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 -