In this paper we propose a unified framework of the mortar domain decomposition method and extended finite element method (X-FEM). This framework allows to deal in an efficient manner with two cumbersome aspects of the finite element methods, namely incompatible interface discretizations and internal discontinuities. Features of mortar methods in the context of mesh tying, and of X-FEM in the context of void/inclusion treatment are exploited to formulate the weak coupling along an inclusion’s surface and the virtual surface of the host mesh. It has a potential to address a multitude of problems
from accurate substructuring to efficient wear simulation in contact problems.
This document proposes a Mesh Superposition Technique (MST) to couple differently discretized subdomains in a finite element model. The MST replaces interfaces between subdomains with transition regions where the meshes are superposed. Weighting factors are used to blend the material properties and boundary conditions in the overlapping transition regions. The MST is applied to simulate low-velocity impact damage in a composite plate, eliminating stress disturbances at discretization interfaces compared to abrupt transitions. When used for multiple time/length scale analysis, the MST reduces CPU time by nearly half compared to sudden discretization transitions.
This research focuses on simulating crack propagation in fluid-saturated porous materials undergoing large deformations. A two-scale numerical model is used, with the micro-scale governing fluid flow through the deformable porous material, and the macro-scale using finite elements coupled to the local momentum and mass balances from the micro-scale. Micro-cracks are modeled using cohesive zone laws, where the traction decreases with crack opening. The resulting equations are nonlinear and solved iteratively using Newton-Raphson and Crank-Nicholson schemes. The goal is to extend the approach to fully capture large material deformations with small crack openings, using hyperelastic constitutive models.
AUTOMATIC FACE NAMING BY LEARNING DISCRIMINATIVE AFFINITY MATRICES FROM WEAKL...Nexgen Technology
Nexgen Technology Address:
Nexgen Technology
No :66,4th cross,Venkata nagar,
Near SBI ATM,
Puducherry.
Email Id: praveen@nexgenproject.com.
www.nexgenproject.com
Mobile: 9751442511,9791938249
Telephone: 0413-2211159.
NEXGEN TECHNOLOGY as an efficient Software Training Center located at Pondicherry with IT Training on IEEE Projects in Android,IEEE IT B.Tech Student Projects, Android Projects Training with Placements Pondicherry, IEEE projects in pondicherry, final IEEE Projects in Pondicherry , MCA, BTech, BCA Projects in Pondicherry, Bulk IEEE PROJECTS IN Pondicherry.So far we have reached almost all engineering colleges located in Pondicherry and around 90km
The document presents a study on using the NURBS-based isogeometric finite element method for free vibration and buckling analysis of laminated composite plates. Key points:
- An isogeometric finite element method is developed using NURBS basis functions for the approximation of deflection fields and geometry parameterization.
- The Lagrange multiplier method is used to enforce essential boundary conditions and an orthogonal transformation technique is applied to the discrete eigenvalue equation.
- Numerical examples are presented to demonstrate the accuracy of the proposed method for laminated composite plates with different boundary conditions, fiber orientations, and modes of vibration/buckling. Results are verified against analytical and other numerical solutions.
Singh gordon-unified-factorization-ecmlHuỳnh Thông
This document presents a unified view of matrix factorization methods that frames the differences among popular methods like NMF, SVD, and probabilistic models in terms of a small number of modeling choices. Many approaches can be viewed as minimizing a generalized Bregman divergence. The authors show that an alternating projection algorithm can be applied to most models in this framework, and the Hessian for each projection has a special structure enabling efficient Newton updates. This allows incorporating constraints like non-negativity or clustering while factorizing matrices.
Automatic face naming by learning discriminative affinity matrices from weakl...Shakas Technologies
Given a collection of images, where each image contains several faces and is associated with a few names in the corresponding caption, the goal of face naming is to infer the correct name for each face
This document summarizes research on predicting the shear strength of reinforced concrete beams without web reinforcement. It begins by introducing the topic and noting that shear strength decreases as beam depth increases. It then reviews existing literature on shear strength mechanisms and factors that influence strength. The document discusses the challenges of theoretical models given complexities and uncertainties. It proposes using genetic programming and fuzzy set theory to develop empirical models from an existing database of over 2000 test results. The models would express shear strength as a function of concrete strength, reinforcement ratio, depth and other variables.
This document proposes a Mesh Superposition Technique (MST) to couple differently discretized subdomains in a finite element model. The MST replaces interfaces between subdomains with transition regions where the meshes are superposed. Weighting factors are used to blend the material properties and boundary conditions in the overlapping transition regions. The MST is applied to simulate low-velocity impact damage in a composite plate, eliminating stress disturbances at discretization interfaces compared to abrupt transitions. When used for multiple time/length scale analysis, the MST reduces CPU time by nearly half compared to sudden discretization transitions.
This research focuses on simulating crack propagation in fluid-saturated porous materials undergoing large deformations. A two-scale numerical model is used, with the micro-scale governing fluid flow through the deformable porous material, and the macro-scale using finite elements coupled to the local momentum and mass balances from the micro-scale. Micro-cracks are modeled using cohesive zone laws, where the traction decreases with crack opening. The resulting equations are nonlinear and solved iteratively using Newton-Raphson and Crank-Nicholson schemes. The goal is to extend the approach to fully capture large material deformations with small crack openings, using hyperelastic constitutive models.
AUTOMATIC FACE NAMING BY LEARNING DISCRIMINATIVE AFFINITY MATRICES FROM WEAKL...Nexgen Technology
Nexgen Technology Address:
Nexgen Technology
No :66,4th cross,Venkata nagar,
Near SBI ATM,
Puducherry.
Email Id: praveen@nexgenproject.com.
www.nexgenproject.com
Mobile: 9751442511,9791938249
Telephone: 0413-2211159.
NEXGEN TECHNOLOGY as an efficient Software Training Center located at Pondicherry with IT Training on IEEE Projects in Android,IEEE IT B.Tech Student Projects, Android Projects Training with Placements Pondicherry, IEEE projects in pondicherry, final IEEE Projects in Pondicherry , MCA, BTech, BCA Projects in Pondicherry, Bulk IEEE PROJECTS IN Pondicherry.So far we have reached almost all engineering colleges located in Pondicherry and around 90km
The document presents a study on using the NURBS-based isogeometric finite element method for free vibration and buckling analysis of laminated composite plates. Key points:
- An isogeometric finite element method is developed using NURBS basis functions for the approximation of deflection fields and geometry parameterization.
- The Lagrange multiplier method is used to enforce essential boundary conditions and an orthogonal transformation technique is applied to the discrete eigenvalue equation.
- Numerical examples are presented to demonstrate the accuracy of the proposed method for laminated composite plates with different boundary conditions, fiber orientations, and modes of vibration/buckling. Results are verified against analytical and other numerical solutions.
Singh gordon-unified-factorization-ecmlHuỳnh Thông
This document presents a unified view of matrix factorization methods that frames the differences among popular methods like NMF, SVD, and probabilistic models in terms of a small number of modeling choices. Many approaches can be viewed as minimizing a generalized Bregman divergence. The authors show that an alternating projection algorithm can be applied to most models in this framework, and the Hessian for each projection has a special structure enabling efficient Newton updates. This allows incorporating constraints like non-negativity or clustering while factorizing matrices.
Automatic face naming by learning discriminative affinity matrices from weakl...Shakas Technologies
Given a collection of images, where each image contains several faces and is associated with a few names in the corresponding caption, the goal of face naming is to infer the correct name for each face
This document summarizes research on predicting the shear strength of reinforced concrete beams without web reinforcement. It begins by introducing the topic and noting that shear strength decreases as beam depth increases. It then reviews existing literature on shear strength mechanisms and factors that influence strength. The document discusses the challenges of theoretical models given complexities and uncertainties. It proposes using genetic programming and fuzzy set theory to develop empirical models from an existing database of over 2000 test results. The models would express shear strength as a function of concrete strength, reinforcement ratio, depth and other variables.
2009_AdvMater_Nanopatterning via pressure-induced instabilities in thin polym...Ximin He
This document describes a new lithographic technique for creating nanometer-scale periodic patterns in thin polymer films using pressure-induced rupturing. The technique involves spincoating a thin polymer film on a substrate, placing a stamp with nanoscale features on the film, and applying pressure below the glass transition temperature of the polymer. This triggers localized rupturing of the film at the stamp contact points due to residual stresses from spincoating. Line patterns and hole arrays are formed in polystyrene films with feature sizes tunable by controlling imprint temperature and film thickness. The patterns are completely dewetted and residue-free. This pressure-induced rupturing technique provides a new method for nanopatterning thin polymer films without the need for
The document describes an extension to the brittle cracking concrete material model in ABAQUS. The extension adds nonlinear compressive behavior using a user subroutine. The extended model is validated by comparing it to the original brittle cracking model and damaged plasticity model under uniaxial loading. The extended model is also shown to capture strain rate effects observed in experiments. Finally, the extended model is used to simulate benchmark cases including a notched concrete beam, demonstrating its ability to model tensile failure of concrete structures.
This document discusses modeling the skewness and kurtosis of box office revenue data using the Box-Cox power exponential (BCPE) distribution within the generalized additive models for location, scale and shape (GAMLSS) framework. It finds that the BCPE distribution provides a better fit than the traditionally used Pareto–Levy–Mandelbrot distribution. The flexible four-parameter BCPE distribution allows modeling the location, scale, skewness, and kurtosis parameters of box office revenues as smooth functions of explanatory variables like opening revenues and number of screens. This overcomes limitations of previous models and provides a better understanding of box office revenues across different time periods.
Quadrangular Bézier Patches in Modeling and Modification of the Curvilinear B...IDES Editor
This paper proposes the use of quadrangular Bézier
patches to model and modify the shape of the boundary for
linear elasticity problems in 3D. The representation of the
boundary in this way derives directly from computer graphics
and have been analytically included in developed by the
authors parametric integral equation systems (PIES). PIES
are the modified classical boundary integral equations (BIE)
in which the shape of the boundary can be modeled using a
wide range of parametric curves and surfaces. The proposed
approach eliminates the need for domain and boundary
discretization in the process of solving boundary value
problems, in contrast to popular traditional methods like FEM
and BEM. On the basis of the proposed approach, a computer
code has been written and examined through numerical
examples.
Project DG method for modelling ductile fractureAhmed Mostafa
The document discusses several applications of the discontinuous Galerkin (DG) finite element method for modeling ductile fracture problems. These include: 1) using an implicit DG algorithm to accurately simulate crack propagation in the Sandia fracture challenge problem; 2) modeling multiple crack opening in ductile materials using a failure potential index to predict crack paths; 3) simulating failure mechanisms in fiber-reinforced composites under transverse loading using pressure-dependent plasticity models; and 4) micromechanical analysis of randomly distributed fiber composites using representative volume elements and pressure-dependent matrix plasticity models.
Influence of channel fading correlation on performance of detector algorithms...csandit
This paper analyzes the impact of fading correlation and cross polarization coupling on the
error performance of V-BLAST MIMO system that employs detector algorithms like ZF, MMSE
and ML with ordering and successive cancellation. Simulation results show the BER
performance of these detectors for different modulation schemes. It is observed that lesser the
channel fading correlation and cross polarization coupling values better is the performance of
these detectors. Study is extended to see the effect of transmit and receive antenna correlation
on Ergodic MIMO capacity.
DESIGN AND ANALYSIS OF BRIDGE WITH TWO ENDS FIXED ON VERTICAL WALL USING FIN...IAEME Publication
The Finite element analyses are conducted to model the tensile capacity of steel fiber-reinforced concrete (SFRC). For this purpose bridge with two ends fixed one specimen are casted and tested under direct and uni-axial tension. Two types of aggregates (brick and stone) are used to cast the SFRC and plain concrete. The fiber volume ratio is maintained 1.5 %. Total 8 numbers of dog-bone specimens are made and tested in a 1000-kN capacity digital universal testing machine (UTM). The strain data are gathered employing digital image correlation technique from high-definition images and high-speed video clips. Then, the strain data are synthesized with the load data obtained from the load cell of the UTM.
Frictional Contact and Wear Along Virtual Interfaces: Coupling the Mortar Met...BasavaRaju Akula
In this work, features of surface-to-surface contact discretization
are combined with the extended finite element method to handle contact problems along virtual surfaces in 2D. We focus on the incorporating of geometrical changes, which result from wear process and are taken into account by mobile virtual interfaces.
This document describes a finite element method for modeling complex 3D crack propagation in quasi-brittle materials under static and dynamic loading conditions. The method embeds cohesive elements, which model potential cracks, between solid elements in regions of interest in the initial mesh. Neither remeshing nor predefined crack paths are required. The method was implemented in Abaqus and used to model crack propagation in four concrete structure examples, showing good agreement with experiments or other simulations. The method offers engineers an efficient tool for modeling 3D fracture problems using Abaqus' preprocessing, solving, and postprocessing capabilities.
This document describes a finite element method for modeling complex 3D crack propagation in quasi-brittle materials like concrete. The method embeds cohesive elements between solid elements in initial finite element meshes to model potential cracks. Neither remeshing nor predefined crack paths are required. The method was implemented in ABAQUS and used to model crack propagation in four concrete structure examples, showing good agreement with tests or other simulations. The method offers engineers an efficient tool for 3D fracture modeling using a commercial finite element package.
This document summarizes the use of numerical modeling techniques for strata control in coal mines. It discusses various numerical modeling approaches including continuum methods like finite difference and finite element methods, and discontinuum methods like discrete element modeling. It provides examples of applying these techniques to model longwall mining. Specifically, it presents a case study using finite element analysis to model shield-strata interaction in a longwall panel of a project in India.
Interfacial delamination failure in bonded concrete overlay systems a review...IAEME Publication
This document reviews theories and modeling methods for describing delamination failure at the interface between two bonded cementitious materials. It discusses traditional stress-based and energy-based failure criteria approaches. It presents the interface cohesive zone model (ICZM) as a viable approach for describing and predicting delamination in bonded concrete overlay systems. The ICZM treats delamination as a progressive failure involving both crack initiation and propagation. It considers distinct analytical cases involving material and structural property variables. The concluding model shows that numerical values of delamination coefficients and energy release rates vary depending on overlay scale, problem type, and material property mismatches.
INTERFACIAL DELAMINATION FAILURE IN BONDED CONCRETE OVERLAY SYSTEMS - A REVIE...IAEME Publication
This study reviews the theories and modelling methods for describing interfacial delamination failure process between two bonded cementitious materials. Complex interfacial stress
conditions at discontinuities and areas of high stress concentrations were primary areas of concern. Distinct analytical cases involving intrinsic material and structural property variables were considered. An approach based on plane strain analysis within the context of Interface Cohesive
Zone Model (ICZM) was cited and presented as viable for describing and predicting delamination mode of failure in bonded concrete overlays systems (BCOs).
A fully integrated discrete fracture model (DFM) is presented for coupled geomechanics and single-phase fluid flow in fractured porous media. The model discretizes the poroelasticity equations using finite elements on an unstructured grid, with special treatment for fractures. The flow equations are discretized using finite volumes. A sequential implicit solution strategy is employed to solve the coupled nonlinear equations. Changes in porosity and fracture permeability due to mechanical deformation are accounted for. The model aims to explicitly represent fracture geometry and its impact on stress/strain fields, unlike dual-continuum approaches. It is implemented within a general-purpose research simulator.
A coupled SPH-DEM model for fluid-structure interaction problems with free-su...Ke Wu
1. The document presents a coupled Smoothed Particle Hydrodynamics (SPH)-Discrete Element Method (DEM) model for simulating fluid-structure interaction problems involving free-surface fluid flow and structural failure.
2. SPH is used to model the fluid domain based on the Navier-Stokes equations, while DEM with a parallel bond model is used to represent the solid structure as a hexagonal packing of bonded particles.
3. Validation tests show good agreement with analytical and published results for DEM fracture modeling, SPH fluid modeling, and coupled SPH-DEM modeling without fracture. Simulation results indicate the model can capture the full fluid-structure interaction process from structural deformation to failure and post-failure movement.
This document describes an implementation of extended finite element method (X-FEM) in Abaqus for 3D fatigue crack growth and life prediction analysis. A level set representation is used to model evolving crack geometry without remeshing. Stress intensity factors are extracted on static and growing cracks to predict fatigue life using fracture mechanics criteria. Several examples are presented to validate the technique.
An Adaptive Moving Mesh Method For Two-Dimensional Relativistic Magnetohydrod...Scott Faria
This document describes an adaptive moving mesh method for solving two-dimensional thin film flow equations that include surface tension. The method uses moving mesh partial differential equations (MMPDEs) and mesh density functions to adaptively move the computational mesh based on solution characteristics like curvature. Numerical results show this r-adaptive moving mesh technique accurately captures the moving contact line and associated fingering instability with reduced computational effort compared to a fixed uniform mesh.
This Ph.D. dissertation develops advanced numerical methods for contact mechanics using the finite element method. It presents a three-dimensional mortar formulation for frictional contact problems and discusses contact detection, discretization, and parallelization. A new MorteX framework combines extended finite elements and mortar methods to handle mesh tying and contact along embedded boundaries, addressing mesh locking issues. The MorteX framework is applied to model frictional wear problems with evolving contact surfaces. Various numerical examples are used to validate the implementation and demonstrate the performance of the proposed methods.
RESULTS OF FINITE ELEMENT ANALYSIS FOR INTERLAMINAR FRACTURE REINFORCED THERM...msejjournal
The double cantilever beam (DCB) is widely used for fracture toughness testing and it has become popular
for opening-mode (mode I) delamination testing of laminated composites. Delamination is a crack that
forms between the adjacent plies of a composite laminate at the brittle polymer resin. This study was
conducted to emphasize the need for a better understanding of the DCB specimen of different fabric
reinforced systems (carbon fibers) with a thermoplastic matrix (EP, PEI), by using the extended finite
element method (X-FEM). It is well known that in fabric reinforced composites fracture mechanisms
include microcracking in front of the crack tip, fiber bridging and multiple cracking, and both contribute
considerably to the high interlaminar fracture toughness measured. That means, the interlaminar fracture
toughness of a composite is not controlled by a single material parameter, but is a result of a complex
interaction of resin, fiber and interface properties.
RESULTS OF FINITE ELEMENT ANALYSIS FOR INTERLAMINAR FRACTURE REINFORCED THERM...MSEJjournal1
The double cantilever beam (DCB) is widely used for fracture toughness testing and it has become popular
for opening-mode (mode I) delamination testing of laminated composites. Delamination is a crack that
forms between the adjacent plies of a composite laminate at the brittle polymer resin. This study was
conducted to emphasize the need for a better understanding of the DCB specimen of different fabric
reinforced systems (carbon fibers) with a thermoplastic matrix (EP, PEI), by using the extended finite
element method (X-FEM). It is well known that in fabric reinforced composites fracture mechanisms
include microcracking in front of the crack tip, fiber bridging and multiple cracking, and both contribute
considerably to the high interlaminar fracture toughness measured. That means, the interlaminar fracture
toughness of a composite is not controlled by a single material parameter, but is a result of a complex
interaction of resin, fiber and interface properties.
RESULTS OF FINITE ELEMENT ANALYSIS FOR INTERLAMINAR FRACTURE REINFORCED THERM...msejjournal
The double cantilever beam (DCB) is widely used for fracture toughness testing and it has become popular
for opening-mode (mode I) delamination testing of laminated composites. Delamination is a crack that
forms between the adjacent plies of a composite laminate at the brittle polymer resin. This study was
conducted to emphasize the need for a better understanding of the DCB specimen of different fabric
reinforced systems (carbon fibers) with a thermoplastic matrix (EP, PEI), by using the extended finite
element method (X-FEM). It is well known that in fabric reinforced composites fracture mechanisms
include microcracking in front of the crack tip, fiber bridging and multiple cracking, and both contribute
considerably to the high interlaminar fracture toughness measured. That means, the interlaminar fracture
toughness of a composite is not controlled by a single material parameter, but is a result of a complex
interaction of resin, fiber and interface properties.
2009_AdvMater_Nanopatterning via pressure-induced instabilities in thin polym...Ximin He
This document describes a new lithographic technique for creating nanometer-scale periodic patterns in thin polymer films using pressure-induced rupturing. The technique involves spincoating a thin polymer film on a substrate, placing a stamp with nanoscale features on the film, and applying pressure below the glass transition temperature of the polymer. This triggers localized rupturing of the film at the stamp contact points due to residual stresses from spincoating. Line patterns and hole arrays are formed in polystyrene films with feature sizes tunable by controlling imprint temperature and film thickness. The patterns are completely dewetted and residue-free. This pressure-induced rupturing technique provides a new method for nanopatterning thin polymer films without the need for
The document describes an extension to the brittle cracking concrete material model in ABAQUS. The extension adds nonlinear compressive behavior using a user subroutine. The extended model is validated by comparing it to the original brittle cracking model and damaged plasticity model under uniaxial loading. The extended model is also shown to capture strain rate effects observed in experiments. Finally, the extended model is used to simulate benchmark cases including a notched concrete beam, demonstrating its ability to model tensile failure of concrete structures.
This document discusses modeling the skewness and kurtosis of box office revenue data using the Box-Cox power exponential (BCPE) distribution within the generalized additive models for location, scale and shape (GAMLSS) framework. It finds that the BCPE distribution provides a better fit than the traditionally used Pareto–Levy–Mandelbrot distribution. The flexible four-parameter BCPE distribution allows modeling the location, scale, skewness, and kurtosis parameters of box office revenues as smooth functions of explanatory variables like opening revenues and number of screens. This overcomes limitations of previous models and provides a better understanding of box office revenues across different time periods.
Quadrangular Bézier Patches in Modeling and Modification of the Curvilinear B...IDES Editor
This paper proposes the use of quadrangular Bézier
patches to model and modify the shape of the boundary for
linear elasticity problems in 3D. The representation of the
boundary in this way derives directly from computer graphics
and have been analytically included in developed by the
authors parametric integral equation systems (PIES). PIES
are the modified classical boundary integral equations (BIE)
in which the shape of the boundary can be modeled using a
wide range of parametric curves and surfaces. The proposed
approach eliminates the need for domain and boundary
discretization in the process of solving boundary value
problems, in contrast to popular traditional methods like FEM
and BEM. On the basis of the proposed approach, a computer
code has been written and examined through numerical
examples.
Project DG method for modelling ductile fractureAhmed Mostafa
The document discusses several applications of the discontinuous Galerkin (DG) finite element method for modeling ductile fracture problems. These include: 1) using an implicit DG algorithm to accurately simulate crack propagation in the Sandia fracture challenge problem; 2) modeling multiple crack opening in ductile materials using a failure potential index to predict crack paths; 3) simulating failure mechanisms in fiber-reinforced composites under transverse loading using pressure-dependent plasticity models; and 4) micromechanical analysis of randomly distributed fiber composites using representative volume elements and pressure-dependent matrix plasticity models.
Influence of channel fading correlation on performance of detector algorithms...csandit
This paper analyzes the impact of fading correlation and cross polarization coupling on the
error performance of V-BLAST MIMO system that employs detector algorithms like ZF, MMSE
and ML with ordering and successive cancellation. Simulation results show the BER
performance of these detectors for different modulation schemes. It is observed that lesser the
channel fading correlation and cross polarization coupling values better is the performance of
these detectors. Study is extended to see the effect of transmit and receive antenna correlation
on Ergodic MIMO capacity.
DESIGN AND ANALYSIS OF BRIDGE WITH TWO ENDS FIXED ON VERTICAL WALL USING FIN...IAEME Publication
The Finite element analyses are conducted to model the tensile capacity of steel fiber-reinforced concrete (SFRC). For this purpose bridge with two ends fixed one specimen are casted and tested under direct and uni-axial tension. Two types of aggregates (brick and stone) are used to cast the SFRC and plain concrete. The fiber volume ratio is maintained 1.5 %. Total 8 numbers of dog-bone specimens are made and tested in a 1000-kN capacity digital universal testing machine (UTM). The strain data are gathered employing digital image correlation technique from high-definition images and high-speed video clips. Then, the strain data are synthesized with the load data obtained from the load cell of the UTM.
Frictional Contact and Wear Along Virtual Interfaces: Coupling the Mortar Met...BasavaRaju Akula
In this work, features of surface-to-surface contact discretization
are combined with the extended finite element method to handle contact problems along virtual surfaces in 2D. We focus on the incorporating of geometrical changes, which result from wear process and are taken into account by mobile virtual interfaces.
This document describes a finite element method for modeling complex 3D crack propagation in quasi-brittle materials under static and dynamic loading conditions. The method embeds cohesive elements, which model potential cracks, between solid elements in regions of interest in the initial mesh. Neither remeshing nor predefined crack paths are required. The method was implemented in Abaqus and used to model crack propagation in four concrete structure examples, showing good agreement with experiments or other simulations. The method offers engineers an efficient tool for modeling 3D fracture problems using Abaqus' preprocessing, solving, and postprocessing capabilities.
This document describes a finite element method for modeling complex 3D crack propagation in quasi-brittle materials like concrete. The method embeds cohesive elements between solid elements in initial finite element meshes to model potential cracks. Neither remeshing nor predefined crack paths are required. The method was implemented in ABAQUS and used to model crack propagation in four concrete structure examples, showing good agreement with tests or other simulations. The method offers engineers an efficient tool for 3D fracture modeling using a commercial finite element package.
This document summarizes the use of numerical modeling techniques for strata control in coal mines. It discusses various numerical modeling approaches including continuum methods like finite difference and finite element methods, and discontinuum methods like discrete element modeling. It provides examples of applying these techniques to model longwall mining. Specifically, it presents a case study using finite element analysis to model shield-strata interaction in a longwall panel of a project in India.
Interfacial delamination failure in bonded concrete overlay systems a review...IAEME Publication
This document reviews theories and modeling methods for describing delamination failure at the interface between two bonded cementitious materials. It discusses traditional stress-based and energy-based failure criteria approaches. It presents the interface cohesive zone model (ICZM) as a viable approach for describing and predicting delamination in bonded concrete overlay systems. The ICZM treats delamination as a progressive failure involving both crack initiation and propagation. It considers distinct analytical cases involving material and structural property variables. The concluding model shows that numerical values of delamination coefficients and energy release rates vary depending on overlay scale, problem type, and material property mismatches.
INTERFACIAL DELAMINATION FAILURE IN BONDED CONCRETE OVERLAY SYSTEMS - A REVIE...IAEME Publication
This study reviews the theories and modelling methods for describing interfacial delamination failure process between two bonded cementitious materials. Complex interfacial stress
conditions at discontinuities and areas of high stress concentrations were primary areas of concern. Distinct analytical cases involving intrinsic material and structural property variables were considered. An approach based on plane strain analysis within the context of Interface Cohesive
Zone Model (ICZM) was cited and presented as viable for describing and predicting delamination mode of failure in bonded concrete overlays systems (BCOs).
A fully integrated discrete fracture model (DFM) is presented for coupled geomechanics and single-phase fluid flow in fractured porous media. The model discretizes the poroelasticity equations using finite elements on an unstructured grid, with special treatment for fractures. The flow equations are discretized using finite volumes. A sequential implicit solution strategy is employed to solve the coupled nonlinear equations. Changes in porosity and fracture permeability due to mechanical deformation are accounted for. The model aims to explicitly represent fracture geometry and its impact on stress/strain fields, unlike dual-continuum approaches. It is implemented within a general-purpose research simulator.
A coupled SPH-DEM model for fluid-structure interaction problems with free-su...Ke Wu
1. The document presents a coupled Smoothed Particle Hydrodynamics (SPH)-Discrete Element Method (DEM) model for simulating fluid-structure interaction problems involving free-surface fluid flow and structural failure.
2. SPH is used to model the fluid domain based on the Navier-Stokes equations, while DEM with a parallel bond model is used to represent the solid structure as a hexagonal packing of bonded particles.
3. Validation tests show good agreement with analytical and published results for DEM fracture modeling, SPH fluid modeling, and coupled SPH-DEM modeling without fracture. Simulation results indicate the model can capture the full fluid-structure interaction process from structural deformation to failure and post-failure movement.
This document describes an implementation of extended finite element method (X-FEM) in Abaqus for 3D fatigue crack growth and life prediction analysis. A level set representation is used to model evolving crack geometry without remeshing. Stress intensity factors are extracted on static and growing cracks to predict fatigue life using fracture mechanics criteria. Several examples are presented to validate the technique.
An Adaptive Moving Mesh Method For Two-Dimensional Relativistic Magnetohydrod...Scott Faria
This document describes an adaptive moving mesh method for solving two-dimensional thin film flow equations that include surface tension. The method uses moving mesh partial differential equations (MMPDEs) and mesh density functions to adaptively move the computational mesh based on solution characteristics like curvature. Numerical results show this r-adaptive moving mesh technique accurately captures the moving contact line and associated fingering instability with reduced computational effort compared to a fixed uniform mesh.
This Ph.D. dissertation develops advanced numerical methods for contact mechanics using the finite element method. It presents a three-dimensional mortar formulation for frictional contact problems and discusses contact detection, discretization, and parallelization. A new MorteX framework combines extended finite elements and mortar methods to handle mesh tying and contact along embedded boundaries, addressing mesh locking issues. The MorteX framework is applied to model frictional wear problems with evolving contact surfaces. Various numerical examples are used to validate the implementation and demonstrate the performance of the proposed methods.
RESULTS OF FINITE ELEMENT ANALYSIS FOR INTERLAMINAR FRACTURE REINFORCED THERM...msejjournal
The double cantilever beam (DCB) is widely used for fracture toughness testing and it has become popular
for opening-mode (mode I) delamination testing of laminated composites. Delamination is a crack that
forms between the adjacent plies of a composite laminate at the brittle polymer resin. This study was
conducted to emphasize the need for a better understanding of the DCB specimen of different fabric
reinforced systems (carbon fibers) with a thermoplastic matrix (EP, PEI), by using the extended finite
element method (X-FEM). It is well known that in fabric reinforced composites fracture mechanisms
include microcracking in front of the crack tip, fiber bridging and multiple cracking, and both contribute
considerably to the high interlaminar fracture toughness measured. That means, the interlaminar fracture
toughness of a composite is not controlled by a single material parameter, but is a result of a complex
interaction of resin, fiber and interface properties.
RESULTS OF FINITE ELEMENT ANALYSIS FOR INTERLAMINAR FRACTURE REINFORCED THERM...MSEJjournal1
The double cantilever beam (DCB) is widely used for fracture toughness testing and it has become popular
for opening-mode (mode I) delamination testing of laminated composites. Delamination is a crack that
forms between the adjacent plies of a composite laminate at the brittle polymer resin. This study was
conducted to emphasize the need for a better understanding of the DCB specimen of different fabric
reinforced systems (carbon fibers) with a thermoplastic matrix (EP, PEI), by using the extended finite
element method (X-FEM). It is well known that in fabric reinforced composites fracture mechanisms
include microcracking in front of the crack tip, fiber bridging and multiple cracking, and both contribute
considerably to the high interlaminar fracture toughness measured. That means, the interlaminar fracture
toughness of a composite is not controlled by a single material parameter, but is a result of a complex
interaction of resin, fiber and interface properties.
RESULTS OF FINITE ELEMENT ANALYSIS FOR INTERLAMINAR FRACTURE REINFORCED THERM...msejjournal
The double cantilever beam (DCB) is widely used for fracture toughness testing and it has become popular
for opening-mode (mode I) delamination testing of laminated composites. Delamination is a crack that
forms between the adjacent plies of a composite laminate at the brittle polymer resin. This study was
conducted to emphasize the need for a better understanding of the DCB specimen of different fabric
reinforced systems (carbon fibers) with a thermoplastic matrix (EP, PEI), by using the extended finite
element method (X-FEM). It is well known that in fabric reinforced composites fracture mechanisms
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toughness of a composite is not controlled by a single material parameter, but is a result of a complex
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forms between the adjacent plies of a composite laminate at the brittle polymer resin. This study was
conducted to emphasize the need for a better understanding of the DCB specimen of different fabric
reinforced systems (carbon fibers) with a thermoplastic matrix (EP, PEI), by using the extended finite
element method (X-FEM). It is well known that in fabric reinforced composites fracture mechanisms
include microcracking in front of the crack tip, fiber bridging and multiple cracking, and both contribute
considerably to the high interlaminar fracture toughness measured. That means, the interlaminar fracture
toughness of a composite is not controlled by a single material parameter, but is a result of a complex
interaction of resin, fiber and interface properties.
RESULTS OF FINITE ELEMENT ANALYSIS FOR INTERLAMINAR FRACTURE REINFORCED THERM...msejjournal
The double cantilever beam (DCB) is widely used for fracture toughness testing and it has become popular
for opening-mode (mode I) delamination testing of laminated composites. Delamination is a crack that
forms between the adjacent plies of a composite laminate at the brittle polymer resin. This study was
conducted to emphasize the need for a better understanding of the DCB specimen of different fabric
reinforced systems (carbon fibers) with a thermoplastic matrix (EP, PEI), by using the extended finite
element method (X-FEM). It is well known that in fabric reinforced composites fracture mechanisms
include microcracking in front of the crack tip, fiber bridging and multiple cracking, and both contribute
considerably to the high interlaminar fracture toughness measured. That means, the interlaminar fracture
toughness of a composite is not controlled by a single material parameter, but is a result of a complex
interaction of resin, fiber and interface properties.
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Domain tying across virtual interfaces: coupling X-FEM with the Mortar method
1. CSMA 2017
13ème Colloque National en Calcul des Structures
15-19 Mai 2017, Presqu’île de Giens (Var)
Domain tying across virtual interfaces:
coupling X-FEM with the Mortar method
B.R. Akula1,2, V.A. Yastrebov1, J. Vignollet2, G. Cailletaud1
1 MINES ParisTech, PSL Research University, Centre des matériaux, CNRS UMR 7633, BP87, 91003 Evry Cedex, France,
{basava-raju.akula, vladislav.yastrebov, georges.cailletaud}@mines-paristech.fr
2 Safran Tech, Safran Group, 78772 Magny-les-Hameaux, France {basava-raju.akula, julien.vignollet}@safrangroup.com
Résumé — In this paper we propose a unified framework of the mortar domain decomposition method
and extended finite element method (X-FEM). This framework allows to deal in an efficient manner with
two cumbersome aspects of the finite element methods, namely incompatible interface discretizations
and internal discontinuities. Features of mortar methods in the context of mesh tying, and of X-FEM in
the context of void/inclusion treatment are exploited to formulate the weak coupling along an inclusion’s
surface and the virtual surface of the host mesh. It has a potential to address a multitude of problems
from accurate substructuring to efficient wear simulation in contact problems.
Mots clés — mortar method, extended finite element method, coupling.
1 Introduction
The finite element methods (FEM) is one of the widely used methods to solve mechanical enginee-
ring problems. The FEM is extremely flexible and can handle complex geometries, highly non-linear
material models, large deformations and multi-physical problems. With the emergence of high perfor-
mance computing its applicability to larger and more complex problems was only made easier. Among
the wide spectrum of engineering applications, the class of problems dealing with interface mechanisms
(composites, fracture, contact) is complex both with regard to its mathematical description and the diffi-
culties arising in numerical treatment. Understanding and accurate modeling of these phenomena would
contribute significantly to the progress across all fields of mechanical engineering scaling from mate-
rial microstructure modeling to complex structural problems involving frictional contacts. However, the
classical FEM is constrained in handling many problems encountered in interface mechanics. These
limitations stem from its inability to independently represent the interface geometry from the under-
lying discretization. One such constraint imposed by conventional FEM methods is the requirement of
conformal meshes along the interfaces. This lays significant restrictions on the possible complexities of
geometries that can be handled.
The family of mortar methods has a potential to address these limitations. These are a subclass of do-
main decomposition methods (DDM), that are tailored for large class of non-conformal spatial interface
discretizations [1, 2]. These were originally introduced as DDM for spectral elements [3, 4]. The cou-
pling of different physical models, discretization schemes, or non-matching meshes/discretizations along
interior interfaces of the domain can be ensured by mortar methods. The mathematical optimality and
applicability of the mortar methods in spectral and finite element frameworks were studied extensively
for elliptic problems [4, 3, 5].
The other notable class of problems are those involving discontinuities. The fundamental requirement
of the classical FEM is that the mesh has to conform to the geometry and with this it is possible to handle
complex geometries comfortably. Since FEM strongly depends on the smoothness of the approximation
polynomials, non-smooth behavior like high gradients or singularities in the stress and strain fields, or
strong discontinuities in the displacement field as encountered with cracked bodies, pose a computational
challenge to attain optimal convergence. However, having conformal geometries across different domains
or contacting solids is not always possible or might demand computationally intensive re-meshing and
field transfer procedures.
An attractive alternative is the partition of unity based enrichment method (PUM) [6] for disconti-
1
2. nuous fields referred to as the extended FEM (X-FEM) in [7]. In X-FEM, special enrichment functions
are added to the finite element approximation using the framework of PUM, to account for non-smooth
behavior such as high gradients or singularities in the stress and strain fields, or strong discontinuities
in the displacement field as in the case of cracked bodies without compromising on the optimal conver-
gence [8].
In an attempt to combine these two requirements of incompatibilities and discontinuities, we propose
a unified solution to these problems. As illustrated in Figure 1, we propose to tie the virtual X-FEM
boundary Γv (discontinuity) introduced on the coarse mesh domain, with the outer boundary Γg of the
finely meshed inclusion which will be embedded into the X-FEM void of the coarse mesh. The enriched
displacement field of the coarse mesh along Γv is constrained to be equal to the displacement of the
boundary (Γg) of the fine mesh via the mortar method. The planned approach for this unified method
includes :
— using the level set method (LSM) [9] to describe the contour of the discontinuity,
— using X-FEM Heaviside enrichment (topological) for the nodes of the elements intersected by
the discontinuity, [10]
— using the mortar method [11] to tie both the discretized models along the boundary of the finer-
mesh patch and the virtual boundary of this patch, which is represented in the parent (coarse)
mesh by a level set.
FIGURE 1 – A finely meshed inclusion with border Γg is embedded in a coarse mesh and is tied with
the corresponding virtual surface Γv using the mortar method : (a) coarse host mesh, (b) fine patch to be
embedded, (c) the resulting combined mesh.
The X-FEM methods are extensively used in applications such as crack modeling, inclusion and void
effects, shock wave front and oxidation front propagation, and other discontinuities (both strong and
weak). Coming to the mortar methods they have been the topic of research in a multitude of applications
like the non-overlapping domain decomposition methods (DDM), contact, wear etc. There are few works
on similar lines where the advantages of these two methods are harnessed in a single application. To name
a few we refer to the following works, an exhaustive pointers on the topic can be found in references
therein. In [12], the authors try to use the node based bonding between domains with crack. In [13, 14],
the authors used the mortar type integration methods to glue a fine mesh surrounding the crack and the
coarser mesh domain, where the crack is represented in the X-FEM formulation. But their coupling is
limited to existing explicit interfaces, i.e. the inclusion does not cut the elements of the coarse domain
but is aligned to the element edges. A dual mortar contact formulation integrated into X-FEM fluid-
structure interaction approach is presented in [15]. In [16], the authors have emphasized on a way to
impose boundary conditions on the internal boundaries represented by virtual X-FEM interfaces. The
proposed method of coupling mortar and X-FEM competes with the volumetric coupling via the Arlequin
method [17] close to the overlapping DDM [18], where unlike the conventional non-overlapping DDM
the artificial internal boundary condition is provided by its neighboring subdomains. The convergence of
the solution on these internal boundaries ensures the convergence of the solution in the entire solution
domain.
With the emphasis laid on the interface discretizations, many applications such as substructuring,
2
3. arbitrary gluing, mesh construction of complex micro structures, localized mesh refinement near the
crack tip, general static and dynamic mesh refinement, and potentially others can be of particular interest
with this unified method of the X-FEM and the mortar. However, the applications are not limited only
to mesh tying. In analogy to how the mortar method, initially used for tying was extended to contact
problems by Belgacem et al. [19], Fischer and Wriggers [20, 21], and Popp et al. [22] the method
suggested here can be used to solve contact problems between a virtual surface (represented by the X-
FEM) and an explicit surface of the homologue solid [23]. This extension would allow to treat efficiently
wear problems without costly remeshing techniques.
The document is structured as follows : In Section 2, we present the core philosophy of the mortar me-
thod with respect to the tying problem and the X-FEM with respect to the modeling of voids (closed
discontinuity). The equations necessary for FEM framework are given for the unified method in Sec-
tion 2.3. In Section 3 we show few initial results from the mortar mesh tying problem. In Section 4, we
give the concluding remarks on our objective and state the prospective works.
2 Methodology
2.1 Mortar mesh tying
Let us consider a classical boundary value problem for a domain Ω. We assume that the domain is
split into n subdomains Ω = ∪Ωi which are glued across their interfaces Γij. The resulting optimization
problem should then include displacement-equality constraints imposed on glued boundaries, e.g. they
take form g(u) = uij − uji = 0, where uij and uji are the displacements of initially coinciding points
of subdomains Ωi and Ωj, respectively. These constraints can be incorporated into the system energy
functional (W(u)) using the Lagrange multiplier method forming a Lagrangian :
L(u,λ) = W(u)+
∀ij Γij
λ·g(u) dΓij, (1)
where λ are the Lagrange multiplier functions representing interface tractions needed to ensure domain
tying. Applying the principle of virtual work, equilibrium is ensured when the total virtual work on the
solution path is zero : δWext(u,δu)−δL(u,δu,λ,δλ) = 0, where δWext corresponds to the virtual work
of external forces, and δu, δλ are test functions chosen from respective functional spaces for primal and
dual quantities.
This weak form can be directly used in the discretized finite element framework formulated for an
extended vector of unknowns including primal (displacements) and dual (Lagrange multipliers) degrees
of freedom : isoparametric elements are used with similar interpolation functions for geometry and dis-
placement on both tied subdomains, whose surfaces will be termed mortar and non-mortar ones (”m“
and ”nm“ indices are used for them, respectively) :
um
(t,ξ,η)|Γm
ij
=
nm
∑
k=1
Nm
k (ξ,η)um
k (t), unm
(t,ζ,µ)|Γnm
ij
=
nnm
∑
l=1
Nnm
l (ζ,µ)unm
l (t), (2)
where nm is the total number of nodes on the discretized mortar side Γm
ij of the interface, and nnm is on the
discretized non-mortar side Γnm
ij . The classical isoparametric shape functions Nm
k and Nnm
l (which are not
necessary similar or of the same order) defined on the parametric space {ξ, η} and {ζ,µ} are used. The
Lagrange multipliers (defined on the mortar surface) are also interpolated using classical shape functions
Φ :
λ(ξ,η,t) =
nlm
∑
i=1
Φm
i (ξm
,ηm
)λi(t). (3)
Here nlm refers to the number of nodes of the mortar side of the interface that carry additional dual dofs.
The virtual work of the equality constrains embedded in the Lagrangian (1) takes the following form :
δWg =
Γm
ij
λ·δg(u)dΓij +
Γm
ij
δλ·g(u)dΓij (4)
3
4. Using Eq. 2, Eq. 3 in Eq. 4 results in the discretized interface virtual work (Eq. 5)
δWg =
nlm
∑
i=1
nm
∑
k=1
λi ·δum
k
Γm
ij
ΦiNm
k dA0
Dik
−
nlm
∑
j=1
nnm
∑
l=1
λj ·δunm
l
Γm
ij
ΦjNnm
l dA0
Mil
+
nlm
∑
i=1
nm
∑
k=1
δλi ·um
k Dik −
nlm
∑
j=1
nnm
∑
l=1
δλj ·unm
l Mjl
(5)
Evaluation of the interface mortar integrals [D] and [M] involves first the determination of the integration
domain by projecting the glued surface elements on an auxiliary plane and their clipping, and second, tri-
angulation of the resulting polygon for Gauss integration (details can be found in [11, 22]). The coupling
achieved with mortar method is through weak satisfaction of the equality constraints, which is much
more accurate than the conventional strong node-wise coupling like in the node-to-segment method [24].
2.2 X-FEM for void modeling
The model presented in Figure. 1(a) involves a strong discontinuity (Γv) encompassing a square
void. Across this virtual interface, the displacement field has a jump. To take this jump into account, the
nodes of blending elements (elements intersected by the discontinuity) are enriched by multiplying the
classical shape function of the node by a Heaviside function. The effective support size of these elements
for integration is reduced to its volume fraction [25]. For the elements which lie entirely within the void,
their dofs are removed from the global system. Here we use a Heaviside function defined for a level set
function φ as
H(X) =
1, φ(X) > 0
0, φ(X) < 0
. (6)
Within every blending element, the interface Γv, defined by the zero level-set function φ(ξ,η) = 0, can be
redefined as : ξ = ξv(η). The shape function of the enriched element then become Ni(X) = H(X)Ni(X).
These enriched blending elements bring in the change in the volume on which the total system potential
is integrated. The blending elements are remeshed to integrate the virtual energy integrals only in the
effective support zones (see Figure. 2). The displacement on the surface Γv within every blending element
is given by classical interpolation function :
˜u(ξ,η,t)|Γv
= ∑
i
Ni(ξv(η),η)ui(t).
FIGURE 2 – Triangulation of the blending element area which lies out the void defined by the level set
function φ. The boundary Γv intersects the element edges (black points). The dofs of nodes marked x are
removed from the global system.
4
5. 2.3 Mortar coupling along level set
The mortar and the X-FEM methods can be combined to ensure weak mortar-type coupling along
virtual interface Γv and the inclusion surface Γg. The enriched blending elements, the standard elements
of the coarsely discretized domain Ωo the elements from discretized inclusion domain Ωi along with
the new mortar-interface elements are to be incorporated into the virtual work formulation of the global
system [see Figure. 1(c)] :
ΩoΩi
˜σ : δ˜εdΩo
δWint
o
+
Ωi
σ : δεdΩi
δWint
i
+
Γg
δ[λ·g( ˜u,u)] dΓ
δWtie
oi
=
Γ
f
o
t0 ·δ˜udΓ+
Γ
f
i
ti ·δudΓ
δWext
, (7)
where the tilde notation is used for the coarser host mesh quantities. Note that the volume forces are
omitted for simplicity. The displacement test functions for both domains are chosen from appropriate
functional spaces and have to satisfy Dirichlet boundary conditions. The contribution δWint
o is evaluated
only outside the inclusion domain by performing additional triangulation [10] as shown in Figure. 2. Of
special interest is the virtual work contribution from the tied interface boundaries Γv and Γg. Typical to the
mortar terminology we classify the virtual boundary Γv as the non-mortar side and the inclusion boundary
Γg as the mortar side, where the mortar integrals are evaluated as in Eq. (5), where the number of non-
mortar nodes nnm are typically the intersection points of the element edges of the blending elements and
Γv. The intersections are not conventional FEM nodes, and so the interpolated values of the element
displacement field ˜u of Ωo is constrained to be integrally equal to the displacement on Γg. The mortar
algorithms of projections, clipping and triangulation are all done with these intersections and the faces
of Γg.
3 Examples
In Figure. 3, the mortar methods are used to tie the two domains along the non-matching curved
interface. The equality constraints are enforced to a high degree precision which is reflected in a smooth
normal stress profiles σyy and σxx across the curved (Figure. 3(a)) and flat interfaces (Figure. 3(b)) res-
pectively.
x
y
z
x
y
Stress, σyy [MPa] (min=5.22787e+06, max=1.68757e+07)
5e+06 7e+06
u
(a)
x
y
-3.7e+05 1.6e+07
u
Stress, σxx [MPa] (min=-374529, max=1.6195e+07)
x
y
z
(b)
FIGURE 3 – Mortar method is used for mesh tying along the non-matching (a) curved and (b) flat inter-
faces.
4 Conclusions and perspectives
The proposed method makes the FEM flexible in its ability to treat efficiently two distinct and fully
non-conformal domains, i.e. incompatibilities both at the interface and within the bulk of elements. It
5
6. encompasses the intricacies of a diverse and well established fields of the non-overlapping domain de-
composition methods and X-FEM, working together to simplify and provide a good alternative solution
compared to the conventional ones (node-wise coupling and/or remeshing). The spectrum of applica-
tions is wide and includes mesh tying and substructuring and a generic framework for frictional contact
including the wear model handled by X-FEM.
The next step is the extension of the implementation to three-dimensional problems. In perspective
the method will be taken forward into the realm of parallel computing, thus enabling to solve large and
complex problems in a flexible and accurate way.
5 Acknowledgement
The authors acknowledge financial support of the ANRT (grant CIFRE no 2015/0799).
Références
[1] Christine Bernardi. A new nonconforming approach to domain decomposition : the mortar element method.
Nonliner Partial Differential Equations and Their Applications, 1994.
[2] Faker Ben Belgacem. The mortar finite element method with Lagrange multipliers. Numerische Mathematik,
84(2) :173–197, 1999.
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