An implicit integration scheme with consistent tangent modulus for Leblond’s model of transformation-induced plasticity in steels

Abstract Thermomechanical treatments involving solid-state phase transformations play an important role for the manufacturing of functional and reliable components in many engineering applications. Accordingly, numerical investigation optimization such processes require considering thermoelastoplasticity under influence ongoing particular impact transformation-induced plasticity (TRIP). While a number elaborate models have been proposed description TRIP, none them seem to received much prevalence applications due their complexity or hard determine model parameters. Instead, overwhelming majority applied research either relies on simplistic formulations dating back early phenomenological approaches neglects TRIP altogether. In this work, we therefore provide accessible, straightforward easy-to-implement solution scheme by Leblond et al. which, despite being widely recognized, is hardly ever employed full form. Specifically, employ implicit backward-Euler integration elastic–plastic operator split approach update stresses order obtain simple concise algorithm which then derive corresponding consistent tangent modulus. Furthermore, work contains application symmetrically cooled plate in-depth discussion means tractable example. highlight discrepancies arising transient residual strains compared conventional $$J_2$$ J 2 -plasticity where transformation accounted merely adapting yield strength compound.