Application of Dimension Extending Technique to Unified Hardening Model

This paper provides the process of incremental constitutive integration for the unified hardening model combined with the transformation stress method. The dimension-extending technique takes the hardening function of the hardening/softening model as the same position as the stress components, so th...

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Published in:	Applied sciences Vol. 14; no. 13; p. 5677
Main Authors:	Chen, Qian, Zheng, Hong, Tian, Dongshuai
Format:	Journal Article
Language:	English
Published:	Basel MDPI AG 01.07.2024
Subjects:	Accuracy Algorithms backward Euler integration constitutive integration dimension-extending technique Gauss–Seidel based Projection–Correction mixed complementarity problem Numerical analysis Ordinary differential equations unified hardening model
ISSN:	2076-3417, 2076-3417
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Abstract	This paper provides the process of incremental constitutive integration for the unified hardening model combined with the transformation stress method. The dimension-extending technique takes the hardening function of the hardening/softening model as the same position as the stress components, so that the constitutive integration of the plasticity can be reduced to an initial value problem of differential–complementarity equations, which is solved using the Gauss–Seidel algorithm-based Projection–Correction for the mixed complementarity problem. The Gauss–Seidel based Projection–Correction algorithm does not require the calculation of the Jacobean matrix of the potential function, making it relatively easy to implement in programming. The unified hardening model is proposed based on the modified Cam–Clay model and the sub-loading surface model, and the elastic properties are pressure-dependent. Two processing methods, backward Euler integration and exact elastic property, are used for the variable elasticity properties. The constitutive integration of the increased dimensional unified hardening model is reduced to a special mixed complementarity problem and solved by the proposed algorithm, which does not need to calculate the Jacobean matrix of the potential function, and greatly simplifies the derivation process. Several numerical examples are given to verify the feasibility of the incremental constitutive integration in the unified hardening model, including the single integral point and the boundary value problems. The research results have expanded the scope of use of the Gauss–Seidel based Projection–Correction algorithm.
AbstractList	This paper provides the process of incremental constitutive integration for the unified hardening model combined with the transformation stress method. The dimension-extending technique takes the hardening function of the hardening/softening model as the same position as the stress components, so that the constitutive integration of the plasticity can be reduced to an initial value problem of differential–complementarity equations, which is solved using the Gauss–Seidel algorithm-based Projection–Correction for the mixed complementarity problem. The Gauss–Seidel based Projection–Correction algorithm does not require the calculation of the Jacobean matrix of the potential function, making it relatively easy to implement in programming. The unified hardening model is proposed based on the modified Cam–Clay model and the sub-loading surface model, and the elastic properties are pressure-dependent. Two processing methods, backward Euler integration and exact elastic property, are used for the variable elasticity properties. The constitutive integration of the increased dimensional unified hardening model is reduced to a special mixed complementarity problem and solved by the proposed algorithm, which does not need to calculate the Jacobean matrix of the potential function, and greatly simplifies the derivation process. Several numerical examples are given to verify the feasibility of the incremental constitutive integration in the unified hardening model, including the single integral point and the boundary value problems. The research results have expanded the scope of use of the Gauss–Seidel based Projection–Correction algorithm.
Author	Tian, Dongshuai Zheng, Hong Chen, Qian
Author_xml	– sequence: 1 givenname: Qian surname: Chen fullname: Chen, Qian – sequence: 2 givenname: Hong surname: Zheng fullname: Zheng, Hong – sequence: 3 givenname: Dongshuai surname: Tian fullname: Tian, Dongshuai
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SubjectTerms	Accuracy Algorithms backward Euler integration constitutive integration dimension-extending technique Gauss–Seidel based Projection–Correction mixed complementarity problem Numerical analysis Ordinary differential equations unified hardening model
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Title	Application of Dimension Extending Technique to Unified Hardening Model
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