Ball–James theory of microstructure

Summary

The Ball–James theory describes the fine microstructures of crystals that undergo a martensitic transformation as limits of minimising sequences of a nonlinear elastic energy. The energy density has several wells, one for each variant of martensite, and it is not quasiconvex, so the minimum is in general not attained. Instead, minimising sequences develop finer and finer oscillations between wells, which are recorded by gradient Young measures. The theory explains twins, austenite–martensite interfaces and laminates through rank-one compatibility conditions.