Return mapping algorithm in principal space for general isotropic elastoplasticity involving multi-surface plasticity and combined isotropic-kinematic hardening within finite deformation framework

The compatibility with complicated elastoplasticity and efficiency of the constitutive integration algorithm both significantly influence the performance of finite element analysis for engineering practical problems. In this work, a numerical integration algorithm in principal space is proposed for...

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Published in:	Finite elements in analysis and design Vol. 150; pp. 1 - 19
Main Authors:	Meng, Chunyu, Tang, Zhengjun, Chen, Mingxiang, Peng, Qi
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 01.10.2018 Elsevier BV
Subjects:	Algorithms Combined hardening Compatibility Constitutive models Deformation Elasticity Elastoplasticity Finite element analysis Finite element method Finite strain elastoplasticity Hardening Kinematics Mapping Mathematical analysis Mathematical models Multi-surface plasticity Numerical integration Operators (mathematics) Plastic flow Plastic properties Representation theorem Return mapping algorithm Combined hardening Representation theorem Finite strain elastoplasticity Multi-surface plasticity Return mapping algorithm
ISSN:	0168-874X, 1872-6925
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Abstract	The compatibility with complicated elastoplasticity and efficiency of the constitutive integration algorithm both significantly influence the performance of finite element analysis for engineering practical problems. In this work, a numerical integration algorithm in principal space is proposed for general isotropic elastoplastic constitutive models that involve multi-surface plasticity with corners in the yield surface and combined isotropic-kinematic hardening law as well as nonlinear elasticity within the framework of finite deformation. For the multi-surface plasticity, a strategy, which uses the mid-direction of two plastic flow directions at a corner as the border of critical regions, is proposed to predict the yield functions activated in the return mapping iterations, making the prediction procedure simpler. By making use of the relative stress, the combined isotropic-kinematic hardening law is incorporated into the numerical integration algorithm in principal space. The consistent tangent operator is also derived. Besides, the fully implicit return mapping algorithm based on representation theorem is employed. The expressions of the first and second derivatives of yield/potential function, which are frequently evaluated in the algorithm, maintain a simple form and reduce the computational cost. Solution of finite element practical problems demonstrates that compatibility and efficiency of the constitutive integration algorithm are improved while accuracy is retained. •A numerical integration algorithm in principal space is proposed for general isotropic elastoplastic constitutive models.•A simpler strategy for predicting multi yield surface activation in the return mapping iterations is proposed.•Combined isotropic-kinematic hardening is incorporated into principal space algorithm along with multi-surface plasticity.•Compatibility and efficiency of the constitutive integration algorithm are improved while accuracy is retained.
AbstractList	The compatibility with complicated elastoplasticity and efficiency of the constitutive integration algorithm both significantly influence the performance of finite element analysis for engineering practical problems. In this work, a numerical integration algorithm in principal space is proposed for general isotropic elastoplastic constitutive models that involve multi-surface plasticity with corners in the yield surface and combined isotropic-kinematic hardening law as well as nonlinear elasticity within the framework of finite deformation. For the multi-surface plasticity, a strategy, which uses the mid-direction of two plastic flow directions at a corner as the border of critical regions, is proposed to predict the yield functions activated in the return mapping iterations, making the prediction procedure simpler. By making use of the relative stress, the combined isotropic-kinematic hardening law is incorporated into the numerical integration algorithm in principal space. The consistent tangent operator is also derived. Besides, the fully implicit return mapping algorithm based on representation theorem is employed. The expressions of the first and second derivatives of yield/potential function, which are frequently evaluated in the algorithm, maintain a simple form and reduce the computational cost. Solution of finite element practical problems demonstrates that compatibility and efficiency of the constitutive integration algorithm are improved while accuracy is retained. The compatibility with complicated elastoplasticity and efficiency of the constitutive integration algorithm both significantly influence the performance of finite element analysis for engineering practical problems. In this work, a numerical integration algorithm in principal space is proposed for general isotropic elastoplastic constitutive models that involve multi-surface plasticity with corners in the yield surface and combined isotropic-kinematic hardening law as well as nonlinear elasticity within the framework of finite deformation. For the multi-surface plasticity, a strategy, which uses the mid-direction of two plastic flow directions at a corner as the border of critical regions, is proposed to predict the yield functions activated in the return mapping iterations, making the prediction procedure simpler. By making use of the relative stress, the combined isotropic-kinematic hardening law is incorporated into the numerical integration algorithm in principal space. The consistent tangent operator is also derived. Besides, the fully implicit return mapping algorithm based on representation theorem is employed. The expressions of the first and second derivatives of yield/potential function, which are frequently evaluated in the algorithm, maintain a simple form and reduce the computational cost. Solution of finite element practical problems demonstrates that compatibility and efficiency of the constitutive integration algorithm are improved while accuracy is retained. •A numerical integration algorithm in principal space is proposed for general isotropic elastoplastic constitutive models.•A simpler strategy for predicting multi yield surface activation in the return mapping iterations is proposed.•Combined isotropic-kinematic hardening is incorporated into principal space algorithm along with multi-surface plasticity.•Compatibility and efficiency of the constitutive integration algorithm are improved while accuracy is retained.
Author	Peng, Qi Chen, Mingxiang Tang, Zhengjun Meng, Chunyu
Author_xml	– sequence: 1 givenname: Chunyu surname: Meng fullname: Meng, Chunyu – sequence: 2 givenname: Zhengjun surname: Tang fullname: Tang, Zhengjun – sequence: 3 givenname: Mingxiang surname: Chen fullname: Chen, Mingxiang – sequence: 4 givenname: Qi surname: Peng fullname: Peng, Qi email: pearqiqi@whu.edu.cn
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Cites_doi	10.1002/nag.179 10.1090/qam/59769 10.1016/j.compstruc.2007.04.002 10.1002/nag.231 10.1016/j.compstruc.2006.10.001 10.1002/zamm.19950750410 10.1016/j.compstruc.2011.11.006 10.1061/(ASCE)0733-9399(1990)116:8(1764) 10.1002/nag.2244 10.1002/nme.970 10.1063/1.1708953 10.1016/S0020-7683(03)00155-0 10.1016/S0022-5096(00)00023-5
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Keywords	Combined hardening Representation theorem Finite strain elastoplasticity Multi-surface plasticity Return mapping algorithm
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Snippet	The compatibility with complicated elastoplasticity and efficiency of the constitutive integration algorithm both significantly influence the performance of...
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SubjectTerms	Algorithms Combined hardening Compatibility Constitutive models Deformation Elasticity Elastoplasticity Finite element analysis Finite element method Finite strain elastoplasticity Hardening Kinematics Mapping Mathematical analysis Mathematical models Multi-surface plasticity Numerical integration Operators (mathematics) Plastic flow Plastic properties Representation theorem Return mapping algorithm
Title	Return mapping algorithm in principal space for general isotropic elastoplasticity involving multi-surface plasticity and combined isotropic-kinematic hardening within finite deformation framework
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