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

authored by: Yi Fan Wang, Xiao Wei Gao, Bing Bing Xu, Hai Feng Peng
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.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Dalian University of Technology
Type: Article
Journal: International Journal of Non-Linear Mechanics
Volume: 175
No. of pages: 11
ISSN: 0020-7462
Publication date: 08.2025
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Mechanics of Materials, Mechanical Engineering, Applied Mathematics
Electronic version(s): https://doi.org/10.1016/j.ijnonlinmec.2025.105102 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{224232d468524cada1e9c98e918c6b11,
title = "Numerical analysis of two-dimensional elastoplastic problems based on zonal free element method",
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.",
keywords = "Elastoplastic mechanics, Isoparametric element, Nonlinear iteration, Zonal free element method",
author = "Wang, {Yi Fan} and Gao, {Xiao Wei} and Xu, {Bing Bing} and Peng, {Hai Feng}",
note = "Publisher Copyright: {\textcopyright} 2025 Elsevier Ltd",
year = "2025",
month = aug,
doi = "10.1016/j.ijnonlinmec.2025.105102",
language = "English",
volume = "175",
journal = "International Journal of Non-Linear Mechanics",
issn = "0020-7462",
publisher = "Elsevier Ltd.",
}