A software tool for automated crack onset and growth simulations based on the eXtended Finite Ele... more A software tool for automated crack onset and growth simulations based on the eXtended Finite Element Method (X-FEM) has been developed. For the first time, this tool is able to simulate arbitrary crack growth and composite delamination without remeshing. The automated tool is integrated with Abaqus/Standard and Abaqus/CAE via the customization interfaces. It seamlessly works with the Commercial, Off-The-Shelf (COTS) Abaqus suite. Its unique features include: 1) CAE-based insertion of 2D or 3D multiple cracks with arbitrary shape of crack front independent of an existing mesh; 2) simulation of crack growth inside or between solid elements, and potentially along a shell/solid interface or along a shell/shell interface; 3) simulation of non self-similar crack growth along an arbitrary path or a user-specified interface; 4) extraction of near tip strain energy release rates via the modified VCCT; and 5) CAE-based data processing and visualization. The levelset method coupled with X-FEM...
The extended finite element method (XFEM), also known as the generalized finite element method (G... more The extended finite element method (XFEM), also known as the generalized finite element method (GFEM), has been a popular area of research since the late 1990s, as evidenced by high volumes of journal publications, organized minisymposiums in leading conferences, and special workshops and conferences dedicated to this field. The key idea of XFEM/GFEM is to locally enrich the standard finite element approximation space with local enrichment functions which are chosen according to the physics of the problem at hand. For fracture problems that involve cracks, dislocations, and other types of strong discontinuities, it provides two main advantages over conventional finite element methods. That is (i) accurate fields in the vicinity of the discontinuities and (ii) mesh independence with respect to the modeling and propagation of discontinuities. Thus this class of methods offers unprecedented flexibility in fracture mechanics, addressing many shortcomings and limitations of the classical...
Computer Methods in Applied Mechanics and Engineering, 2021
Abstract Cracking in quasi-brittle geomaterials is a complex mechanical phenomenon, driven by var... more Abstract Cracking in quasi-brittle geomaterials is a complex mechanical phenomenon, driven by various dissipation mechanisms across multiple length scales. While some recent promising works have employed the phase-field method to model the damage and fracture of geomaterials, several open questions still remain. In particular, capturing frictional sliding along the lips of microcracks , incorporating lower scale physics, and calibrating the length scale parameter, are some examples. The present paper addresses these essential problems. By leveraging homogenization-based damage-friction coupling formulations for microcracked solids, the linkage is built between the macroscopic phase-field damage variable and the microcrack density parameter. The phase-field is thus treated not only as an indicator for the location of cracks but also accounts for the density of microcracks. A unified Helmholtz free energy function is then constructed as a sum of the bulk energy ( including elastic strain energy and plastic free energy) and the crack surface energy. Furthermore, a new set of degradation functions for the plastic free energy are provided, and a calibration procedure for the length scale parameter is proposed by reflecting a more realistic description of fracture process zone. In addition, an accelerated staggered iteration algorithm is developed to solve the strongly coupled problem more efficiently. Four numerical examples concerning a system of macroscopic cracks are investigated to illustrate the predictive capability of the proposed model in simulating tensile fracture, fault slippage and shear bands.
Computer Methods in Applied Mechanics and Engineering, 2021
Abstract A new formulation is proposed for incorporating local ductile failure constraints and bu... more Abstract A new formulation is proposed for incorporating local ductile failure constraints and buckling resistance into elastoplastic structural design in the context of extreme loading. Many strides have been made in recent years regarding continuum topology optimization with elastoplasticity and buckling separately, but these phenomena are typically not considered together. The formulation we propose is computationally efficient and robust, partly due to its reliance on small strain kinematics and a separation of the elastoplastic response from the buckling load factors computed during the optimization procedure. An aggregate objective function is constructed in which the total work in an elastoplastic analysis is maximized and an aggregation function of the load factors from a separate linear elastic buckling analysis is included. Additionally, local ductile failure constraints are handled via a framework without aggregation functions and a new pseudo buckling mode filter is proposed. Each of the obtained topologies are then subject to a verification step in which a large strain ductile failure model is used in order to compare the performance of the optimized designs obtained for three numerical examples. The results demonstrate that structural responses such as peak load carrying capacity and total external work required to reach the peak load may be significantly improved using the suggested framework. Other interesting observations are also discussed.
Computer Methods in Applied Mechanics and Engineering, 2020
Abstract We present a novel phase field method for modeling hydraulic fracture propagation in por... more Abstract We present a novel phase field method for modeling hydraulic fracture propagation in poroelastic media. In this approach, a new phase field evolution equation is derived to account for damage dependent poro-elastic parameters (Biot’s coefficient, Biot’s modulus and porosity). The fluid flow obeys Darcy’s seepage law in the entire domain including the damage zone, where the rock permeability is assumed to be anisotropic, following the maximum principal strain. The fully coupled problem is solved by a staggered scheme in which the mechanical equilibrium and fluid flow equations are linearized and solved using a Newton–Raphson(NR) method. Several numerical results are presented to investigate the effectiveness of the proposed formulation. First, stability and convergence of the method are verified on a set of benchmark problems considering different time steps and mesh sizes. Second, it is shown that if the poroelastic parameters are kept constant and do not change with the phase field parameter, i.e. reducing to standard phase field approaches in the literature, the model will tend to underestimate the fracture length and overestimate the pore pressure. Finally, we study the interaction of a propagating hydraulic fracture in porous media with inclined natural fractures, and simulate the hydraulic fracture propagation with different perforation phase angle.
AbstractA viscoelastic constitutive model for an asphalt–concrete (AC) material that accounts for... more AbstractA viscoelastic constitutive model for an asphalt–concrete (AC) material that accounts for temperature and material degradation effects is proposed. The model is implemented within a finite-...
International Journal for Numerical Methods in Biomedical Engineering, 2019
A proximal humerus fracture is an injury to the shoulder joint that necessitates medical attentio... more A proximal humerus fracture is an injury to the shoulder joint that necessitates medical attention. While it is one of the most common fracture injuries impacting the elder community and those who suffer from traumatic falls or forceful collisions, there are almost no validated computational methods that can accurately model these fractures. This could be due to the complex, inhomogeneous bone microstructure, complex geometries and the limitations of current fracture mechanics methods. In this paper, we develop and implement a novel phase field method to investigate the proximal humerus fracture. To model the fracture in the inhomogeneous domain, we propose a power law relationship between bone mineral density and critical energy release rate. The method is validated by an in vitro experiment, in which a human humerus is constrained on both ends while subjected to compressive loads on its head in the longitudinal direction that lead to fracture at the anatomical neck. CT-scans are employed to acquire the bone geometry and material parameters, from which detailed finite element meshes with inhomogeneous Young modulus distribution in the bone are generated. The numerical method, implemented in a high performance computing environment, is used to quantitatively predict the complex 3D brittle fracture of the bone, and is shown to be in good agreement with experimental observations. Furthermore, our findings show that the damage is initiated in the trabecular bone-head and propagates outward towards the bone cortex. We conclude that the proposed phase field method is a promising approach to model bone fracture.
High strain rate loading of metals typically leads to material instabilities known as shear bands... more High strain rate loading of metals typically leads to material instabilities known as shear bands. These are narrow bands of intense plastic deformation that weaken the load bearing capacity of the material and serve as a precursor to fracture. Shear bands are modeled as a coupled thermo-mechanical set of nonlinear PDEs and a plastic flow rule that depends on strain rate, strain hardening and thermal softening is used to describe their behavior. In addition, thermal conductivity, which counterbalances thermal heating and creates a weak length scale, must also be employed in order to regularize the PDE system and yield mesh insensitive results. In this paper, we employ mixed finite element formulations to discretize the system in space, and investigate the performance of implicit, explicit and semi-explicit time integration schemes. Small deformation kinematics is assumed in the current work. Stability, accuracy and computational efficiency of the integration schemes are studied on two benchmark examples: a plate in tension with a shear band formed in $$45^{\circ }$$45∘ and an impact onto a notched steel plate. Our findings confirm that implicit methods with larger time steps outperform explicit schemes in terms of cpu modeling time and also yield orders of magnitude more accurate results.
Abstract Numerical modeling of cohesive crack growth in quasi-brittle materials is challenging, p... more Abstract Numerical modeling of cohesive crack growth in quasi-brittle materials is challenging, primarily due to the combination of (i) nonlinearity associated with the fracture process zone (FPZ), (ii) arbitrary directions to which a crack may propagate, and (iii) snap-back or snap-through instabilities encountered in the response of the structure. To address these challenges, we propose a novel arc-length method that can follow the equilibrium path of cohesive crack propagation. The proposed approach is based on the extended finite element method (XFEM) with scalar high-order enrichment functions and Irwin’s crack closure integral, which allows for direct control of the applied loads necessary to propagate cohesive cracks. This is achieved by augmenting a constraint equation written in terms of stress intensity factors (SIFs), and expressed explicitly in terms of the enriched degrees of freedom, which is an attractive feature achieved with Irwin’s integral, since SIFs can be written in closed-form. Note that singular enrichments are active in an unstable crack propagation state and automatically vanish in stable crack configurations. Furthermore, to propagate cracks in arbitrary directions, we employ a maximum circumferential stress criterion implemented by (i) direct usage of the SIFs, and by (ii) a new stress-based nonlocal implementation of this principle. Various benchmark problems including pure mode I and mixed-mode fracture are solved to demonstrate the predictive capability of the present framework for cohesive crack modeling.
In the conventional Newmark family for time integration of hyperbolic problems, both explicit and... more In the conventional Newmark family for time integration of hyperbolic problems, both explicit and implicit methods are inherently sequential in the time domain and not well suited for parallel implementations due to unavoidable processor communication at every time step. In this work we propose a Waveform Relaxation Newmark (WRN$$_\beta $$β) algorithm for the solution of linear second-order hyperbolic systems of ODEs in time, which retains the unconditional stability of the implicit Newmark scheme with the advantage of the lower computational cost of explicit time integration schemes. This method is unstructured in the time domain and is well suited for parallel implementation. We consider a Jacobi and Gauss–Seidel type splitting and study their convergence and stability. The performance of the WRN$$_\beta $$β algorithm is compared to a standard implicit Newmark method and the obtained results confirm the effectiveness of the Waveform Relaxation Newmark algorithm as a new class of more efficient time integrators, which is applicable, as shown in the numerical examples, to both the finite element method and meshfree methods (e.g. the reproducing kernel particle method).
In the past decade, a dominant theme in computational fracture mechanics has been to obtain a mor... more In the past decade, a dominant theme in computational fracture mechanics has been to obtain a more fundamental understanding of material deterioration process, rather than relying on phenomenological or empirical approaches to make predictions. This is driven by a growing need to make predictions of the failure behavior of materials across length scales starting from first principles and going up to the continuum scale. In order to predict such material response, the development of rigorous computational models for modeling material deterioration process at various time and length scales has been of importance to the computational mechanics community. Several interesting approaches have thus been proposed to increase our understanding of the inter-related materials deterioration processes at disparate length scales. While experimental fracture mechanics is important for identifying the physical
Computer Methods in Applied Mechanics and Engineering, 2017
Abstract We present a novel damage-poroelastic model for analyzing the failure response of porous... more Abstract We present a novel damage-poroelastic model for analyzing the failure response of porous media in geomechanics applications. In this new approach, a gradient non-local permeability that leads to non-local transport and consequently non local damage, is introduced. Damage evolution is a function of an equivalent strain measure that is computed from non-local permeability using an inverse permeability–strain constitutive relation. A monolithic, mixed finite element method is proposed to solve the coupled system with a displacement–pressure–regularized permeability ( u − p − κ ) element formulation. The system is linearized and solved using Newton’s method and a backward Euler scheme is used to evolve the system in time. A consistent Jacobian matrix and residual vector are derived analytically and a bilinear damage model is used to evolve the damage. Numerical examples considering hydraulic fracture problems in 1-d and 2-d and damage enhanced consolidation are presented and discussed. The proposed non-local model results are compared with local damage–permeability models. While the local models are shown to suffer from mesh dependence and non-physical spurious oscillations in strain, permeability and fluid pressure evolution, the proposed model is reliable and seems to overcome all these limitations.
A local physical stability criterion for multidimensional fracture problems modeled by the phase ... more A local physical stability criterion for multidimensional fracture problems modeled by the phase field method is developed and studied. Stability analysis provides a rigorous mathematical way to determine the onset of an unstable damage growth and fracture of the structure. In this work, stability is determined by examining the roots of a characteristic equation that arise when a linear perturbation technique is applied to the instantaneous partial differential equation system in a general viscoplastic material. It is shown that such analysis is not limited to a particular degradation function or energy split and could therefore be applied to a wide range of cases. Numerical results are presented to verify the theoretical predictions assuming quadratic and cubic degradation functions. Additionally we show that this stability criterion can be directly expanded to 2D with robust mesh-insensitive predictive capabilities with respect to crack nucleation and path. Several numerical examples are presented to verify these results.
Computer Methods in Applied Mechanics and Engineering, 2017
Abstract For materials that display viscoelastic behavior, adequate description of their failure ... more Abstract For materials that display viscoelastic behavior, adequate description of their failure requires accurate prediction of damage initiation, propagation and growth rate in addition to their time-dependent response. While many local damage models are available in the literature, they all lack a length scale needed to regularize the solution and lead to mesh independent results. In this work, we propose a new damage regularization approach based on an equivalent stress measure concept and apply it to a Prony Series type viscoelastic solid with a Murakami type damage-rate law. Viscoelastic behavior is achieved by a semi-analytical integration of the constitutive law and damage regularization is obtained by solving an additional second-order gradient equation of an equivalent stress. The scheme leads to a coupled set of nonlinear equations which are solved simultaneously using a monolithic Newton framework to obtain displacement and damage fields as a function of time. The formulation is shown to be thermodynamically consistent and the energy dissipation of the model is studied. Mesh-insensitive behavior under creep, relaxation and strain rate conditions is demonstrated for one and two dimensional problems. Moreover, for different viscoelastic materials with different dominant damage terms, the proposed model is shown to provide consistent damage growth results.
A software tool for automated crack onset and growth simulations based on the eXtended Finite Ele... more A software tool for automated crack onset and growth simulations based on the eXtended Finite Element Method (X-FEM) has been developed. For the first time, this tool is able to simulate arbitrary crack growth and composite delamination without remeshing. The automated tool is integrated with Abaqus/Standard and Abaqus/CAE via the customization interfaces. It seamlessly works with the Commercial, Off-The-Shelf (COTS) Abaqus suite. Its unique features include: 1) CAE-based insertion of 2D or 3D multiple cracks with arbitrary shape of crack front independent of an existing mesh; 2) simulation of crack growth inside or between solid elements, and potentially along a shell/solid interface or along a shell/shell interface; 3) simulation of non self-similar crack growth along an arbitrary path or a user-specified interface; 4) extraction of near tip strain energy release rates via the modified VCCT; and 5) CAE-based data processing and visualization. The levelset method coupled with X-FEM...
The extended finite element method (XFEM), also known as the generalized finite element method (G... more The extended finite element method (XFEM), also known as the generalized finite element method (GFEM), has been a popular area of research since the late 1990s, as evidenced by high volumes of journal publications, organized minisymposiums in leading conferences, and special workshops and conferences dedicated to this field. The key idea of XFEM/GFEM is to locally enrich the standard finite element approximation space with local enrichment functions which are chosen according to the physics of the problem at hand. For fracture problems that involve cracks, dislocations, and other types of strong discontinuities, it provides two main advantages over conventional finite element methods. That is (i) accurate fields in the vicinity of the discontinuities and (ii) mesh independence with respect to the modeling and propagation of discontinuities. Thus this class of methods offers unprecedented flexibility in fracture mechanics, addressing many shortcomings and limitations of the classical...
Computer Methods in Applied Mechanics and Engineering, 2021
Abstract Cracking in quasi-brittle geomaterials is a complex mechanical phenomenon, driven by var... more Abstract Cracking in quasi-brittle geomaterials is a complex mechanical phenomenon, driven by various dissipation mechanisms across multiple length scales. While some recent promising works have employed the phase-field method to model the damage and fracture of geomaterials, several open questions still remain. In particular, capturing frictional sliding along the lips of microcracks , incorporating lower scale physics, and calibrating the length scale parameter, are some examples. The present paper addresses these essential problems. By leveraging homogenization-based damage-friction coupling formulations for microcracked solids, the linkage is built between the macroscopic phase-field damage variable and the microcrack density parameter. The phase-field is thus treated not only as an indicator for the location of cracks but also accounts for the density of microcracks. A unified Helmholtz free energy function is then constructed as a sum of the bulk energy ( including elastic strain energy and plastic free energy) and the crack surface energy. Furthermore, a new set of degradation functions for the plastic free energy are provided, and a calibration procedure for the length scale parameter is proposed by reflecting a more realistic description of fracture process zone. In addition, an accelerated staggered iteration algorithm is developed to solve the strongly coupled problem more efficiently. Four numerical examples concerning a system of macroscopic cracks are investigated to illustrate the predictive capability of the proposed model in simulating tensile fracture, fault slippage and shear bands.
Computer Methods in Applied Mechanics and Engineering, 2021
Abstract A new formulation is proposed for incorporating local ductile failure constraints and bu... more Abstract A new formulation is proposed for incorporating local ductile failure constraints and buckling resistance into elastoplastic structural design in the context of extreme loading. Many strides have been made in recent years regarding continuum topology optimization with elastoplasticity and buckling separately, but these phenomena are typically not considered together. The formulation we propose is computationally efficient and robust, partly due to its reliance on small strain kinematics and a separation of the elastoplastic response from the buckling load factors computed during the optimization procedure. An aggregate objective function is constructed in which the total work in an elastoplastic analysis is maximized and an aggregation function of the load factors from a separate linear elastic buckling analysis is included. Additionally, local ductile failure constraints are handled via a framework without aggregation functions and a new pseudo buckling mode filter is proposed. Each of the obtained topologies are then subject to a verification step in which a large strain ductile failure model is used in order to compare the performance of the optimized designs obtained for three numerical examples. The results demonstrate that structural responses such as peak load carrying capacity and total external work required to reach the peak load may be significantly improved using the suggested framework. Other interesting observations are also discussed.
Computer Methods in Applied Mechanics and Engineering, 2020
Abstract We present a novel phase field method for modeling hydraulic fracture propagation in por... more Abstract We present a novel phase field method for modeling hydraulic fracture propagation in poroelastic media. In this approach, a new phase field evolution equation is derived to account for damage dependent poro-elastic parameters (Biot’s coefficient, Biot’s modulus and porosity). The fluid flow obeys Darcy’s seepage law in the entire domain including the damage zone, where the rock permeability is assumed to be anisotropic, following the maximum principal strain. The fully coupled problem is solved by a staggered scheme in which the mechanical equilibrium and fluid flow equations are linearized and solved using a Newton–Raphson(NR) method. Several numerical results are presented to investigate the effectiveness of the proposed formulation. First, stability and convergence of the method are verified on a set of benchmark problems considering different time steps and mesh sizes. Second, it is shown that if the poroelastic parameters are kept constant and do not change with the phase field parameter, i.e. reducing to standard phase field approaches in the literature, the model will tend to underestimate the fracture length and overestimate the pore pressure. Finally, we study the interaction of a propagating hydraulic fracture in porous media with inclined natural fractures, and simulate the hydraulic fracture propagation with different perforation phase angle.
AbstractA viscoelastic constitutive model for an asphalt–concrete (AC) material that accounts for... more AbstractA viscoelastic constitutive model for an asphalt–concrete (AC) material that accounts for temperature and material degradation effects is proposed. The model is implemented within a finite-...
International Journal for Numerical Methods in Biomedical Engineering, 2019
A proximal humerus fracture is an injury to the shoulder joint that necessitates medical attentio... more A proximal humerus fracture is an injury to the shoulder joint that necessitates medical attention. While it is one of the most common fracture injuries impacting the elder community and those who suffer from traumatic falls or forceful collisions, there are almost no validated computational methods that can accurately model these fractures. This could be due to the complex, inhomogeneous bone microstructure, complex geometries and the limitations of current fracture mechanics methods. In this paper, we develop and implement a novel phase field method to investigate the proximal humerus fracture. To model the fracture in the inhomogeneous domain, we propose a power law relationship between bone mineral density and critical energy release rate. The method is validated by an in vitro experiment, in which a human humerus is constrained on both ends while subjected to compressive loads on its head in the longitudinal direction that lead to fracture at the anatomical neck. CT-scans are employed to acquire the bone geometry and material parameters, from which detailed finite element meshes with inhomogeneous Young modulus distribution in the bone are generated. The numerical method, implemented in a high performance computing environment, is used to quantitatively predict the complex 3D brittle fracture of the bone, and is shown to be in good agreement with experimental observations. Furthermore, our findings show that the damage is initiated in the trabecular bone-head and propagates outward towards the bone cortex. We conclude that the proposed phase field method is a promising approach to model bone fracture.
High strain rate loading of metals typically leads to material instabilities known as shear bands... more High strain rate loading of metals typically leads to material instabilities known as shear bands. These are narrow bands of intense plastic deformation that weaken the load bearing capacity of the material and serve as a precursor to fracture. Shear bands are modeled as a coupled thermo-mechanical set of nonlinear PDEs and a plastic flow rule that depends on strain rate, strain hardening and thermal softening is used to describe their behavior. In addition, thermal conductivity, which counterbalances thermal heating and creates a weak length scale, must also be employed in order to regularize the PDE system and yield mesh insensitive results. In this paper, we employ mixed finite element formulations to discretize the system in space, and investigate the performance of implicit, explicit and semi-explicit time integration schemes. Small deformation kinematics is assumed in the current work. Stability, accuracy and computational efficiency of the integration schemes are studied on two benchmark examples: a plate in tension with a shear band formed in $$45^{\circ }$$45∘ and an impact onto a notched steel plate. Our findings confirm that implicit methods with larger time steps outperform explicit schemes in terms of cpu modeling time and also yield orders of magnitude more accurate results.
Abstract Numerical modeling of cohesive crack growth in quasi-brittle materials is challenging, p... more Abstract Numerical modeling of cohesive crack growth in quasi-brittle materials is challenging, primarily due to the combination of (i) nonlinearity associated with the fracture process zone (FPZ), (ii) arbitrary directions to which a crack may propagate, and (iii) snap-back or snap-through instabilities encountered in the response of the structure. To address these challenges, we propose a novel arc-length method that can follow the equilibrium path of cohesive crack propagation. The proposed approach is based on the extended finite element method (XFEM) with scalar high-order enrichment functions and Irwin’s crack closure integral, which allows for direct control of the applied loads necessary to propagate cohesive cracks. This is achieved by augmenting a constraint equation written in terms of stress intensity factors (SIFs), and expressed explicitly in terms of the enriched degrees of freedom, which is an attractive feature achieved with Irwin’s integral, since SIFs can be written in closed-form. Note that singular enrichments are active in an unstable crack propagation state and automatically vanish in stable crack configurations. Furthermore, to propagate cracks in arbitrary directions, we employ a maximum circumferential stress criterion implemented by (i) direct usage of the SIFs, and by (ii) a new stress-based nonlocal implementation of this principle. Various benchmark problems including pure mode I and mixed-mode fracture are solved to demonstrate the predictive capability of the present framework for cohesive crack modeling.
In the conventional Newmark family for time integration of hyperbolic problems, both explicit and... more In the conventional Newmark family for time integration of hyperbolic problems, both explicit and implicit methods are inherently sequential in the time domain and not well suited for parallel implementations due to unavoidable processor communication at every time step. In this work we propose a Waveform Relaxation Newmark (WRN$$_\beta $$β) algorithm for the solution of linear second-order hyperbolic systems of ODEs in time, which retains the unconditional stability of the implicit Newmark scheme with the advantage of the lower computational cost of explicit time integration schemes. This method is unstructured in the time domain and is well suited for parallel implementation. We consider a Jacobi and Gauss–Seidel type splitting and study their convergence and stability. The performance of the WRN$$_\beta $$β algorithm is compared to a standard implicit Newmark method and the obtained results confirm the effectiveness of the Waveform Relaxation Newmark algorithm as a new class of more efficient time integrators, which is applicable, as shown in the numerical examples, to both the finite element method and meshfree methods (e.g. the reproducing kernel particle method).
In the past decade, a dominant theme in computational fracture mechanics has been to obtain a mor... more In the past decade, a dominant theme in computational fracture mechanics has been to obtain a more fundamental understanding of material deterioration process, rather than relying on phenomenological or empirical approaches to make predictions. This is driven by a growing need to make predictions of the failure behavior of materials across length scales starting from first principles and going up to the continuum scale. In order to predict such material response, the development of rigorous computational models for modeling material deterioration process at various time and length scales has been of importance to the computational mechanics community. Several interesting approaches have thus been proposed to increase our understanding of the inter-related materials deterioration processes at disparate length scales. While experimental fracture mechanics is important for identifying the physical
Computer Methods in Applied Mechanics and Engineering, 2017
Abstract We present a novel damage-poroelastic model for analyzing the failure response of porous... more Abstract We present a novel damage-poroelastic model for analyzing the failure response of porous media in geomechanics applications. In this new approach, a gradient non-local permeability that leads to non-local transport and consequently non local damage, is introduced. Damage evolution is a function of an equivalent strain measure that is computed from non-local permeability using an inverse permeability–strain constitutive relation. A monolithic, mixed finite element method is proposed to solve the coupled system with a displacement–pressure–regularized permeability ( u − p − κ ) element formulation. The system is linearized and solved using Newton’s method and a backward Euler scheme is used to evolve the system in time. A consistent Jacobian matrix and residual vector are derived analytically and a bilinear damage model is used to evolve the damage. Numerical examples considering hydraulic fracture problems in 1-d and 2-d and damage enhanced consolidation are presented and discussed. The proposed non-local model results are compared with local damage–permeability models. While the local models are shown to suffer from mesh dependence and non-physical spurious oscillations in strain, permeability and fluid pressure evolution, the proposed model is reliable and seems to overcome all these limitations.
A local physical stability criterion for multidimensional fracture problems modeled by the phase ... more A local physical stability criterion for multidimensional fracture problems modeled by the phase field method is developed and studied. Stability analysis provides a rigorous mathematical way to determine the onset of an unstable damage growth and fracture of the structure. In this work, stability is determined by examining the roots of a characteristic equation that arise when a linear perturbation technique is applied to the instantaneous partial differential equation system in a general viscoplastic material. It is shown that such analysis is not limited to a particular degradation function or energy split and could therefore be applied to a wide range of cases. Numerical results are presented to verify the theoretical predictions assuming quadratic and cubic degradation functions. Additionally we show that this stability criterion can be directly expanded to 2D with robust mesh-insensitive predictive capabilities with respect to crack nucleation and path. Several numerical examples are presented to verify these results.
Computer Methods in Applied Mechanics and Engineering, 2017
Abstract For materials that display viscoelastic behavior, adequate description of their failure ... more Abstract For materials that display viscoelastic behavior, adequate description of their failure requires accurate prediction of damage initiation, propagation and growth rate in addition to their time-dependent response. While many local damage models are available in the literature, they all lack a length scale needed to regularize the solution and lead to mesh independent results. In this work, we propose a new damage regularization approach based on an equivalent stress measure concept and apply it to a Prony Series type viscoelastic solid with a Murakami type damage-rate law. Viscoelastic behavior is achieved by a semi-analytical integration of the constitutive law and damage regularization is obtained by solving an additional second-order gradient equation of an equivalent stress. The scheme leads to a coupled set of nonlinear equations which are solved simultaneously using a monolithic Newton framework to obtain displacement and damage fields as a function of time. The formulation is shown to be thermodynamically consistent and the energy dissipation of the model is studied. Mesh-insensitive behavior under creep, relaxation and strain rate conditions is demonstrated for one and two dimensional problems. Moreover, for different viscoelastic materials with different dominant damage terms, the proposed model is shown to provide consistent damage growth results.
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Papers by Haim Waisman