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Numerical analysis of two-dimensional elastoplastic problems based on zonal free element method

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autorschaft

  • Yi Fan Wang
  • Xiao Wei Gao
  • Bing Bing Xu
  • Hai Feng Peng

Organisationseinheiten

Externe Organisationen

  • Dalian University of Technology

Details

OriginalspracheEnglisch
Aufsatznummer105102
Seitenumfang11
FachzeitschriftInternational Journal of Non-Linear Mechanics
Jahrgang175
Frühes Online-Datum1 Apr. 2025
PublikationsstatusElektronisch veröffentlicht (E-Pub) - 1 Apr. 2025

Abstract

In this paper, a weak-form numerical method, the zonal free element method (ZFrEM) is introduced to solve two-dimensional elastoplastic problems. In ZFrEM, the whole domain is divided into several sub-domains, and then a series of points are used to discretize each sub-domain. The Lagrange isoparametric element concept in the finite element method (FEM) is employed to form the collocation element for each collocation node with the neighboring points, and the system equations are generated with the point-by-point. The continuous model separates strain into elastic and plastic components, ensuring that stress variation is solely dependent on the elastic component of the strain, which is consistent with classical elasticity theory, and assuming that plastic strain is independent of stress increments, which results in a nonlinear system of equations with the coefficient matrix dependent on the current incremental stress state. For the nodes in the plastic state, a stress regression technique aligns stresses with defined yield surfaces. Three numerical examples are given to verify the accuracy and convergence of the present method for solving the elastoplastic problems.

ASJC Scopus Sachgebiete

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Numerical analysis of two-dimensional elastoplastic problems based on zonal free element method. / Wang, Yi Fan; Gao, Xiao Wei; Xu, Bing Bing et al.
in: International Journal of Non-Linear Mechanics, Jahrgang 175, 105102, 08.2025.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Wang YF, Gao XW, Xu BB, Peng HF. Numerical analysis of two-dimensional elastoplastic problems based on zonal free element method. International Journal of Non-Linear Mechanics. 2025 Aug;175:105102. Epub 2025 Apr 1. doi: 10.1016/j.ijnonlinmec.2025.105102
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abstract = "In this paper, a weak-form numerical method, the zonal free element method (ZFrEM) is introduced to solve two-dimensional elastoplastic problems. In ZFrEM, the whole domain is divided into several sub-domains, and then a series of points are used to discretize each sub-domain. The Lagrange isoparametric element concept in the finite element method (FEM) is employed to form the collocation element for each collocation node with the neighboring points, and the system equations are generated with the point-by-point. The continuous model separates strain into elastic and plastic components, ensuring that stress variation is solely dependent on the elastic component of the strain, which is consistent with classical elasticity theory, and assuming that plastic strain is independent of stress increments, which results in a nonlinear system of equations with the coefficient matrix dependent on the current incremental stress state. For the nodes in the plastic state, a stress regression technique aligns stresses with defined yield surfaces. Three numerical examples are given to verify the accuracy and convergence of the present method for solving the elastoplastic problems.",
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AU - Wang, Yi Fan

AU - Gao, Xiao Wei

AU - Xu, Bing Bing

AU - Peng, Hai Feng

N1 - Publisher Copyright: © 2025 Elsevier Ltd

PY - 2025/4/1

Y1 - 2025/4/1

N2 - In this paper, a weak-form numerical method, the zonal free element method (ZFrEM) is introduced to solve two-dimensional elastoplastic problems. In ZFrEM, the whole domain is divided into several sub-domains, and then a series of points are used to discretize each sub-domain. The Lagrange isoparametric element concept in the finite element method (FEM) is employed to form the collocation element for each collocation node with the neighboring points, and the system equations are generated with the point-by-point. The continuous model separates strain into elastic and plastic components, ensuring that stress variation is solely dependent on the elastic component of the strain, which is consistent with classical elasticity theory, and assuming that plastic strain is independent of stress increments, which results in a nonlinear system of equations with the coefficient matrix dependent on the current incremental stress state. For the nodes in the plastic state, a stress regression technique aligns stresses with defined yield surfaces. Three numerical examples are given to verify the accuracy and convergence of the present method for solving the elastoplastic problems.

AB - In this paper, a weak-form numerical method, the zonal free element method (ZFrEM) is introduced to solve two-dimensional elastoplastic problems. In ZFrEM, the whole domain is divided into several sub-domains, and then a series of points are used to discretize each sub-domain. The Lagrange isoparametric element concept in the finite element method (FEM) is employed to form the collocation element for each collocation node with the neighboring points, and the system equations are generated with the point-by-point. The continuous model separates strain into elastic and plastic components, ensuring that stress variation is solely dependent on the elastic component of the strain, which is consistent with classical elasticity theory, and assuming that plastic strain is independent of stress increments, which results in a nonlinear system of equations with the coefficient matrix dependent on the current incremental stress state. For the nodes in the plastic state, a stress regression technique aligns stresses with defined yield surfaces. Three numerical examples are given to verify the accuracy and convergence of the present method for solving the elastoplastic problems.

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