A plane strain problem in the theory of elastic materials with voids

Abstract

This article is concerned with the linear theory of elastic materials with voids. With respect to the classical theory of elasticity, this model is characterized by four independent kinematic variables: the displacement field [Formula: see text][Formula: see text] and the change in volume fraction [Formula: see text]. First, we present the field equations in the equilibrium theory and derive the equations of the plane strain problem. Then, the problem of a cylindrical rigid inclusion in an infinite body is investigated. The results are obtained in closed form. The solution can be considered as a generalization of the corresponding problem in the classical theory of elasticity. The displacement field and the stresses are expressed by mean of explicit formulas. The maximum tensile stress and the stress concentration factor are calculated.