1 2
2 2 2 2 2 2
22 2 3xx yy zz xy yz xzS S S S S S J
.
III.Isotropy postulate in terms of the synthetic theory
According to Ilyushin (1963), isotropy postulate reads that if the stress path in 3
R is rotated in stress
deviator space, then the corresponding strain path is rotated by the same amount (this postulate is valid for only
von-Mises’s medium). Consider an arbitrary loading path in 3
R as shown in Fig. 5. Let the corresponding strain
vector be e
, which makes angle η with the stress vector S
. Now, we rotate the loading path by a certain angle,
δ. To demonstrate the fulfillment of the isotropy postulate, we rotate the coordinate system by the same angle δ.
Within the rotated coordinate system, we obtain an analog of the previous loading and, therefore, it is easy to
conclude that the angle between vectors e
and S
must be the same as in the initial case. It is clear that the value
of strain strongly depends on the inner geometry of the loading path, but the rotation of loading path as a rigid
figure does not affect the relation between vectors e
and S
at any point of loading path.
IV. Feigen’s phenomenon in terms of synthetic theory
Relying upon isotropy postulate, we can model Feigen’s phenomenon. We consider the following case:
(i) an initial biaxial loading is proportional, i.e. the loading path of the stress vector S
is a straight line and (ii)
after the loading an infinitesimal orthogonal additional loading is applied ( d S S
). It is clear that such a
loading regime falls within the scope of Feigen’s experiment due to the additional loading gives an increase in
tension and decrease in torsion. Let the vector S
make angle with 1S -axis. Let us introduce a new system of
4. Andrew Rusinko Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 4, Issue 3( Version 1), March 2014, pp.172-180
www.ijera.com 175 | P a g e
coordinates ( 1 2 3' ' 'S S S ) by rotating the initial system by the angle so that the stress vector is along the 1 'S -
axis. In fact, we obtain an analog of two-segment loading, uniaxial tension and additional torsion. Consequently,
according to isotropy postulate, techniques developed in Rusinko’s previous works (2009, 2011) can be readily
used. In terms of the rotated coordinate system, the stress vector for the initial portion of loading has the only
nonzero component:
1 ' 2 3 'xS , 2 ' 0S 3 ' 0S , SSS
. (4.1)
On the base of Eqs. (2.3)-(2.5), the distance to plane and strain intensity are
1 1' ' ' 2 3 'cos 'cos 'm xh S m , (4.2)
2 2 2 22
' ' cos 'cos '
3
m x S
r
, (4.3)
where angles ' and ' are measured within 1 2 3' ' 'S S S coordinate system in the same way as within the
original system. The only non-zero component of plastic strain vector S
e
in 1 2 3' ' 'S S S coordinate system is (by
analogy with calculations from Rusinko’s works (2009, 2011))
1 1
1 1
2 2 2 2 2
1 1
' '
2
' ' ' ' cos 'cos ' cos 'cos ' ' '
3
S
m x Se m dV d d
r
, (4.4)
where
1cos '
cos '
b
, 1cos b ,
'
S
x
b
. (4.5)
By integrating (4.4) over domain (4.5) we obtain
2
1
4
'
3
S S
e b
r
,
2
2
2
1
1b b
b
, 1 0 . (4.6)
Due to the action of dS
, which is analogous to additional torsion ( 'xzd ) within 1 2 3' ' 'S S S coordinate system,
the strain intensity acquires the following increment
' 2 ' 'm m mrd h dh , (4.7)
where
' ' ' 2 sin ' 'm m m xzdh h h d , (4.8)
where 'mh stands for the distance to planes under the action of dS S
vector:
' 2 3 'cos 'cos ' 2 sin ' 'm x xzh d . (4.9)
As follows from the analysis of two segment orthogonal loading (Rusinko, 2009), plastic strain vector increment
components, 1 'S
de and 3 'S
de , are calculated as
1 1
1
2 3
1 1
' ' 0
4 ' '
' ' ' cos 'cos 'sin ' ' '
3
S x xz
m
d
de d m dV d d
r
, (4.10)
1 1
1
2 2
3 3
' ' 0
4 ' '
' ' ' cos 'cos 'sin ' ' '
3
S x xz
m
d
de d m dV d d
r
, (4.11)
Comparison of Eqs. (4.10) and (4.11) to Eq. (4.4) – ' -domain is 10, and 1 1, , respectively – shows
that the set of planes being at the endpoint of S
vector is two times less than that due to the action of dS S
.
Integrating in (4.10) and (4.11) yields
2
1 ' '
3 '
S S
xz
x
de b d
r
, 2
2
1 1
arccos 1 1 2b b b b
bb
, (4.12)
5. Andrew Rusinko Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 4, Issue 3( Version 1), March 2014, pp.172-180
www.ijera.com 176 | P a g e
1
3
3 '
' '
2 '
S
S
xz
x
e
de d
. (4.13)
The plot of b is shown in Fig. 6. As we can see from the formulae above, the value of strain
increments strongly depends on the value of initial loading.
The set of planes displaced by the vector S
is shown in Fig. 7a. For the case when the loading path of the vector
S
is a straight line (proportional loading) (i) the normal vectors of displaced planes are symmetric above 1 'S -
axis, (ii) planes on either side of the S
incurs identical displacements. This means that the total plastic strain
vector S
e
, which is calculated as the sum of strain vectors, each of which is normal to the plane displaced by
the S
, lies along the 1 'S -axis.
To model Feigen’s phenomenon, one needs to analyze the sign of 3
S
e
vector during additional loading.
In Fig. 7b, planes with 3 0m are depicted by solid lines; they give positive increments in 3
S
e
caused by an
orthogonal increment in stress. For planes depicted by dashed lines 3 0m , and, consequently, they stand with
negative signs in the sum for the 3
S
e
. It is clear that the sign of 3
S
e
depends on the set of ―positive‖ and
―negative‖ planes and the distances they traveled on the endpoint of stress vector.
The number of planes displaced by additional vector dS
is two times less than under the action of S
(Fig. 7b), and this set of the planes contains the same number of planes with negative normals (i.e. normals with
negative components on 3S -axis), while the number of planes with positive normals halves. This fact implies
that the slope of the strain vector due to the action of dS S
vector is less than that due to the S
vector.
Feigen’s phenomenon, an negative increment in plastic shear deformation during additional loading dS
, is
observed when the sum of plastic deformation increments having negative components on 3S -axis is greater
than that having positive components on 3S -axis.
Now, we wish to establish a criterion for occurring of Feigen’s phenomenon. In other words, we need
to establish such an angle between stress vector S
and 1S -axis, angle in Fig. 8, so that the orthogonal
additional loading results in the negative component of S
de
on 3S -axis, 3 0S
de . By projecting vector
1 3' 'S S S
d d d e e e
on 3S - axis and using Eqs. (4.12) and (4.13), we obtain
3 1 3'sin 'cosS S S
de de de (4.14)
Eq. (4.14) at 3 0S
de , together with (4.12) and (4.13), gives
1
3 1
0 2 2
1
3 '
'
' 2 ' 3 '
tan
' 2
'
3 '
S
xzS S
x
S
S S
xz
x
e
d
de re
de b
b d
r
. (4.15)
If 0 , then 3 0S
de , meaning that Feigen’s phenomenon will be observed. This situation is shown
in Fig. 8a. For the case 0 (Fig. 8b), we have 3 0S
de implying a positive increment in plastic torsional
deformation due to dS
, which contradicts Feigen’s phenomenon.
Therefore, Eq. (4.15) can be treated as a criterion for occurring Feigen’s phenomenon as a function of the
parameters of initial loading.
V. Conclusion
The present paper has modeled Feigen’s phenomenon in terms of the synthetic theory. A condition for
the onset of negative shear plastic strain under the additional loading has been derived. We restrict ourselves to
the case when the additional loading is perpendicular to the initial one. It has been shown that parameters of
initial loading, the orientation and magnitude of stress vector, considerably affects the behavior of specimen
under the second portion of loading.
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References
[1] Batdorf, S., Budiansky, B. (1949). Mathematical theory of plasticity based on the concept of slip.
NACA, Technical note, 871
[2] Feigen, M. (1954), Inelastic behavior under combined tension and torsion, 2nd
USNCAM, pp. 469-476.
[3] Ilyushin, A.A. (1963). Plasticity, Moscow.
[4] Kharchenko, Y., Sobkowski, S. (2005) Modelowanie matematyczne procesów rozruchu układów
napędowych podnośników budowlanych, Diagnostyka, 35: 37-42. (in Polish)
[5] Lehmann, Th. (1962). Zur Besehreibung groBer plastischer Form~nderungen unter Beriicksichtigung
der Werkstoffverfestigung, Rheol. Acta 2: 247-254.
[6] Lichatchev, V., Malinin, V. (1993). Structural-analytic theory of strength, St. Petersburg (in Russian).
[7] Malinin, V. (2011) Structural and analytical criterion of the fragile destruction for matter with
macroconcentration tension, J. Fundamental and Applied Problems of Engineering and Technology, 2:
36-42.
[8] Mazilu, P. (1985). Decreasing of the Initial Shear Modulus with Increasing Axial Strain Explained by
Means of a Plastic-Hypoelastic Model, Acta Mechanica 55: 93-115.
[9] Mirsalimov, V., Veliyev, F. (2013) Inverse Problem of Failure Mechanics for a Drawing Die
Strengthened with a Holder, Acta Polytechnica Hungarica, 10: 121-138.
[10] Rees, D.W.A. (1987). Application of Classical Plasticity Theory to Non-Radial Loading Paths, Proc. R.
Soc. Lond. A, 410: 443-475.
[11] Rusinko, A., Rusinko, K. (2009). Synthetic theory of irreversible deformation in the context of
fundamental bases of plasticity, Int. J. Mech. Mater. 41: 106-120.
[12] Rusinko, A., Rusinko, K. (2011). Plasticity and Creep of Metals, Springer, Berlin.
[13] Sanders, I. (1954). Plastic stress-strain relations based on linear loading function, 2nd
USNCAM, p. 455-
460.
[14] Szekeres, A. (2012) Cross-Coupled Heat and Moisture Transport: Part 1—Theory, Journal of Thermal
Stresses, 35: 248-268.
[15] Zabłocka, M., Wieczorek, P., Kłysz, S. (2012) Filtration properties of track membranes, Inżynieria
Materiałowa, 33: 51-55.
7. Andrew Rusinko Int. Journal of Engineering Research and Applications www.ijera.com
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Fig. 1 Loading regime in Feigen’s experiment; S denotes stretching force and T does torque
Fig. 2 Loading path in σ-τ plane in Feigen’s experiment
Fig. 3 Scheme of the displacement of tangent plane
σ
τ
A
B
C
Yield surface
S
m
mh
3S
2S
Initial position
Traveled distance
Current position on the
endpoint of stress vector
S
m
mh
1S
2S
Plastic strain vector
1S
3S
x
σx
z
y
x
z
y
T1
T1
S1
S1
S2 > S1
T2 < T1
S2
T2
a) b)
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Fig. 4 Loading surface in terms of the synthetic theory
Fig. 5 On isotropy postulate
Fig. 6 Function b from Eq. (4.12)
b
Φ(b)
SS
S
1S
3S
Boundary plane
Boundary plane
Loading surface
Displaced planes
Stationary
planes
Yield surface: sphere (2.2)
η
η
'1S
1S
'2S
δ
δ
e
S
S
e
Loading path
2S
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Fig. 7 Set of planes displaced by vector S
(a) and dS
(b) in 1 3S S coordinate plane ( 0 ).
Fig. 8 The sign of 3de in additional loading depending on the angle of initial loading ( ); superscripts ―S ‖ in
strain vectors and components are avoided.
SS
S
S
e
SS
S
S
d
1S
3S
'1S
'3S
m
m
m
m
1β
1β
1β
3S
'3S
1S
a) b)
'1S
γ > γ0
S
d
S
e
d
3e
d
03 de
03 de e
d3e
d
S
S
d
'1S
1S
3S
'3S
'1S
1S
3S
'3S
'3e
d
'1e
d
'3e
d
'1e
d
1e
d
0
1e
d
a)
b)