Stress-induced phase transformations in elastic solids under anti-plane deformations: dissipative constitutive models and numerical simulation Original Research Article

The present paper addresses modeling and numerical description of stress-induced phase transformations in solids. The study is developed in the setting of a generalized neo-Hookean elastic material under anti-plane deformations. It is assumed that the kinetics of phase transformation is governed by inequality constraints which lead to a dissipative behavior of the material. A thermodynamic analysis motivates the assumption of stress continuity across the surface of separation between phases. We propose a new finite element for the description of phase boundaries (characterized by strain discontinuities) in any position within the element. The inequality constraints of the problem are enforced by means of a return mapping algorithm. Dendritic formations are represented in the numerical results corresponding to the resulting model.