Implicit Stress Integration for High-Temperature Inelastic Constitutive Models Using Linearization

Abstract

In this study, a linearization approach is used to develop an implicit integration scheme for high-temperature inelastic constitutive models based on non-linear kinematic hardening. A non-unified model is considered in which inelastic strain rate is divided into the transient and steady parts driven, respectively, by effective stress and applied stress. By discretizing the constitutive relations using the backward Euler method, and by linearizing the resulting discretized relations, a tensor equation is derived to iteratively achieve the implicit integration of constitutive variables. The integration scheme is then programmed as a subroutine in a finite element code and applied to a lead-free solder joint analysis. It is thus demonstrated that the integration scheme affords the quadratic convergence of iteration even for considerably large increments.