Bifurcation and metastability in a new one-dimensional model for martensitic phase transitions

Materials undergoing stress-induced martensitic phase transitions often for m complex twinned microstructures with multiple phase boundaries. They also exhibit hysteretic mechanical behavior. We propose and analyze a one-dimen sional model for twinning. We consider two elastic bars coupled by a system of continuously distributed linear springs. One of the bars has a two-well nonconvex elastic energy density that models a two-variant martensitic pha se. The other bar is linearly elastic and is meant to model the parent aust enite phase. Interfacial energy is modeled by a strain-gradient term. Vario us types of boundary conditions model parameter-dependent loading. A local bifurcation analysis shows that local energy minima (metastable states) oft en involve a large number of phase boundaries. This is confirmed by the glo bal-bifurcation diagrams obtained numerically. We observe that this microst ructure emerges via both sudden (finite) and gradual (infinitesimal) phase nucleation. We propose an energetic argument that predicts hysteresis in ov erall load-deformation behavior due to metastability of multiple equilibria . A limiting case with zero interfacial energy is treated analytically, yie lding global solution diagrams. (C) 1999 Elsevier Science S.A. All rights r eserved.