Numerical implementation of modified Chaboche kinematic hardening model for multiaxial ratcheting

•Implicit numerical implementation of the modified Chaboche model is discussed.•By using Voigt notations, all equations in numerical algorithm are solved by matrix operations.•Transition of the fourth hardening rule is reflected in the iterative calculation process.•A simple way for verification of...

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Vydáno v:	Computers & structures Ročník 231; s. 106222
Hlavní autoři:	Han, Jungmoo, Marimuthu, Karuppasamy Pandian, Koo, Sungyong, Lee, Hyungyil
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York Elsevier Ltd 15.04.2020 Elsevier BV
Témata:	Algorithms Computer simulation Constitutive relationships Evanescence Exact solutions Finite element analysis Finite element method Hardening Implicit radial return method Indentation Kinematics Mathematical models Modified Chaboche model Multiaxial cyclic plasticity Numerical implementation Numerical integration Ratcheting Strain Stress analysis Modified Chaboche model Implicit radial return method Finite element analysis Multiaxial cyclic plasticity Numerical implementation
ISSN:	0045-7949, 1879-2243
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Abstract	•Implicit numerical implementation of the modified Chaboche model is discussed.•By using Voigt notations, all equations in numerical algorithm are solved by matrix operations.•Transition of the fourth hardening rule is reflected in the iterative calculation process.•A simple way for verification of consistent tangent operator is presented.•Cyclic indentation test is simulated as a numerical example of multiaxial ratcheting. For simulating multiaxial ratcheting behavior, the modified Chaboche kinematic hardening model was numerically implemented by using the framework of a small-strain elastic-plastic theory. Unlike early models, this improved multiaxial model is difficult to implement using finite element methods owing to its complicated constitutive relations, such as radial evanescence terms and the fourth hardening rule with a threshold. We present an effective procedure for numerical implementation using Voigt notations and the implicit radial return method with Newton-Raphson iterations. All the equations of constitute numerical integration and consistent tangent operator (CTO) are simply solved using matrix operations. The integration algorithm is validated by using both numerical examples and analytical solutions. The CTO is verified by additional stress calculations. The model detects variations in the cyclic indentation response with changes in a multiaxial-dependent parameter. The numerical implementation allows simulations of both biaxial and general multiaxial ratcheting behaviors.
AbstractList	For simulating multiaxial ratcheting behavior, the modified Chaboche kinematic hardening model was numerically implemented by using the framework of a small-strain elastic-plastic theory. Unlike early models, this improved multiaxial model is difficult to implement using finite element methods owing to its complicated constitutive relations, such as radial evanescence terms and the fourth hardening rule with a threshold. We present an effective procedure for numerical implementation using Voigt notations and the implicit radial return method with Newton-Raphson iterations. All the equations of constitute numerical integration and consistent tangent operator (CTO) are simply solved using matrix operations. The integration algorithm is validated by using both numerical examples and analytical solutions. The CTO is verified by additional stress calculations. The model detects variations in the cyclic indentation response with changes in a multiaxial-dependent parameter. The numerical implementation allows simulations of both biaxial and general multiaxial ratcheting behaviors. •Implicit numerical implementation of the modified Chaboche model is discussed.•By using Voigt notations, all equations in numerical algorithm are solved by matrix operations.•Transition of the fourth hardening rule is reflected in the iterative calculation process.•A simple way for verification of consistent tangent operator is presented.•Cyclic indentation test is simulated as a numerical example of multiaxial ratcheting. For simulating multiaxial ratcheting behavior, the modified Chaboche kinematic hardening model was numerically implemented by using the framework of a small-strain elastic-plastic theory. Unlike early models, this improved multiaxial model is difficult to implement using finite element methods owing to its complicated constitutive relations, such as radial evanescence terms and the fourth hardening rule with a threshold. We present an effective procedure for numerical implementation using Voigt notations and the implicit radial return method with Newton-Raphson iterations. All the equations of constitute numerical integration and consistent tangent operator (CTO) are simply solved using matrix operations. The integration algorithm is validated by using both numerical examples and analytical solutions. The CTO is verified by additional stress calculations. The model detects variations in the cyclic indentation response with changes in a multiaxial-dependent parameter. The numerical implementation allows simulations of both biaxial and general multiaxial ratcheting behaviors.
ArticleNumber	106222
Author	Han, Jungmoo Marimuthu, Karuppasamy Pandian Koo, Sungyong Lee, Hyungyil
Author_xml	– sequence: 1 givenname: Jungmoo surname: Han fullname: Han, Jungmoo – sequence: 2 givenname: Karuppasamy Pandian surname: Marimuthu fullname: Marimuthu, Karuppasamy Pandian – sequence: 3 givenname: Sungyong surname: Koo fullname: Koo, Sungyong – sequence: 4 givenname: Hyungyil surname: Lee fullname: Lee, Hyungyil email: hylee@sogang.ac.kr
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CitedBy_id	crossref_primary_10_1016_j_engappai_2023_106724 crossref_primary_10_1016_j_ijmecsci_2021_106336 crossref_primary_10_1016_j_jobe_2021_102168 crossref_primary_10_1016_j_jobe_2023_106151 crossref_primary_10_1016_j_mechmat_2024_105184 crossref_primary_10_1016_j_jcsr_2021_106738 crossref_primary_10_1016_j_enganabound_2024_02_019 crossref_primary_10_1016_j_jmrt_2025_06_048 crossref_primary_10_1016_j_microrel_2024_115441 crossref_primary_10_1016_j_ijplas_2022_103503
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Keywords	Modified Chaboche model Implicit radial return method Finite element analysis Multiaxial cyclic plasticity Numerical implementation
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Snippet	•Implicit numerical implementation of the modified Chaboche model is discussed.•By using Voigt notations, all equations in numerical algorithm are solved by... For simulating multiaxial ratcheting behavior, the modified Chaboche kinematic hardening model was numerically implemented by using the framework of a...
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SubjectTerms	Algorithms Computer simulation Constitutive relationships Evanescence Exact solutions Finite element analysis Finite element method Hardening Implicit radial return method Indentation Kinematics Mathematical models Modified Chaboche model Multiaxial cyclic plasticity Numerical implementation Numerical integration Ratcheting Strain Stress analysis
Title	Numerical implementation of modified Chaboche kinematic hardening model for multiaxial ratcheting
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