Modelling of Thin Martensitic Films with Nonpolynomial Stored Energies

Abstract

A study of the thin film limit of martensitic materials is presented, with the film height tending to zero. The behaviour of the material is modelled by a stored elastic energy which grows to infinity if the normal to the deformed film tends to zero. We show that the macroscopic behaviour of the material can be described by gradient Young measures if Dirichlet boundary conditions are prescribed at the boundary of the film. In this situation, we also formulate a rate-independent problem describing evolution of the material. A second approach, perhaps useful in case of non-Dirichlet loading, is presented as well, relying on suitable generalised Young measures. © Springer Basel 2013.