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

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.

An effect of a purely dissipative process of microstresses on plane strain gradient plasticity problems

This article considers a plane strain gradient plasticity theory of the Gurtin?Anand model [M. Gurtin, L. Anand, A theory of strain gradient plasticity for isotropic, plastically irrotational materials Part I: Small deformations, J. Mech. Phys. Solids 53 (2005), 1624?1649] for an isotropic material undergoing small deformation in the absence of plastic spin. It is assumed that the system of microstresses is purely dissipative, so that the free energy reduces to a function of the elastic strain, while the microstresses are only related to the plastic strain rate and gradient of the plastic strain rate via the constitutive relations. The plane strain problem of the Gurtin?Anand model for a purely dissipative process gives rise to elastic incompressibility. A weak formulation of the flow rule is derived, making the plane strain problem suitable for finite element implementation.

Equilibrium equations and boundary conditions of strain gradient theory in arbitrary curvilinear coordinates

Equilibrium equations and boundary conditions of the strain gradient theory in arbitrary curvilinear coordinates have been obtained. Their special form for an axisymmetric plane strain problem is also given.