Finite-scale Microstructures and Metastability In One-dimensional Elasticity

This paper addresses the non-uniqueness pointed out by Ericksen in his classical analysis of the equilibrium of a one-dimensional elastic bar with non-convex energy [1]. Following some previous work in this area, we suitably regularize the problem in order to investigate this degenerancy. Our approach gives an explicit framework for the the study of the rich variety of finite-scale equilibrium microstructures for the bar in a hard loading device, and their stability properties. In this way we clarify the role of interfacial energy in creating finite-scale microstructures, by considering the combined effect of the oscillation-inducing and oscillation-inhibiting terms in the energy functional.