Integration of nonlinear mixed hardening models

Abstract

Purpose -The purpose of this paper is to present a new effective integration method for cyclic plasticity models. Design/methodology/approach -By defining an integrating factor and an augmented stress vector, the system of differential equations of the constitutive model is converted into a nonlinear dynamical system, which could be solved by an exponential map algorithm. Findings -The numerical tests show the robustness and high efficiency of the proposed integration scheme.Research limitations/implications -The von-Mises yield criterion in the regime of small deformation is assumed. In addition, the model obeys a general nonlinear kinematic hardening and an exponential isotropic hardening. Practical implications -Integrating the constitutive equations in order to update the material state is one of the most important steps in a nonlinear finite element analysis. The accuracy of the integration method could directly influence the result of the elastoplastic analyses. Originality/value -The paper deals with integrating the constitutive equations in a nonlinear finite element analysis. This subject could be interesting for the academy as well as industry. The proposed exponential-based integration method is more efficient than the classical strategies.

Computational Studies for the Yield-Point Phenomenon of Metals

“…Associated with the well-known radial return mapping in stress integration presented by Wilkins [58], many research subjects such as consistent tangent operator, iso-error map, and integration stability were studied [59][60][61]. Recently introduced exponential map based stress integration schemes showed their robustness [62][63][64][65]. However, these studies were hardly utilized to overcome the non-convergent issues in YPP applications.…”

A nonlinear constitutive model for whole stress–strain behaviors of compressed rocks incorporating crack closure effect

“…On the other hand, implementing the models into the finite element method (FEM) commercial software is significant for applying in the practical engineering. Diverse algorithms for integration of complex and highly nonlinear constitutive models have been developed, which can be generally divided into the following three categories, implicit algorithms, [31][32][33] explicit algorithms, [34][35][36] and semi-implicit algorithms. 37,38 The implicit integrations update the unknown values of the variables at current loading step through an iterative process.…”