One-dimensional structured phase transformations under prescribed loads

Abstract : The authors consider a one-dimensional elastic bar acted on by end loads. To allow for the possibility of phase transitions they consider a stored-energy function of the form W(gamma) + epsilon sub 2(gamma')sub 2 with W(gamma) a nonconvex function of strain gamma, a function of the type capable of supporting two-phases. The term involving the strain gradient gamma, is added to model the region of rapidly varying strain in the vicinity of a phase transition. It is shown that this problem has smooth solutions which, for epsilon small, correspond to the single-phase and two-phase solutions of the problem with epsilon = O. It is shown further that the only stable solutions of this problem are the single-phase solutions gamma = constant. (Author)