Details
| Original language | English |
|---|---|
| Article number | 116418 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 417 |
| Early online date | 15 Sept 2023 |
| Publication status | Published - 1 Dec 2023 |
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
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 417, 116418, 01.12.2023.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A return mapping algorithm based on the hyper dual step derivative approximation for elastoplastic models
AU - Zhou, Xin
AU - Shi, Anyu
AU - Lu, Dechun
AU - Zhuang, Xiaoying
AU - Lu, Xinzheng
AU - Du, Xiuli
AU - Chen, Yun
N1 - 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 ).
PY - 2023/12/1
Y1 - 2023/12/1
N2 - 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.
AB - 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.
KW - Consistent tangent operator
KW - Hyper dual step approximation
KW - Line search method
KW - Plastic model
KW - Stress update algorithm
UR - http://www.scopus.com/inward/record.url?scp=85171345529&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2023.116418
DO - 10.1016/j.cma.2023.116418
M3 - Article
AN - SCOPUS:85171345529
VL - 417
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
M1 - 116418
ER -