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http://hdl.handle.net/10985/11189
AKPAMA, Holanyo K.; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
Latin American Journal of solids and structures
The aim of this paper is to investigate the impact of the microscopic yield surface (i.e., at the single crystal scale) on the forming limit diagrams (FLDs) of face centred cubic (FCC) materials. To predict these FLDs, the bifurcation approach is used within the framework of rate-independent crystal plasticity theory. For this purpose, two
micromechanical models are developed and implemented. The first one uses the classical Schmid law, which results in the formation of vertices (or corners) at the yield surface, while the second is based on regularization of the Schmid law, which induces rounded corners at the yield surface. In both cases, the overall macroscopic behavior
is derived from the behavior of the microscopic constituents (the single crystals) by using two different scale-transition schemes: the selfconsistent approach and the Taylor model. The simulation results show that the use of the classical Schmid law allows predicting localized necking at realistic strain levels for the whole range of strain
paths that span the FLD. However, the application of a regularized Schmid law results in much higher limit strains in the range of negative strain paths. Moreover, rounding the yield surface vertices through regularization of the Schmid law leads to unrealistically high limit strains in the range of positive strain paths.
Wed, 09 Mar 2016 00:00:00 GMThttp://hdl.handle.net/10985/111892016-03-09T00:00:00ZAKPAMA, Holanyo K.BEN BETTAIEB, MohamedABED-MERAIM, FaridThe aim of this paper is to investigate the impact of the microscopic yield surface (i.e., at the single crystal scale) on the forming limit diagrams (FLDs) of face centred cubic (FCC) materials. To predict these FLDs, the bifurcation approach is used within the framework of rate-independent crystal plasticity theory. For this purpose, two
micromechanical models are developed and implemented. The first one uses the classical Schmid law, which results in the formation of vertices (or corners) at the yield surface, while the second is based on regularization of the Schmid law, which induces rounded corners at the yield surface. In both cases, the overall macroscopic behavior
is derived from the behavior of the microscopic constituents (the single crystals) by using two different scale-transition schemes: the selfconsistent approach and the Taylor model. The simulation results show that the use of the classical Schmid law allows predicting localized necking at realistic strain levels for the whole range of strain
paths that span the FLD. However, the application of a regularized Schmid law results in much higher limit strains in the range of negative strain paths. Moreover, rounding the yield surface vertices through regularization of the Schmid law leads to unrealistically high limit strains in the range of positive strain paths.Micromechanics-Based Damage Analysis of Fracture in Ti5553 Alloy with Application to Bolted Sectors
http://hdl.handle.net/10985/10046
BEN BETTAIEB, Mohamed; VAN HOOF, Thibaut; MINNEBO, Hans; PARDOEN, Thomas; DUFOUR, Philippe; JACQUES, Pascal J.; HABRAKEN, Anne-Marie
Journal of Materials Engineering and Performance
A physics-based, uncoupled damage model is calibrated using cylindrical notched round tensile specimens made of Ti5553 and Ti-6Al-4V alloys. The fracture strain of Ti5553 is lower than for Ti-6Al-4V in the full range of stress triaxiality. This lower ductility originates from a higher volume fraction of damage sites. By proper heat treatment, the fracture strain of Ti5553 increases by almost a factor of two, as a result of a larger damage nucleation stress. This result proves the potential for further optimization of the damage resistance of the Ti5553 alloy. The damage model is combined with an elastoviscoplastic law in order to predict failure in a wide range of loading conditions. In particular, a specific application involving bolted sectors is addressed in order to determine the potential of replacing the Ti-6Al-4V by the Ti5553 alloy.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/100462015-01-01T00:00:00ZBEN BETTAIEB, MohamedVAN HOOF, ThibautMINNEBO, HansPARDOEN, ThomasDUFOUR, PhilippeJACQUES, Pascal J.HABRAKEN, Anne-MarieA physics-based, uncoupled damage model is calibrated using cylindrical notched round tensile specimens made of Ti5553 and Ti-6Al-4V alloys. The fracture strain of Ti5553 is lower than for Ti-6Al-4V in the full range of stress triaxiality. This lower ductility originates from a higher volume fraction of damage sites. By proper heat treatment, the fracture strain of Ti5553 increases by almost a factor of two, as a result of a larger damage nucleation stress. This result proves the potential for further optimization of the damage resistance of the Ti5553 alloy. The damage model is combined with an elastoviscoplastic law in order to predict failure in a wide range of loading conditions. In particular, a specific application involving bolted sectors is addressed in order to determine the potential of replacing the Ti-6Al-4V by the Ti5553 alloy.A comparative study of Forming Limit Diagrams predicted by two different plasticity theories involving vertex effects
http://hdl.handle.net/10985/10048
AKPAMA, Holanyo K.; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
Key Engineering Materials
The main objective of this contribution is to compare the Forming Limit Diagrams
(FLDs) predicted by the use of two different vertex theories. The first theory is micromechanical and is based on the use of the Schmid law, within the framework of crystal plasticity coupled with the Taylor scale-transition scheme. The second theory is phenomenological and is based on the deformation theory of plasticity. For both theories, the mechanical behavior is formulated in the finite strain framework and is assumed to be isotropic and rate-independent. The theoretical framework of these approaches will be presented in details. In the micro-macro modeling, the isotropy is ensured by considering an isotropic initial texture. In the phenomenological modeling, the material parameters are identified on the basis of micro-macro simulations of tensile tests.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/100482015-01-01T00:00:00ZAKPAMA, Holanyo K.BEN BETTAIEB, MohamedABED-MERAIM, FaridThe main objective of this contribution is to compare the Forming Limit Diagrams
(FLDs) predicted by the use of two different vertex theories. The first theory is micromechanical and is based on the use of the Schmid law, within the framework of crystal plasticity coupled with the Taylor scale-transition scheme. The second theory is phenomenological and is based on the deformation theory of plasticity. For both theories, the mechanical behavior is formulated in the finite strain framework and is assumed to be isotropic and rate-independent. The theoretical framework of these approaches will be presented in details. In the micro-macro modeling, the isotropy is ensured by considering an isotropic initial texture. In the phenomenological modeling, the material parameters are identified on the basis of micro-macro simulations of tensile tests.On the elasto-viscoplastic behavior of the Ti5553 alloy
http://hdl.handle.net/10985/11196
BEN BETTAIEB, Mohamed; VAN HOOF, Thibaut; PARDOEN, Thomas; DUFOUR, Philippe; LENAIN, Astrid; JACQUES, Pascal J.; HABRAKEN, Anne-Marie
Materials Science and Engineering: A
The elastoviscoplastic behavior of the Ti5553 alloy is characterized and compared to the classical Ti–6Al–4V alloy. The true stress–strain curves are determined based on tensile tests performed under different strain rates at room temperature and at 1501C, from which the elastic constants and the parameters of a Norton–Hoff viscoplastic model are identified. The strength of the Ti5553 alloy is 20–40% higher than the strength of the Ti–6Al–4V alloy. The Ti5553 alloy constitutes thus a promising candidate for advanced structural applications. In view of modeling structural applications of forming operations, the elastic and plastic initial anisotropy of the two alloys is investigated by combining compression on cylinders with elliptical sections, uniaxial tensile tests in different material directions, plane strain and
shear tests. The initial anisotropy of the different alloys is very weak which justifies the modeling of the mechanical behavior with an isotropic yield surface. The identified elastoviscoplastic model is validated by comparing experimental results with FE predictions both on cylindrical notched specimens subjected to tensile tests and onflat specimens subjected to plane strain conditions.
Mon, 01 Sep 2014 00:00:00 GMThttp://hdl.handle.net/10985/111962014-09-01T00:00:00ZBEN BETTAIEB, MohamedVAN HOOF, ThibautPARDOEN, ThomasDUFOUR, PhilippeLENAIN, AstridJACQUES, Pascal J.HABRAKEN, Anne-MarieThe elastoviscoplastic behavior of the Ti5553 alloy is characterized and compared to the classical Ti–6Al–4V alloy. The true stress–strain curves are determined based on tensile tests performed under different strain rates at room temperature and at 1501C, from which the elastic constants and the parameters of a Norton–Hoff viscoplastic model are identified. The strength of the Ti5553 alloy is 20–40% higher than the strength of the Ti–6Al–4V alloy. The Ti5553 alloy constitutes thus a promising candidate for advanced structural applications. In view of modeling structural applications of forming operations, the elastic and plastic initial anisotropy of the two alloys is investigated by combining compression on cylinders with elliptical sections, uniaxial tensile tests in different material directions, plane strain and
shear tests. The initial anisotropy of the different alloys is very weak which justifies the modeling of the mechanical behavior with an isotropic yield surface. The identified elastoviscoplastic model is validated by comparing experimental results with FE predictions both on cylindrical notched specimens subjected to tensile tests and onflat specimens subjected to plane strain conditions.Combined effect of damage and plastic anisotropy on the ductility limit of thin metal sheets
http://hdl.handle.net/10985/11234
MSOLLI, Sabeur; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
Procedia Structural Integrity
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, 24 Jun 2016 00:00:00 GMThttp://hdl.handle.net/10985/112342016-06-24T00:00:00ZMSOLLI, 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.Prediction of Localized Necking Based on Crystal Plasticity: Comparison of Bifurcation and Imperfection Approaches
http://hdl.handle.net/10985/11858
AKPAMA, Holanyo; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
Key Engineering Materials
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.
Mon, 17 Oct 2016 00:00:00 GMThttp://hdl.handle.net/10985/118582016-10-17T00:00:00ZAKPAMA, HolanyoBEN 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.Numerical integration of rate-independent BCC single crystal plasticity models: comparative study of two classes of numerical algorithms
http://hdl.handle.net/10985/10654
AKPAMA, Holanyo K.; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
International Journal for Numerical Methods in Engineering
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).
Mon, 22 Feb 2016 00:00:00 GMThttp://hdl.handle.net/10985/106542016-02-22T00:00:00ZAKPAMA, 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).Prediction of Plastic Instability in Sheet Metals During Forming Processes Using the Loss of Ellipticity Approach
http://hdl.handle.net/10985/11915
AKPAMA, Holanyo; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
Latin American Journal of Solids and Structures
The prediction of plastic instability in sheet metals during forming processes represents nowadays an ambitious challenge. To reach this goal, a new numerical approach, based on the loss of ellipticity criterion, is proposed in the present contribution. A polycrystalline model is implemented as a user-material subroutine into the
ABAQUS/Implicit finite element (FE) code. The polycrystalline constitutive model is assigned to each integration point of the FE mesh. To derive the mechanical behavior of this polycrystalline aggregate from the behavior of its microscopic constituents, the
multiscale self-consistent scheme is used. The mechanical behavior of the single crystals is described by a finite strain rateindependent constitutive framework, where the Schmid law is used to model the plastic flow. The condition of loss of ellipticity at the
macroscale is used as plastic instability criterion in the FE modeling. This numerical approach, which couples the FE method with the self-consistent scheme, is used to simulate a deep drawing process, and the above criterion is used to predict the formability limit of the studied sheets during this operation.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/119152017-01-01T00:00:00ZAKPAMA, HolanyoBEN BETTAIEB, MohamedABED-MERAIM, FaridThe prediction of plastic instability in sheet metals during forming processes represents nowadays an ambitious challenge. To reach this goal, a new numerical approach, based on the loss of ellipticity criterion, is proposed in the present contribution. A polycrystalline model is implemented as a user-material subroutine into the
ABAQUS/Implicit finite element (FE) code. The polycrystalline constitutive model is assigned to each integration point of the FE mesh. To derive the mechanical behavior of this polycrystalline aggregate from the behavior of its microscopic constituents, the
multiscale self-consistent scheme is used. The mechanical behavior of the single crystals is described by a finite strain rateindependent constitutive framework, where the Schmid law is used to model the plastic flow. The condition of loss of ellipticity at the
macroscale is used as plastic instability criterion in the FE modeling. This numerical approach, which couples the FE method with the self-consistent scheme, is used to simulate a deep drawing process, and the above criterion is used to predict the formability limit of the studied sheets during this operation.Localized necking predictions based on rate-independent self-consistent polycrystal plasticity: Bifurcation analysis versus imperfection approach
http://hdl.handle.net/10985/11856
AKPAMA, Holanyo; BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
International Journal of Plasticity
The present study focuses on the development of a relevant numerical tool for predicting
the onset of localized necking in polycrystalline aggregates. The latter are assumed to be representative of thin metal sheets. In this tool, a micromechanical model, based on the rate-independent self-consistent multi-scale scheme, is developed to accurately describe the mechanical behavior of polycrystalline aggregates from that of their single crystal constituents. In the current paper, the constitutive framework at the single crystal scale follows a finite strain formulation of the rate-independent theory of crystal elastoplasticity. To predict the occurrence of localized necking in polycrystalline aggregates, this micromechanical modeling is combined with two main strain localization approaches: the bifurcation analysis and the initial imperfection method. The formulation of both strain localization indicators takes into consideration the plane stress conditions to which thin metal sheets are subjected during deformation. From a numerical point of view, strain localization analysis with this crystal plasticity approach can be viewed as a strongly nonlinear problem. Hence, several numerical algorithms and techniques are developed and implemented in the aim of efficiently solving this non-linear problem. Various simulation results obtained by the application of the developed numerical tool are presented and extensively discussed. It is demonstrated from these results that the predictions obtained with the MarciniakeKuczynski procedure tend towards those yielded by the bifurcation theory, when the initial imperfection ratio tends towards zero. Furthermore, the above result is shown to be valid for both scale-transition schemes, namely the full-constraint Taylor model and self-consistent scheme.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/118562017-01-01T00:00:00ZAKPAMA, HolanyoBEN BETTAIEB, MohamedABED-MERAIM, FaridThe present study focuses on the development of a relevant numerical tool for predicting
the onset of localized necking in polycrystalline aggregates. The latter are assumed to be representative of thin metal sheets. In this tool, a micromechanical model, based on the rate-independent self-consistent multi-scale scheme, is developed to accurately describe the mechanical behavior of polycrystalline aggregates from that of their single crystal constituents. In the current paper, the constitutive framework at the single crystal scale follows a finite strain formulation of the rate-independent theory of crystal elastoplasticity. To predict the occurrence of localized necking in polycrystalline aggregates, this micromechanical modeling is combined with two main strain localization approaches: the bifurcation analysis and the initial imperfection method. The formulation of both strain localization indicators takes into consideration the plane stress conditions to which thin metal sheets are subjected during deformation. From a numerical point of view, strain localization analysis with this crystal plasticity approach can be viewed as a strongly nonlinear problem. Hence, several numerical algorithms and techniques are developed and implemented in the aim of efficiently solving this non-linear problem. Various simulation results obtained by the application of the developed numerical tool are presented and extensively discussed. It is demonstrated from these results that the predictions obtained with the MarciniakeKuczynski procedure tend towards those yielded by the bifurcation theory, when the initial imperfection ratio tends towards zero. Furthermore, the above result is shown to be valid for both scale-transition schemes, namely the full-constraint Taylor model and self-consistent scheme.Effect of kinematic hardening on localized necking in substrate-supported metal layers
http://hdl.handle.net/10985/11855
BEN BETTAIEB, Mohamed; ABED-MERAIM, Farid
Effect of kinematic hardening on localized necking in substrate-supported metal layers
Prediction of necking limits in thin substrate-supported metal layers, which are typically used as functional components in electronic devices, represents nowadays an ambitious challenge. The specific purpose of the current work is, first, to numerically investigate the effect of kinematic hardening on localized necking in a
freestanding metal layer. Second, the impact of adding a substrate layer on the ductility evolution of the resulting elastomer/metal bilayer will be analyzed. The materials in the metal and substrate layers are assumed to be isotropic, incompressible and strain-rate independent. The behavior of the metal layer is described by a rigid–plastic model with mixed (isotropic and kinematic) hardening. The isotropic hardening contribution is
modeled by the Hollomon law, while kinematic hardening is modeled by the Armstrong–Frederick law. The substrate layer is made of elastomer material whose mechanical behavior is assumed to be hyperelastic and
modeled by a neo-Hookean constitutive law. The Marciniak–Kuczynski imperfection analysis is used to predict plastic flow localization. Through various numerical simulations, the influence of kinematic hardening on localized necking as well as the impact of the addition of an elastomer layer are specifically emphasized.
Comparisons with experimental results are also carried out to assess the relevance of incorporating kinematic hardening in the constitutive modeling of freestanding metal sheets.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10985/118552017-01-01T00:00:00ZBEN BETTAIEB, MohamedABED-MERAIM, FaridPrediction of necking limits in thin substrate-supported metal layers, which are typically used as functional components in electronic devices, represents nowadays an ambitious challenge. The specific purpose of the current work is, first, to numerically investigate the effect of kinematic hardening on localized necking in a
freestanding metal layer. Second, the impact of adding a substrate layer on the ductility evolution of the resulting elastomer/metal bilayer will be analyzed. The materials in the metal and substrate layers are assumed to be isotropic, incompressible and strain-rate independent. The behavior of the metal layer is described by a rigid–plastic model with mixed (isotropic and kinematic) hardening. The isotropic hardening contribution is
modeled by the Hollomon law, while kinematic hardening is modeled by the Armstrong–Frederick law. The substrate layer is made of elastomer material whose mechanical behavior is assumed to be hyperelastic and
modeled by a neo-Hookean constitutive law. The Marciniak–Kuczynski imperfection analysis is used to predict plastic flow localization. Through various numerical simulations, the influence of kinematic hardening on localized necking as well as the impact of the addition of an elastomer layer are specifically emphasized.
Comparisons with experimental results are also carried out to assess the relevance of incorporating kinematic hardening in the constitutive modeling of freestanding metal sheets.