The static state of a two-phase solid mixture in a stressed elastic bar

We consider the equilibrium state and phase separation of a stressed elastic cylindrical bar which is composed of a mixture of two materials of tixed amounts. The Young’s modulus of the mixture is a function of the local volume fraction, which itself depends on the position in the bar. We determine the distribution of the two pure components and the field of internal strain throughout the bar so that the total potential energy is minimized. The problem is one of nonconvex minimization, and because of this we find that the two materials which comprise the bar are separated in the stressed equilibrium state. Copyright 0 1996 Elsevier Science Ltd.