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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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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ISSN:0168-874X
1872-6925
DOI:10.1016/j.finel.2018.07.001