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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Thu, 07 Dec 2023 23:39:55 GMT2023-12-07T23:39:55ZNumerical integration of rate-independent BCC single crystal plasticity models: comparative study of two classes of numerical algorithms
http://hdl.handle.net/10985/13535
Numerical integration of rate-independent BCC single crystal plasticity models: comparative study of two classes of numerical algorithms
AKPAMA, Holanyo K.; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
In an incremental formulation suitable to numerical implementation, the use of rate-independent theory of crystal plasticity essentially leads to four fundamental problems. The first is to determine the set of potentially active slip systems over a time increment. The second is to select the active slip systems among the potentially active ones. The third is to compute the slip rates (or the slip increments) for the active slip systems. And the last problem is the possible non-uniqueness of slip rates. The purpose of this paper is to propose satisfactory responses to the above-mentioned first three issues by presenting and comparing two novel numerical algorithms. The first algorithm is based on the usual return-mapping integration scheme, while the second follows the so-called ultimate scheme. The latter is shown to be more relevant and efficient than the former. These comparative performances are illustrated through various numerical simulations of the mechanical behavior of single crystals and polycrystalline aggregates subjected to monotonic and complex loadings. Although these algorithms are applied in this paper to Body-Centered-Cubic (BCC) crystal structures, they are quite general and suitable for integrating the constitutive equations for other crystal structures (e.g., FCC and HCP).
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/135352016-01-01T00:00:00ZAKPAMA, Holanyo K.BEN BETTAIEB, MohamedABED-MERAIM, FaridIn an incremental formulation suitable to numerical implementation, the use of rate-independent theory of crystal plasticity essentially leads to four fundamental problems. The first is to determine the set of potentially active slip systems over a time increment. The second is to select the active slip systems among the potentially active ones. The third is to compute the slip rates (or the slip increments) for the active slip systems. And the last problem is the possible non-uniqueness of slip rates. The purpose of this paper is to propose satisfactory responses to the above-mentioned first three issues by presenting and comparing two novel numerical algorithms. The first algorithm is based on the usual return-mapping integration scheme, while the second follows the so-called ultimate scheme. The latter is shown to be more relevant and efficient than the former. These comparative performances are illustrated through various numerical simulations of the mechanical behavior of single crystals and polycrystalline aggregates subjected to monotonic and complex loadings. Although these algorithms are applied in this paper to Body-Centered-Cubic (BCC) crystal structures, they are quite general and suitable for integrating the constitutive equations for other crystal structures (e.g., FCC and HCP).Combined effect of damage and plastic anisotropy on the ductility limit of thin metal sheets
http://hdl.handle.net/10985/20264
Combined effect of damage and plastic anisotropy on the ductility limit of thin metal sheets
MSOLLI, Sabeur; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
It is well known that both damage and plastic anisotropy strongly affect the ductility limit of thin metal sheets. Due to the manufacturing processes, initial defects, such as inclusions and voids, are commonly present in the produced sheet metals. Plastic anisotropy is a direct outcome of the rolling process, where the resulting metal sheets exhibit preferred crystallographic orientations or strong texture. In the present study, the combined effect of plastic anisotropy and damage on localized necking is numerically investigated and analyzed. To this aim, an improved version of the Gurson—Tvergaard—Needleman (GTN) constitutive framework is used to model the mechanical behavior of the studied sheet. This version, which is an extension of the original GTN model, incorporates Hill’s anisotropic yield function to take into account the plastic anisotropy of the matrix material. Particular attention is devoted to the derivation of the analytical tangent modulus associated with this constitutive model. This extended GTN model is successfully coupled with bifurcation theory to predict sheet metal ductility limits, which are represented in terms of forming limit diagrams (FLDs). The effect of some material parameters (e.g., anisotropy parameters of the metallic matrix) on the shape and the location of the predicted FLDs is then investigated and discussed through numerical simulations.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/202642016-01-01T00:00:00ZMSOLLI, SabeurBEN BETTAIEB, MohamedABED-MERAIM, FaridIt is well known that both damage and plastic anisotropy strongly affect the ductility limit of thin metal sheets. Due to the manufacturing processes, initial defects, such as inclusions and voids, are commonly present in the produced sheet metals. Plastic anisotropy is a direct outcome of the rolling process, where the resulting metal sheets exhibit preferred crystallographic orientations or strong texture. In the present study, the combined effect of plastic anisotropy and damage on localized necking is numerically investigated and analyzed. To this aim, an improved version of the Gurson—Tvergaard—Needleman (GTN) constitutive framework is used to model the mechanical behavior of the studied sheet. This version, which is an extension of the original GTN model, incorporates Hill’s anisotropic yield function to take into account the plastic anisotropy of the matrix material. Particular attention is devoted to the derivation of the analytical tangent modulus associated with this constitutive model. This extended GTN model is successfully coupled with bifurcation theory to predict sheet metal ductility limits, which are represented in terms of forming limit diagrams (FLDs). The effect of some material parameters (e.g., anisotropy parameters of the metallic matrix) on the shape and the location of the predicted FLDs is then investigated and discussed through numerical simulations.Strain localization analysis for planar polycrystals based on bifurcation theory
http://hdl.handle.net/10985/13575
Strain localization analysis for planar polycrystals based on bifurcation theory
BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
In the present paper, an efficient numerical tool is developed to investigate the ductility limit of polycrystalline aggregates under in-plane biaxial loading. These aggregates are assumed to be representative of very thin sheet metals (with typically few grains through the thickness). Therefore, the plane-stress assumption is naturally adopted to numerically predict the occurrence of strain localization. Furthermore, the initial crystallographic texture is assumed to be planar. Considering the latter assumptions, a two-dimensional single crystal model is advantageously chosen to describe the mechanical behavior at the microscopic scale. The mechanical behavior of the planar polycrystalline aggregate is derived from that of single crystals by using the full-constraint Taylor scale-transition scheme. To predict the occurrence of localized necking, the developed multiscale model is coupled with the bifurcation theory. As will be demonstrated through various numerical results, in the case of biaxial loading under plane-stress conditions, the planar single crystal model provides the same predictions as those given by the more commonly used three-dimensional single crystal model. Moreover, the use of the two-dimensional model instead of the three-dimensional one allows dividing the number of active slip systems by two and, hence, significantly reducing the CPU time required for the integration of the constitutive equations at the single crystal scale. Furthermore, the planar polycrystal model seems to be more suitable to study the ductility of very thin sheet metals, as its use allows us to rigorously ensure the plane-stress state, which is not always the case when the fully three-dimensional polycrystalline model is employed. Consequently, the adoption of this planar formulation, instead of the three-dimensional one, allows us to simplify the computational aspects and, accordingly, to considerably reduce the CPU time required for the numerical predictions.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/135752018-01-01T00:00:00ZBEN BETTAIEB, MohamedABED-MERAIM, FaridIn the present paper, an efficient numerical tool is developed to investigate the ductility limit of polycrystalline aggregates under in-plane biaxial loading. These aggregates are assumed to be representative of very thin sheet metals (with typically few grains through the thickness). Therefore, the plane-stress assumption is naturally adopted to numerically predict the occurrence of strain localization. Furthermore, the initial crystallographic texture is assumed to be planar. Considering the latter assumptions, a two-dimensional single crystal model is advantageously chosen to describe the mechanical behavior at the microscopic scale. The mechanical behavior of the planar polycrystalline aggregate is derived from that of single crystals by using the full-constraint Taylor scale-transition scheme. To predict the occurrence of localized necking, the developed multiscale model is coupled with the bifurcation theory. As will be demonstrated through various numerical results, in the case of biaxial loading under plane-stress conditions, the planar single crystal model provides the same predictions as those given by the more commonly used three-dimensional single crystal model. Moreover, the use of the two-dimensional model instead of the three-dimensional one allows dividing the number of active slip systems by two and, hence, significantly reducing the CPU time required for the integration of the constitutive equations at the single crystal scale. Furthermore, the planar polycrystal model seems to be more suitable to study the ductility of very thin sheet metals, as its use allows us to rigorously ensure the plane-stress state, which is not always the case when the fully three-dimensional polycrystalline model is employed. Consequently, the adoption of this planar formulation, instead of the three-dimensional one, allows us to simplify the computational aspects and, accordingly, to considerably reduce the CPU time required for the numerical predictions.Prediction of Localized Necking Based on Crystal Plasticity: Comparison of Bifurcation and Imperfection Approaches
http://hdl.handle.net/10985/11858
Prediction of Localized Necking Based on Crystal Plasticity: Comparison of Bifurcation and Imperfection Approaches
AKPAMA, Holanyo K.; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
In the present work, a powerful modeling tool is developed to predict and analyze the onset of strain localization in polycrystalline aggregates. The predictions of localized necking are based on two plastic instability criteria, namely the bifurcation theory and the initial imperfection approach. In this tool, a micromechanical model, based on the self-consistent scale-transition scheme, is used to accurately derive the mechanical behavior of polycrystalline aggregates from that of their microscopic constituents (the single crystals). The mechanical behavior of the single crystals is developed within a large strain rate-independent constitutive framework. This micromechanical constitutive modeling takes into account the essential microstructure-related features that are relevant at the microscale. These microstructural aspects include key physical mechanisms, such as initial and induced crystallographic textures, morphological anisotropy and interactions between the grains and their surrounding medium. The developed tool is used to predict sheet metal formability through the concept of forming limit diagrams (FLDs). The results obtained by the self-consistent averaging scheme, in terms of predicted FLDs, are compared with those given by the more classical full-constraint Taylor model. Moreover, the predictions obtained by the imperfection approach are systematically compared with those given by the bifurcation analysis, and it is demonstrated that the former tend to the latter in the limit of a vanishing size for the initial imperfection.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/118582016-01-01T00:00:00ZAKPAMA, Holanyo K.BEN BETTAIEB, MohamedABED-MERAIM, FaridIn the present work, a powerful modeling tool is developed to predict and analyze the onset of strain localization in polycrystalline aggregates. The predictions of localized necking are based on two plastic instability criteria, namely the bifurcation theory and the initial imperfection approach. In this tool, a micromechanical model, based on the self-consistent scale-transition scheme, is used to accurately derive the mechanical behavior of polycrystalline aggregates from that of their microscopic constituents (the single crystals). The mechanical behavior of the single crystals is developed within a large strain rate-independent constitutive framework. This micromechanical constitutive modeling takes into account the essential microstructure-related features that are relevant at the microscale. These microstructural aspects include key physical mechanisms, such as initial and induced crystallographic textures, morphological anisotropy and interactions between the grains and their surrounding medium. The developed tool is used to predict sheet metal formability through the concept of forming limit diagrams (FLDs). The results obtained by the self-consistent averaging scheme, in terms of predicted FLDs, are compared with those given by the more classical full-constraint Taylor model. Moreover, the predictions obtained by the imperfection approach are systematically compared with those given by the bifurcation analysis, and it is demonstrated that the former tend to the latter in the limit of a vanishing size for the initial imperfection.Prediction of the ductility limit of magnesium AZ31B alloy
http://hdl.handle.net/10985/19660
Prediction of the ductility limit of magnesium AZ31B alloy
JEDIDI, Mohamed Yassine; BEN BETTAIEB, Mohamed; BOUGUECHA, Anas; ABED-MERAIM, Farid; KHABOU, Mohamed Taoufik; HADDAR, Mohamed
In many engineering applications (automotive, computer and mobile device industries, etc.), magnesium alloys have been widely used owing to their interesting physical and mechanical parameters. However, magnesium alloys are identified by the low ductility at room temperature, due to their strong plastic anisotropy and the yielding asymmetry between tension and compression. In this work, the ductility limit of a rolled magnesium AZ31 sheet metal at room temperature is numerically investigated. This investigation is based on the coupling between a reduced-order crystal plasticity model and the Marciniak– Kuczyński localized necking approach. This reduced-order model is used to describe the anisotropic behavior of this material taking into account the strong plastic anisotropy (e.g., yielding asymmetry between tension and compression) due to the limited number of slip systems (i.e., twinning mode). To accurately describe the plastic anisotropy due to slip and twinning modes, a combination of two separate yield functions (according to Barlat and Cazacu) is used. The coupling between the adopted constitutive framework and the Marciniak–Kuczyński instability approach is numerically implemented via an implicit algorithm. Comparisons between experimental results from the literature and numerical results obtained by using our calculation tool are carried out to validate the choice of the reducedorder crystal plasticity model.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/196602018-01-01T00:00:00ZJEDIDI, Mohamed YassineBEN BETTAIEB, MohamedBOUGUECHA, AnasABED-MERAIM, FaridKHABOU, Mohamed TaoufikHADDAR, MohamedIn many engineering applications (automotive, computer and mobile device industries, etc.), magnesium alloys have been widely used owing to their interesting physical and mechanical parameters. However, magnesium alloys are identified by the low ductility at room temperature, due to their strong plastic anisotropy and the yielding asymmetry between tension and compression. In this work, the ductility limit of a rolled magnesium AZ31 sheet metal at room temperature is numerically investigated. This investigation is based on the coupling between a reduced-order crystal plasticity model and the Marciniak– Kuczyński localized necking approach. This reduced-order model is used to describe the anisotropic behavior of this material taking into account the strong plastic anisotropy (e.g., yielding asymmetry between tension and compression) due to the limited number of slip systems (i.e., twinning mode). To accurately describe the plastic anisotropy due to slip and twinning modes, a combination of two separate yield functions (according to Barlat and Cazacu) is used. The coupling between the adopted constitutive framework and the Marciniak–Kuczyński instability approach is numerically implemented via an implicit algorithm. Comparisons between experimental results from the literature and numerical results obtained by using our calculation tool are carried out to validate the choice of the reducedorder crystal plasticity model.Modeling of void coalescence initiation and its impact on the prediction of material failure
http://hdl.handle.net/10985/18917
Modeling of void coalescence initiation and its impact on the prediction of material failure
MSOLLI, Sabeur; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
In the present paper, Thomason’s criterion is coupled with the well-known Gurson–Tvergaard–Needleman (GTN) damage model and used for the determination of the critical void volume fraction fc , which marks the initiation of the coalescence stage. The onset of void coalescence predicted by Thomason’s criterion is compared to that obtained by using a predefined fc , which is usually fitted on the basis of experimental results, as originally proposed in the GTN model. Comparisons are made in terms of both single finite element simulations and numerical results of deep drawing of a cup.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/189172016-01-01T00:00:00ZMSOLLI, SabeurBEN BETTAIEB, MohamedABED-MERAIM, FaridIn the present paper, Thomason’s criterion is coupled with the well-known Gurson–Tvergaard–Needleman (GTN) damage model and used for the determination of the critical void volume fraction fc , which marks the initiation of the coalescence stage. The onset of void coalescence predicted by Thomason’s criterion is compared to that obtained by using a predefined fc , which is usually fitted on the basis of experimental results, as originally proposed in the GTN model. Comparisons are made in terms of both single finite element simulations and numerical results of deep drawing of a cup.An elasto-plastic self-consistent model for damaged polycrystalline materials: Theoretical formulation and numerical implementation
http://hdl.handle.net/10985/19156
An elasto-plastic self-consistent model for damaged polycrystalline materials: Theoretical formulation and numerical implementation
PAUX, J.; BEN BETTAIEB, Mohamed; BADREDDINE, H.; ABED-MERAIM, Farid; LABERGERE, C.; SAANOUNI, K.
Elasto-plastic multiscale approaches are known to be suitable to model the mechanical behavior of metallic materials during forming processes. These approaches are classically adopted to explicitly link relevant microstructural effects to the macroscopic behavior. This paper presents a finite strain elastoplastic self-consistent model for damaged polycrystalline aggregates and its implementation into ABAQUS/Standard finite element (FE) code. Material degradation is modeled by the introduction of a scalar damage variable at each crystallographic slip system for each individual grain. The single crystal plastic flow is described by both the classical and a regularized version of the Schmid criterion. To integrate the single crystal constitutive equations, two new numerical algorithms are developed (one for each plastic flow rule). Then, the proposed single crystal modeling is embedded into the self-consistent scheme to predict the mechanical behavior of elasto-plastic polycrystalline aggregates in the finite strain range. This strategy is implemented into ABAQUS/Standard FE code through a user-defined material (UMAT) subroutine. Special attention is paid to the satisfaction of the incremental objectivity and the efficiency of the convergence of the global resolution scheme, related to the computation of the consistent tangent modulus. The capability of the new constitutive modeling to capture the interaction between the damage evolution and the microstructural properties is highlighted through several simulations at both single crystal and polycrystalline scales. It appears from the numerical tests that the use of the classical Schmid criterion leads to a poor numerical convergence of the self-consistent scheme (due to the abrupt changes in the activity of the slip systems), which sometimes causes the computations to be prematurely stopped. By contrast, the use of the regularized version of the Schmid law allows a better convergence of the self-consistent approach, but induces an important increase in the computation time devoted to the integration of the single crystal constitutive equations (because of the high value of the power-law exponent used to regularize the Schmid yield function). To avoid these difficulties, a numerical strategy is built to combine the benefits of the two approaches: the classical Schmid criterion is used to integrate the single crystal constitutive equations, while its regularized version is used to compute the microscopic tangent modulus required for solving the self-consistent equations. The robustness and the accuracy of this novel numerical strategy are particularly analyzed through several numerical simulations (prediction of the mechanical behavior of polycrystalline aggregates and simulation of a circular cup-drawing forming process).
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10985/191562020-01-01T00:00:00ZPAUX, J.BEN BETTAIEB, MohamedBADREDDINE, H.ABED-MERAIM, FaridLABERGERE, C.SAANOUNI, K.Elasto-plastic multiscale approaches are known to be suitable to model the mechanical behavior of metallic materials during forming processes. These approaches are classically adopted to explicitly link relevant microstructural effects to the macroscopic behavior. This paper presents a finite strain elastoplastic self-consistent model for damaged polycrystalline aggregates and its implementation into ABAQUS/Standard finite element (FE) code. Material degradation is modeled by the introduction of a scalar damage variable at each crystallographic slip system for each individual grain. The single crystal plastic flow is described by both the classical and a regularized version of the Schmid criterion. To integrate the single crystal constitutive equations, two new numerical algorithms are developed (one for each plastic flow rule). Then, the proposed single crystal modeling is embedded into the self-consistent scheme to predict the mechanical behavior of elasto-plastic polycrystalline aggregates in the finite strain range. This strategy is implemented into ABAQUS/Standard FE code through a user-defined material (UMAT) subroutine. Special attention is paid to the satisfaction of the incremental objectivity and the efficiency of the convergence of the global resolution scheme, related to the computation of the consistent tangent modulus. The capability of the new constitutive modeling to capture the interaction between the damage evolution and the microstructural properties is highlighted through several simulations at both single crystal and polycrystalline scales. It appears from the numerical tests that the use of the classical Schmid criterion leads to a poor numerical convergence of the self-consistent scheme (due to the abrupt changes in the activity of the slip systems), which sometimes causes the computations to be prematurely stopped. By contrast, the use of the regularized version of the Schmid law allows a better convergence of the self-consistent approach, but induces an important increase in the computation time devoted to the integration of the single crystal constitutive equations (because of the high value of the power-law exponent used to regularize the Schmid yield function). To avoid these difficulties, a numerical strategy is built to combine the benefits of the two approaches: the classical Schmid criterion is used to integrate the single crystal constitutive equations, while its regularized version is used to compute the microscopic tangent modulus required for solving the self-consistent equations. The robustness and the accuracy of this novel numerical strategy are particularly analyzed through several numerical simulations (prediction of the mechanical behavior of polycrystalline aggregates and simulation of a circular cup-drawing forming process).Analyticity of solutions to thermo-elastic-plastic flow problem with microtemperatures
http://hdl.handle.net/10985/20375
Analyticity of solutions to thermo-elastic-plastic flow problem with microtemperatures
AOUADI, Moncef; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
In this paper, we study some qualitative and numerical properties of new equations including the coupled effects of thermal elastic-plastic theory with microtemperatures. We establish the necessary and sufficient conditions to guarantee that the model dissipates energy. The one-dimensional case, which corresponds to isotropic hardening problem, is chosen in order to present some qualitative and numerical properties. With the help of the semigroup theory of linear operators, we prove the well-posedness of the one-dimensional problem corresponding to plastic flow. Then, we show that the associated C0−semigroup is not analytical in general, except for a special case. The exponential stability of the solutions is kept in all cases. Finally, a numerical tool, based on the finite element method, is developed to validate the proposed model and to show its capability. Particular attention is paid to the consideration of the elastoplastic behavior in the development of this tool.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/203752021-01-01T00:00:00ZAOUADI, MoncefBEN BETTAIEB, MohamedABED-MERAIM, FaridIn this paper, we study some qualitative and numerical properties of new equations including the coupled effects of thermal elastic-plastic theory with microtemperatures. We establish the necessary and sufficient conditions to guarantee that the model dissipates energy. The one-dimensional case, which corresponds to isotropic hardening problem, is chosen in order to present some qualitative and numerical properties. With the help of the semigroup theory of linear operators, we prove the well-posedness of the one-dimensional problem corresponding to plastic flow. Then, we show that the associated C0−semigroup is not analytical in general, except for a special case. The exponential stability of the solutions is kept in all cases. Finally, a numerical tool, based on the finite element method, is developed to validate the proposed model and to show its capability. Particular attention is paid to the consideration of the elastoplastic behavior in the development of this tool.Formability prediction of substrate-supported metal layers using a non-associated plastic flow rule
http://hdl.handle.net/10985/19155
Formability prediction of substrate-supported metal layers using a non-associated plastic flow rule
BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
When manufacturing flexible devices, it is quite common that localized necking appears due to the low ductility of the metal sheets used. To delay the inception of such localized necking, several industrial companies have proposed a promising technical solution based on the bonding of elastomer substrates to the metal sheets used in the manufacturing processes. In this context, the comprehensive numerical understanding of the impact of such substrate coating on the improvement of the ductility of elastomer-supported metal layers still remains a challenging goal. To achieve this goal, the bifurcation approach as well as the Marciniak and Kuczynski model are used to predict the occurrence of localized necking. The mechanical behavior of the metal layer is modeled by a non-associated anisotropic plasticity model. The adoption of non-associated plastic flow rule allows separating the description of the plastic potential from that of the yield function, which is essential to accurately model strong plastic anisotropy characterizing cold-rolled sheets. As to the elastomer substrate, its mechanical behavior is described by a neo-Hookean law. The paper presents a variety of numerical results relating to the prediction of plastic strain localization in both freestanding and elastomercoated metal layers. The effects of the non-associativity of the plastic flow rule for the metal layer and the addition of an elastomer substrate on the predictions of localized necking are especially underlined. It is shown that the ductility limits predicted by the non-associated elasto-plastic model are lower than their counterparts determined by an associated plasticity model. It is also proven that adhering an elastomer layer to the metal layer can substantially delay the initiation of plastic strain localization.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/191552021-01-01T00:00:00ZBEN BETTAIEB, MohamedABED-MERAIM, FaridWhen manufacturing flexible devices, it is quite common that localized necking appears due to the low ductility of the metal sheets used. To delay the inception of such localized necking, several industrial companies have proposed a promising technical solution based on the bonding of elastomer substrates to the metal sheets used in the manufacturing processes. In this context, the comprehensive numerical understanding of the impact of such substrate coating on the improvement of the ductility of elastomer-supported metal layers still remains a challenging goal. To achieve this goal, the bifurcation approach as well as the Marciniak and Kuczynski model are used to predict the occurrence of localized necking. The mechanical behavior of the metal layer is modeled by a non-associated anisotropic plasticity model. The adoption of non-associated plastic flow rule allows separating the description of the plastic potential from that of the yield function, which is essential to accurately model strong plastic anisotropy characterizing cold-rolled sheets. As to the elastomer substrate, its mechanical behavior is described by a neo-Hookean law. The paper presents a variety of numerical results relating to the prediction of plastic strain localization in both freestanding and elastomercoated metal layers. The effects of the non-associativity of the plastic flow rule for the metal layer and the addition of an elastomer substrate on the predictions of localized necking are especially underlined. It is shown that the ductility limits predicted by the non-associated elasto-plastic model are lower than their counterparts determined by an associated plasticity model. It is also proven that adhering an elastomer layer to the metal layer can substantially delay the initiation of plastic strain localization.Development of a new algorithm for the time integration of rate-independent crystal plasticity models
http://hdl.handle.net/10985/19095
Development of a new algorithm for the time integration of rate-independent crystal plasticity models
BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
The aim of this paper is to develop a new efficient integration scheme, able to integrate the constitutive equations for rate-independent theory of crystal plasticity at finite strain. This algorithm proposes an efficient method to determine the set of active slip systems and the corresponding slip rates. This method is based on the use of a smooth formulation of the Schmid law. The issue of nonuniqueness in the determination of slip rates can be overcome by using two different numerical techniques.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/190952016-01-01T00:00:00ZBEN BETTAIEB, MohamedABED-MERAIM, FaridThe aim of this paper is to develop a new efficient integration scheme, able to integrate the constitutive equations for rate-independent theory of crystal plasticity at finite strain. This algorithm proposes an efficient method to determine the set of active slip systems and the corresponding slip rates. This method is based on the use of a smooth formulation of the Schmid law. The issue of nonuniqueness in the determination of slip rates can be overcome by using two different numerical techniques.