Theory and finite element computation of cyclic martensitic phase transformation at finite strain

A generalized variational formulation, including quasi‐convexification of energy wells for arbitrarily many martensitic variants in case of mono‐crystals for linearized strains, was developed by Govindjee and Miehe ( Comp. Meth. Appl. Mech. Eng. 2001; 191 (3–5):215–238) and computationally extended by Stein and Zwickert ( Comput. Mech. 2006; in press). This work is generalized here for finite strain kinematics with monotonous hyperelastic stress–strain functions in order to account for large transformation strains that can reach up to 15%. A major theoretical and numerical difficulty herein is the convexification of the finite deformation phase transformation (PT) problems for multiple phase variants, n ⩾2. A lower bound of the mixing energy is provided by the Reuss bound in case of linear kinematics and an arbitrary number of variants, shown by Govindjee et al. ( J. Mech. Phys. Solids 2003; 51 (4):I–XXVI). In case of finite strains, a generalized representation of free energy of mixing is introduced for a quasi‐Reuss bound, which in general holds for n ⩽2. Numerical validation of the used micro–macro material model is presented by comparing verified numerical results with the experimental data for Cu 82 Al 14 Ni 4 monocrystals for quasiplastic PT, provided by Xiangyang et al. ( J. Mech. Phys. Solids 2000; 48 :2163–2182). The zigzag‐type experimental stress–strain curve within PT at loading, called ‘yield tooth’, is approximated within the finite element analysis by a smoothly decreasing and then increasing axial stress which could not be achieved with linearized kinematics yielding a constant axial stress during PT. Copyright © 2007 John Wiley & Sons, Ltd.