Elastoplastic materials with martensitic phase transition and twinning at finite strains: numerical solution with the finite element method

A new quasistatic problem formulation and finite element (FE) algorithm for martensitic phase transition (PT) and twinning in elastoplastic materials at large strains, based on a recently proposed thermomechanical approach [1 ,2] are presented. The instantaneous occurrence of PT in some region based on thermodynamics, without introduction of volume fraction and prescribing the kinetic equations for it, is considered. Stress history dependence duri ng the transformation process is a characteristic feature of the PT criteri on. The deformation model is based on the multiplicative decomposition of t he total deformation gradient into elastic, transformation and plastic part s and the generalization of Prandtl-Reuss equations to the case of large st rains and PT. The case of small elastic, but large plastic and transformati on strains is assumed. For numerical simulation of PT the 'inverse' problem is considered, i.e. the position and size of the PT region (nucleus) are p rescribed in advance, and then the condition for PT is defined from the PT criterion. Such an approach includes a finite element solution of the elast oplastic problem with the prescribed transformation deformation gradient an d the changing elastoplastic properties in the transforming region during P T. The usage of the current configuration and the true Cauchy stresses alon g with assumptions of small elastic strains and zero modified plastic spin allows us to use-with small modifications-the radial return algorithm and t he consistent elastoplastic moduli for the case of small strains. Some modi fications of the iterative algorithm related to the numerical integration o f constitutive equations along with the radial return algorithm are suggest ed in order to improve the accuracy of solutions for large increments of ex ternal load (such modifications can be used for any elastoplastic problem w ithout phase transition as well). The model problems of nucleation at shear -band intersection and appearance of a single martensitic plate and a singl e twin are solved and analyzed. (C) 1999 Elsevier Science B.V. All rights r eserved.