Implicit numerical integration of highly nonlinear plasticity models. (April 2021)

• Record Type: Journal Article
• Authors: Geng, Dajiang; Dai, Ning; Guo, Peijun; Zhou, Shunhua; Di, Honggui
• Is Part Of: Computers and geotechnics. Volume 132(2021)
• Publication Date: 2021-04
• Subjects: Highly nonlinear -- Elasto-plastic constitutive models -- Implicit numerical integration -- Homotopy continuation method -- Conjugate gradient method -- Two-stage iterative algorithm; Engineering geology -- Data processing -- Periodicals; Soil mechanics -- Data processing -- Periodicals; Rock mechanics -- Data processing -- Periodicals; 624.1510285
• DOI: 10.1016/j.compgeo.2020.103961
• Languages: English
• ISSNs: 0266-352X

Abstract

Abstract: When using an implicit numerical integration algorithm to implement a highly nonlinear elasto-plastic constitutive models in FEM simulations, some difficulties would encounter including Jacobian matrix singularity and non-convergence. Based on the composition of the elastoplastic constitutive model and the characteristics of the traditional implicit algorithms, this paper proposes three improved implicit algorithms, namely the Homotopy-Newton-CPPM algorithm, the CG-Newton-CPPM algorithm and the two-stage algorithm, which would contribute to improve the convergence and deal with singularity of the Jacobian matrix. Besides, the convergence and the computational efficiency as well as the accuracy of five algorithms, including a conventional explicit algorithm, a conventional implicit algorithm and three improved implicit algorithms, are compared with reference to numerical simulations of single element tests and multi-element analysis.