A return mapping algorithm based on the hyper dual step derivative approximation for elastoplastic models

authored by: Xin Zhou, Anyu Shi, Dechun Lu, Xiaoying Zhuang, Xinzheng Lu, Xiuli Du, Yun Chen
Abstract: Accurately evaluating derivatives poses a key challenge when numerically implementing complex constitutive models. This work presents an implicit stress update algorithm that utilizes the hyper dual step derivative approximation to address derivative evaluations in elastoplastic problems. Initially, the performance of various numerical differentiation methods is discussed and compared by examining their numerical errors in the representative example. Subsequently, the hyper dual step derivative approximation, without truncation and subtractive cancellation errors, is employed to compute the Jacobian matrix and consistent tangent operator, ensuring quadratic convergence in both local and global computations. The size of the Newton search step is optimized by the line search technique, thereby enhancing the convergence in solving nonlinear stress integral equations. Finally, the proposed stress update algorithm is used to implement the non-associated Mohr–Coulomb plastic model in the ABAQUS software using the UMAT subroutine. The stress update algorithm's performance and its practical application in geotechnical engineering problems are demonstrated using five boundary value problems.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Beijing University of Technology
Tsinghua University
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 417
ISSN: 0045-7825
Publication date: 01.12.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy, Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.cma.2023.116418 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{9dba2365bf7f4dc0af26829b5bcb0c92,
title = "A return mapping algorithm based on the hyper dual step derivative approximation for elastoplastic models",
abstract = "Accurately evaluating derivatives poses a key challenge when numerically implementing complex constitutive models. This work presents an implicit stress update algorithm that utilizes the hyper dual step derivative approximation to address derivative evaluations in elastoplastic problems. Initially, the performance of various numerical differentiation methods is discussed and compared by examining their numerical errors in the representative example. Subsequently, the hyper dual step derivative approximation, without truncation and subtractive cancellation errors, is employed to compute the Jacobian matrix and consistent tangent operator, ensuring quadratic convergence in both local and global computations. The size of the Newton search step is optimized by the line search technique, thereby enhancing the convergence in solving nonlinear stress integral equations. Finally, the proposed stress update algorithm is used to implement the non-associated Mohr–Coulomb plastic model in the ABAQUS software using the UMAT subroutine. The stress update algorithm's performance and its practical application in geotechnical engineering problems are demonstrated using five boundary value problems.",
keywords = "Consistent tangent operator, Hyper dual step approximation, Line search method, Plastic model, Stress update algorithm",
author = "Xin Zhou and Anyu Shi and Dechun Lu and Xiaoying Zhuang and Xinzheng Lu and Xiuli Du and Yun Chen",
note = "Funding Information: Support for this study is provided by the National Natural Science Foundation of China (Grant Nos., 52238011 , 52008231 , and 52025084 ), the Postdoctoral Science Foundation of China (Grant Nos., 2022M721884 ), and the National Key R&D Program of China (Grant Nos., 2022YFC3800901 ). ",
year = "2023",
month = dec,
day = "1",
doi = "10.1016/j.cma.2023.116418",
language = "English",
volume = "417",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}