A re-formulation of extended subloading surface model for cyclic plasticity within small strain framework: hyperelastic-based formulation and fully implicit return-mapping scheme

Abstract

This paper presents a re-formulation of the extended subloading surface model within the ‘unconventional plasticity’ concept applicable to cyclic loadings. The small strain theory is adopted in the model formulation. The rate-independent von Mises plasticity with nonlinear isotropic and kinematic combined hardening is adopted as a specific prototype model. A fully-implicit stress calculation algorithm based on the return-mapping scheme for the proposed anisotropic elasto-plastic constitutive model is also developed. In addition to the usual additive decomposition of the small strain tensor into elastic and plastic parts, we primarily make a kinematic assumption in which the plastic strain tensor is further additively decomposed into an energetic and dissipative parts. This idea is a small strain counterpart of the one recently adopted in finite strain models with nonlinear kinematic hardening based on the dual multiplicative decompositions of the deformation gradient tensors. The energetic part of the plastic strain is related to the back-stress for kinematic hardening via a hyperelastic-like constitutive equation. This enables the incorporation of Armstrong–Frederick nonlinear kinematic hardening into the model without using a rate-type evolution law for the back-stress. Based on a similar idea, we introduce another additive decomposition of the plastic strain, and thereby a nonlinear evolution for the elastic-core tensor, i.e. a key internal variable in the extended subloading surface model, which stands for a stress state where the material exhibits most elastic responses, can be introduced in a reasonable way. Fundamental property of the proposed model as well as the accuracy assessment of the developed numerical algorithm is demonstrated by numerical examples. A particular attention is focused on the accuracy of stress calculation in unloading and reverse-loading processes during cyclic deformation. An issue on convergence property in Newton-type iteration for the return-mapping scheme is also discussed, and an effective initial value for iteration is proposed.