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<title>SAM</title>
<link>https://sam.ensam.eu:443</link>
<description>The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.</description>
<pubDate xmlns="http://apache.org/cocoon/i18n/2.1">Fri, 12 Jun 2026 11:46:59 GMT</pubDate>
<dc:date>2026-06-12T11:46:59Z</dc:date>
<item>
<title>Evaluation of a new solid-shell finite element on the simulation of sheet metal forming processes</title>
<link>http://hdl.handle.net/10985/10071</link>
<description>Evaluation of a new solid-shell finite element on the simulation of sheet metal forming processes
CHALAL, Hocine; SALAHOUELHADJ, Abdellah; ABED-MERAIM, Farid
In this paper, the performance of the solid-shell finite element SHB8PS is assessed in the context of sheet metal forming simulation using anisotropic elastic-plastic behavior models. This finite element technology has been implemented into the commercial implicit finite element code Abaqus/Standard via the UEL subroutine. It consists of an eight-node three-dimensional hexahedron with reduced integration, provided with an arbitrary number of integration points along the thickness direction. The use of an in-plane reduced integration scheme prevents some locking phenomena, resulting in a computationally efficient formulation when compared to conventional 3D solid elements. Another interesting feature lies in the possibility of increasing the number of through-thickness integration points within a single element layer, which enables an accurate description of various phenomena in sheet forming simulations. A general elastic-plastic model has been adopted in the constitutive modeling for sheet forming applications with plastic anisotropy. As an illustrative example, the performance of the element is shown in the earing prediction of a cylindrical cup drawing process.
</description>
<pubDate>Sun, 01 Jan 2012 00:00:00 GMT</pubDate>
<guid isPermaLink="false">http://hdl.handle.net/10985/10071</guid>
<dc:date>2012-01-01T00:00:00Z</dc:date>
<dc:creator>CHALAL, Hocine</dc:creator>
<dc:creator>SALAHOUELHADJ, Abdellah</dc:creator>
<dc:creator>ABED-MERAIM, Farid</dc:creator>
<dc:description>In this paper, the performance of the solid-shell finite element SHB8PS is assessed in the context of sheet metal forming simulation using anisotropic elastic-plastic behavior models. This finite element technology has been implemented into the commercial implicit finite element code Abaqus/Standard via the UEL subroutine. It consists of an eight-node three-dimensional hexahedron with reduced integration, provided with an arbitrary number of integration points along the thickness direction. The use of an in-plane reduced integration scheme prevents some locking phenomena, resulting in a computationally efficient formulation when compared to conventional 3D solid elements. Another interesting feature lies in the possibility of increasing the number of through-thickness integration points within a single element layer, which enables an accurate description of various phenomena in sheet forming simulations. A general elastic-plastic model has been adopted in the constitutive modeling for sheet forming applications with plastic anisotropy. As an illustrative example, the performance of the element is shown in the earing prediction of a cylindrical cup drawing process.</dc:description>
</item>
<item>
<title>Springback of thick sheet AHSS subject to bending under tension</title>
<link>http://hdl.handle.net/10985/6870</link>
<description>Springback of thick sheet AHSS subject to bending under tension
RACZ, Sever-Gabriel; CHALAL, Hocine; BALAN, Tudor
The springback behavior of four advanced high-strength sheet steels (Dual-Phase, TRIP, ferrite-bainite) with thicknesses ranging from 1.2 to 4 mm was investigated by means of the bending-under-tension (BUT) test. The applicability of several guidelines from the literature was investigated experimentally and numerically. The monotonic decrease of springback as back force increased was confirmed for this category of sheet steels, and a general trend for the non-linear influence of the tool radius was observed. The influence of numerical factors on the predicted values of springback was investigated, and conclusions and simple guidelines were drawn from the analysis with industrial sheet forming applications in mind.
Lien vers la version éditeur : http://www.sciencedirect.com/science/article/pii/S0020740312000677
</description>
<pubDate>Sun, 01 Jan 2012 00:00:00 GMT</pubDate>
<guid isPermaLink="false">http://hdl.handle.net/10985/6870</guid>
<dc:date>2012-01-01T00:00:00Z</dc:date>
<dc:creator>RACZ, Sever-Gabriel</dc:creator>
<dc:creator>CHALAL, Hocine</dc:creator>
<dc:creator>BALAN, Tudor</dc:creator>
<dc:description>The springback behavior of four advanced high-strength sheet steels (Dual-Phase, TRIP, ferrite-bainite) with thicknesses ranging from 1.2 to 4 mm was investigated by means of the bending-under-tension (BUT) test. The applicability of several guidelines from the literature was investigated experimentally and numerically. The monotonic decrease of springback as back force increased was confirmed for this category of sheet steels, and a general trend for the non-linear influence of the tool radius was observed. The influence of numerical factors on the predicted values of springback was investigated, and conclusions and simple guidelines were drawn from the analysis with industrial sheet forming applications in mind.</dc:description>
</item>
<item>
<title>Hardening effects on strain localization predictions in porous ductile materials using the bifurcation approach</title>
<link>http://hdl.handle.net/10985/9972</link>
<description>Hardening effects on strain localization predictions in porous ductile materials using the bifurcation approach
CHALAL, Hocine; ABED-MERAIM, Farid
The localization of deformation into planar bands is often considered as the ultimate stage of strain prior to ductile fracture. In this study, ductility limits of metallic materials are predicted using the Gurson–Tvergaard–Needleman (GTN) damage model combined with the bifurcation approach. Both the GTN constitutive equations and the Rice bifurcation criterion are implemented into the finite element (FE) code ABAQUS/Standard within the framework of large plastic strains and a fully three-dimensional formulation. The current contribution focuses on the effect of strain hardening on ductility limit predictions. It is shown that the choice of void nucleation mechanism has an important influence on the sensitivity of the predicted ductility limits to strain hardening. When strain-controlled nucleation is considered, varying the hardening parameters of the fully dense matrix material has no effect on the porosity evolution and, consequently, very small impact on the predicted ductility limits. For stress-controlled nucleation, the porosity evolution is directly affected by the strain hardening characteristics, which induce a significant effect on the predicted ductility limits. This paper also discusses the use of a micromechanics-based calibration for the GTN q -parameters in the case of strain-controlled nucleation, which is also shown to allow accounting for the hardening effects on plastic strain localization.
</description>
<pubDate>Thu, 01 Jan 2015 00:00:00 GMT</pubDate>
<guid isPermaLink="false">http://hdl.handle.net/10985/9972</guid>
<dc:date>2015-01-01T00:00:00Z</dc:date>
<dc:creator>CHALAL, Hocine</dc:creator>
<dc:creator>ABED-MERAIM, Farid</dc:creator>
<dc:description>The localization of deformation into planar bands is often considered as the ultimate stage of strain prior to ductile fracture. In this study, ductility limits of metallic materials are predicted using the Gurson–Tvergaard–Needleman (GTN) damage model combined with the bifurcation approach. Both the GTN constitutive equations and the Rice bifurcation criterion are implemented into the finite element (FE) code ABAQUS/Standard within the framework of large plastic strains and a fully three-dimensional formulation. The current contribution focuses on the effect of strain hardening on ductility limit predictions. It is shown that the choice of void nucleation mechanism has an important influence on the sensitivity of the predicted ductility limits to strain hardening. When strain-controlled nucleation is considered, varying the hardening parameters of the fully dense matrix material has no effect on the porosity evolution and, consequently, very small impact on the predicted ductility limits. For stress-controlled nucleation, the porosity evolution is directly affected by the strain hardening characteristics, which induce a significant effect on the predicted ductility limits. This paper also discusses the use of a micromechanics-based calibration for the GTN q -parameters in the case of strain-controlled nucleation, which is also shown to allow accounting for the hardening effects on plastic strain localization.</dc:description>
</item>
<item>
<title>Plastic Instability Based on Bifurcation Analysis: Effect of Hardening  and Gurson Damage Parameters on Strain Localization</title>
<link>http://hdl.handle.net/10985/10026</link>
<description>Plastic Instability Based on Bifurcation Analysis: Effect of Hardening  and Gurson Damage Parameters on Strain Localization
MANSOURI, Lotfi; CHALAL, Hocine; ABED-MERAIM, Farid; BALAN, Tudor
In  this  work,  we  propose  to  couple  the  Gurson-Tvergaard-Needleman  (GTN)  model, known  for  its  widespread  use  to  describe  damage  evolution  in  metallic  materials,  to  the  Rice localization  criterion.  The  implementation  of  the  constitutive  modeling  is  achieved  via  a  user material (UMAT) subroutine in the commercial finiteelement code ABAQUS. Large deformations are taken into account within a three dimensional co-rotational framework. The effectiveness of the proposed  coupling  for  the  prediction  of  the  formability  of  stretched  metal  sheets  is  shown  and Forming  Limit  Diagrams  (FLDs)  are  plotted  for  an  Aluminum  alloy.  A  sensitivity  analysis  with respect to hardening parameters is carried out, andit is shown that these effects are much smaller for the case of the Rice criterion when compared toclassical criteria commonly utilized in metal forming.
</description>
<pubDate>Sun, 01 Jan 2012 00:00:00 GMT</pubDate>
<guid isPermaLink="false">http://hdl.handle.net/10985/10026</guid>
<dc:date>2012-01-01T00:00:00Z</dc:date>
<dc:creator>MANSOURI, Lotfi</dc:creator>
<dc:creator>CHALAL, Hocine</dc:creator>
<dc:creator>ABED-MERAIM, Farid</dc:creator>
<dc:creator>BALAN, Tudor</dc:creator>
<dc:description>In  this  work,  we  propose  to  couple  the  Gurson-Tvergaard-Needleman  (GTN)  model, known  for  its  widespread  use  to  describe  damage  evolution  in  metallic  materials,  to  the  Rice localization  criterion.  The  implementation  of  the  constitutive  modeling  is  achieved  via  a  user material (UMAT) subroutine in the commercial finiteelement code ABAQUS. Large deformations are taken into account within a three dimensional co-rotational framework. The effectiveness of the proposed  coupling  for  the  prediction  of  the  formability  of  stretched  metal  sheets  is  shown  and Forming  Limit  Diagrams  (FLDs)  are  plotted  for  an  Aluminum  alloy.  A  sensitivity  analysis  with respect to hardening parameters is carried out, andit is shown that these effects are much smaller for the case of the Rice criterion when compared toclassical criteria commonly utilized in metal forming.</dc:description>
</item>
<item>
<title>Efficient solid–shell finite elements for quasi-static and dynamic  analyses and their application to sheet metal forming simulation</title>
<link>http://hdl.handle.net/10985/10006</link>
<description>Efficient solid–shell finite elements for quasi-static and dynamic  analyses and their application to sheet metal forming simulation
WANG, Peng; CHALAL, Hocine; ABED-MERAIM, Farid
Thin structures are commonly designed and employedin engineering industries to save material, reduce weight and improve the overall performance of products. The finite element (FE) simulation of such thin structural components has become a powerful and useful tool in this field. For the last few decades, much attention and effort have been paid to establish accurate and efficient FE. In this regard, the solid–shell concept proved to be very attractive due to its multiple advantages. Several treatments are additionally applied to the  formulation of solid–shell elements to avoid all locking  phenomena  and  to  guarantee  the  accuracy  and efficiency  during  the  simulation  of  thin structures. The current contribution presents a family  of  prismatic  and  hexahedral  assumed-strain  based solid–shell elements, in which an arbitrary number of integration points are distributed along the thickness direction. Both linear and quadratic formulations of the solid–shell family elements are implemented into ABAQUS static/implicit and dynamic/explicit software to model thin 3D problems with only a single layer through the thickness. Twopopular benchmark tests are first conducted, in both static and dynamic analyses, for validation purposes. Then, attention is focused on a complex sheet metal forming process involving large strain,plasticity and contact.
</description>
<pubDate>Thu, 01 Jan 2015 00:00:00 GMT</pubDate>
<guid isPermaLink="false">http://hdl.handle.net/10985/10006</guid>
<dc:date>2015-01-01T00:00:00Z</dc:date>
<dc:creator>WANG, Peng</dc:creator>
<dc:creator>CHALAL, Hocine</dc:creator>
<dc:creator>ABED-MERAIM, Farid</dc:creator>
<dc:description>Thin structures are commonly designed and employedin engineering industries to save material, reduce weight and improve the overall performance of products. The finite element (FE) simulation of such thin structural components has become a powerful and useful tool in this field. For the last few decades, much attention and effort have been paid to establish accurate and efficient FE. In this regard, the solid–shell concept proved to be very attractive due to its multiple advantages. Several treatments are additionally applied to the  formulation of solid–shell elements to avoid all locking  phenomena  and  to  guarantee  the  accuracy  and efficiency  during  the  simulation  of  thin structures. The current contribution presents a family  of  prismatic  and  hexahedral  assumed-strain  based solid–shell elements, in which an arbitrary number of integration points are distributed along the thickness direction. Both linear and quadratic formulations of the solid–shell family elements are implemented into ABAQUS static/implicit and dynamic/explicit software to model thin 3D problems with only a single layer through the thickness. Twopopular benchmark tests are first conducted, in both static and dynamic analyses, for validation purposes. Then, attention is focused on a complex sheet metal forming process involving large strain,plasticity and contact.</dc:description>
</item>
<item>
<title>Prediction of strain localization during sheet metal forming using bifurcation analysis and Gurson-type damage</title>
<link>http://hdl.handle.net/10985/10014</link>
<description>Prediction of strain localization during sheet metal forming using bifurcation analysis and Gurson-type damage
MANSOURI, Lotfi; CHALAL, Hocine; ABED-MERAIM, Farid; BALAN, Tudor
The strain localization phenomenon that may occur during sheet metal forming represents a major cause of defective parts produced in the industry. Several instability criteria have been developed in the literature to predict the occurrence of these instabilities. The proposed work aims to couple a Gurson-type model to the Rice’s localization criterion. The implementation of the modeling is achieved via a user subroutine (Umat) in Abaqus/std using a Runge-Kutta explicit integration scheme. Finally, we show the effectiveness of the proposed coupling for the prediction of the formability of stretched metal sheets.
</description>
<pubDate>Sat, 01 Jan 2011 00:00:00 GMT</pubDate>
<guid isPermaLink="false">http://hdl.handle.net/10985/10014</guid>
<dc:date>2011-01-01T00:00:00Z</dc:date>
<dc:creator>MANSOURI, Lotfi</dc:creator>
<dc:creator>CHALAL, Hocine</dc:creator>
<dc:creator>ABED-MERAIM, Farid</dc:creator>
<dc:creator>BALAN, Tudor</dc:creator>
<dc:description>The strain localization phenomenon that may occur during sheet metal forming represents a major cause of defective parts produced in the industry. Several instability criteria have been developed in the literature to predict the occurrence of these instabilities. The proposed work aims to couple a Gurson-type model to the Rice’s localization criterion. The implementation of the modeling is achieved via a user subroutine (Umat) in Abaqus/std using a Runge-Kutta explicit integration scheme. Finally, we show the effectiveness of the proposed coupling for the prediction of the formability of stretched metal sheets.</dc:description>
</item>
<item>
<title>Quadratic solid–shell finite elements for geometrically nonlinear analysis of functionally graded material plates</title>
<link>http://hdl.handle.net/10985/17476</link>
<description>Quadratic solid–shell finite elements for geometrically nonlinear analysis of functionally graded material plates
CHALAL, Hocine; ABED-MERAIM, Farid
In the current contribution, prismatic and hexahedral quadratic solid–shell (SHB) finite elements are proposed for the geometrically nonlinear analysis of thin structures made of functionally graded material (FGM). The proposed SHB finite elements are developed within a purely 3D framework, with displacements as the only degrees of freedom. Also, the in-plane reduced-integration technique is combined with the assumed-strain method to alleviate various locking phenomena. Furthermore, an arbitrary number of integration points are placed along a special direction, which represents the thickness. The developed elements are coupled with functionally graded behavior for the modeling of thin FGM plates. To this end, the Young modulus of the FGM plate is assumed to vary gradually in the thickness direction, according to a volume fraction distribution. The resulting formulations are implemented into the quasi-static ABAQUS/Standard finite element software in the framework of large displacements and rotations. Popular nonlinear benchmark problems are considered to assess the performance and accuracy of the proposed SHB elements. Comparisons with reference solutions from the literature demonstrate the good capabilities of the developed SHB elements for the 3D simulation of thin FGM plates.
</description>
<pubDate>Mon, 01 Jan 2018 00:00:00 GMT</pubDate>
<guid isPermaLink="false">http://hdl.handle.net/10985/17476</guid>
<dc:date>2018-01-01T00:00:00Z</dc:date>
<dc:creator>CHALAL, Hocine</dc:creator>
<dc:creator>ABED-MERAIM, Farid</dc:creator>
<dc:description>In the current contribution, prismatic and hexahedral quadratic solid–shell (SHB) finite elements are proposed for the geometrically nonlinear analysis of thin structures made of functionally graded material (FGM). The proposed SHB finite elements are developed within a purely 3D framework, with displacements as the only degrees of freedom. Also, the in-plane reduced-integration technique is combined with the assumed-strain method to alleviate various locking phenomena. Furthermore, an arbitrary number of integration points are placed along a special direction, which represents the thickness. The developed elements are coupled with functionally graded behavior for the modeling of thin FGM plates. To this end, the Young modulus of the FGM plate is assumed to vary gradually in the thickness direction, according to a volume fraction distribution. The resulting formulations are implemented into the quasi-static ABAQUS/Standard finite element software in the framework of large displacements and rotations. Popular nonlinear benchmark problems are considered to assess the performance and accuracy of the proposed SHB elements. Comparisons with reference solutions from the literature demonstrate the good capabilities of the developed SHB elements for the 3D simulation of thin FGM plates.</dc:description>
</item>
<item>
<title>Quadratic prismatic and hexahedral solid‒shell elements for geometric nonlinear analysis of laminated composite structures</title>
<link>http://hdl.handle.net/10985/17481</link>
<description>Quadratic prismatic and hexahedral solid‒shell elements for geometric nonlinear analysis of laminated composite structures
WANG, Peng; CHALAL, Hocine; ABED-MERAIM, Farid
The current contribution proposes two quadratic, prismatic and hexahedral, solid–shell elements for the geometric nonlinear analysis of laminated composite structures. The formulation of the proposed solid–shell elements is based on a fully three-dimensional approach combining the assumed-strain method and the reduced-integration technique. In particular, only translational degrees of freedom are considered in the formulation and a preferential direction is chosen as the thickness direction, along which an arbitrary number of integration points are arranged. Making use of different physical local frames, these elements are coupled with fully three-dimensional orthotropic constitutive equations, which allows modeling multilayered composite structures with only a single element layer through the thickness. A series of popular nonlinear benchmark tests for laminated composite structures is performed to assess the performance of the proposed SHB elements. Compared to reference solutions taken from the literature, the results provided by the SHB elements show excellent agreement. Moreover, on the whole, the proposed SHB elements perform better than state-of-the-art ABAQUS elements, which have the same geometry and kinematics, using comparable mesh discretizations.
</description>
<pubDate>Sun, 01 Jan 2017 00:00:00 GMT</pubDate>
<guid isPermaLink="false">http://hdl.handle.net/10985/17481</guid>
<dc:date>2017-01-01T00:00:00Z</dc:date>
<dc:creator>WANG, Peng</dc:creator>
<dc:creator>CHALAL, Hocine</dc:creator>
<dc:creator>ABED-MERAIM, Farid</dc:creator>
<dc:description>The current contribution proposes two quadratic, prismatic and hexahedral, solid–shell elements for the geometric nonlinear analysis of laminated composite structures. The formulation of the proposed solid–shell elements is based on a fully three-dimensional approach combining the assumed-strain method and the reduced-integration technique. In particular, only translational degrees of freedom are considered in the formulation and a preferential direction is chosen as the thickness direction, along which an arbitrary number of integration points are arranged. Making use of different physical local frames, these elements are coupled with fully three-dimensional orthotropic constitutive equations, which allows modeling multilayered composite structures with only a single element layer through the thickness. A series of popular nonlinear benchmark tests for laminated composite structures is performed to assess the performance of the proposed SHB elements. Compared to reference solutions taken from the literature, the results provided by the SHB elements show excellent agreement. Moreover, on the whole, the proposed SHB elements perform better than state-of-the-art ABAQUS elements, which have the same geometry and kinematics, using comparable mesh discretizations.</dc:description>
</item>
<item>
<title>Linear and Quadratic Solid-Shell Elements for Quasi-Static and Dynamic Simulations of Thin 3D Structures: Application to a Deep Drawing Process</title>
<link>http://hdl.handle.net/10985/17479</link>
<description>Linear and Quadratic Solid-Shell Elements for Quasi-Static and Dynamic Simulations of Thin 3D Structures: Application to a Deep Drawing Process
WANG, Peng; CHALAL, Hocine; ABED-MERAIM, Farid
A family of prismatic and hexahedral solid–shell (SHB) elements, with their linear and quadratic versions, is proposed in this work to model thin structures. The formulation of these SHB elements is extended to explicit dynamic analysis and large-strain anisotropic plasticity on the basis of a fully three-dimensional approach using an arbitrary number of integration points along the thickness direction. Several special treatments are applied to the SHB elements in order to avoid all locking phenomena and to guarantee the accuracy and efficiency of the simulations. These solid-shell elements have been implemented into ABAQUS standard/quasi-static and explicit/dynamic software packages. A number of static and dynamic benchmark problems, as well as a simulation of the deep drawing of a cylindrical cup, have been conducted to assess the performance of these SHB elements.
</description>
<pubDate>Sun, 01 Jan 2017 00:00:00 GMT</pubDate>
<guid isPermaLink="false">http://hdl.handle.net/10985/17479</guid>
<dc:date>2017-01-01T00:00:00Z</dc:date>
<dc:creator>WANG, Peng</dc:creator>
<dc:creator>CHALAL, Hocine</dc:creator>
<dc:creator>ABED-MERAIM, Farid</dc:creator>
<dc:description>A family of prismatic and hexahedral solid–shell (SHB) elements, with their linear and quadratic versions, is proposed in this work to model thin structures. The formulation of these SHB elements is extended to explicit dynamic analysis and large-strain anisotropic plasticity on the basis of a fully three-dimensional approach using an arbitrary number of integration points along the thickness direction. Several special treatments are applied to the SHB elements in order to avoid all locking phenomena and to guarantee the accuracy and efficiency of the simulations. These solid-shell elements have been implemented into ABAQUS standard/quasi-static and explicit/dynamic software packages. A number of static and dynamic benchmark problems, as well as a simulation of the deep drawing of a cylindrical cup, have been conducted to assess the performance of these SHB elements.</dc:description>
</item>
<item>
<title>Prediction of necking in thin sheet metals using an elastic‒plastic model coupled with ductile damage and bifurcation criteria</title>
<link>http://hdl.handle.net/10985/17483</link>
<description>Prediction of necking in thin sheet metals using an elastic‒plastic model coupled with ductile damage and bifurcation criteria
BOUKTIR, Yasser; CHALAL, Hocine; ABED-MERAIM, Farid
In this paper, the conditions for the occurrence of diffuse and localized necking in thin sheet metals are investigated. The prediction of these necking phenomena is undertaken using an elastic‒plastic model coupled with ductile damage, which is then combined with various plastic instability criteria based on bifurcation theory. The bifurcation criteria are first formulated within a general three-dimensional modeling framework, and then specialized to the particular case of plane-stress conditions. Some theoretical relationships or links between the different investigated bifurcation criteria are established, which allows a hierarchical classification in terms of their conservative character in predicting critical necking strains. The resulting numerical tool is implemented into the finite element code ABAQUS/Standard to predict forming limit diagrams (FLDs), in both situations of a fully three-dimensional formulation and a plane-stress framework. The proposed approach is then applied to the prediction of diffuse and localized necking for a DC06 mild steel material. The predicted FLDs confirm the above-established theoretical classification, revealing that the general bifurcation criterion provides a lower bound for diffuse necking prediction, while the loss of ellipticity criterion represents an upper bound for localized necking prediction. Some numerical aspects related to the prestrain effect on the development of necking are also investigated, which demonstrates the capability of the present approach in capturing the strain-path changes commonly encountered in complex sheet metal forming operations.
</description>
<pubDate>Mon, 01 Jan 2018 00:00:00 GMT</pubDate>
<guid isPermaLink="false">http://hdl.handle.net/10985/17483</guid>
<dc:date>2018-01-01T00:00:00Z</dc:date>
<dc:creator>BOUKTIR, Yasser</dc:creator>
<dc:creator>CHALAL, Hocine</dc:creator>
<dc:creator>ABED-MERAIM, Farid</dc:creator>
<dc:description>In this paper, the conditions for the occurrence of diffuse and localized necking in thin sheet metals are investigated. The prediction of these necking phenomena is undertaken using an elastic‒plastic model coupled with ductile damage, which is then combined with various plastic instability criteria based on bifurcation theory. The bifurcation criteria are first formulated within a general three-dimensional modeling framework, and then specialized to the particular case of plane-stress conditions. Some theoretical relationships or links between the different investigated bifurcation criteria are established, which allows a hierarchical classification in terms of their conservative character in predicting critical necking strains. The resulting numerical tool is implemented into the finite element code ABAQUS/Standard to predict forming limit diagrams (FLDs), in both situations of a fully three-dimensional formulation and a plane-stress framework. The proposed approach is then applied to the prediction of diffuse and localized necking for a DC06 mild steel material. The predicted FLDs confirm the above-established theoretical classification, revealing that the general bifurcation criterion provides a lower bound for diffuse necking prediction, while the loss of ellipticity criterion represents an upper bound for localized necking prediction. Some numerical aspects related to the prestrain effect on the development of necking are also investigated, which demonstrates the capability of the present approach in capturing the strain-path changes commonly encountered in complex sheet metal forming operations.</dc:description>
</item>
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