Numerical Justification of Branched Laminated Microstructure with Surface Energy

Abstract

A mathematical model is given to study the branched laminated microstructure in austenite-martensite phase transition. A numerical method based on a mesh transformation method is applied to a two dimensional elastic crystal model, and the numerical results show that, for sufficiently small surface energy density and sufficiently long laminates, the branched laminates are energetically favorable; the numerical results also show that there is certain finite order asymptotically self-similar structure in the branched laminates.