Large Deformations of Inelastic Shells

In this note we discuss the derivation of two-dimensional governing equations of a nonlinear shell made of material containing continuously distributed dislocations. We apply the trough-the-thickness integration procedure to a nonlinear shell-like three-dimensional body with dislocations. This procedure gives the exact equilibrium equations with the stress resultant and couple stress tensors. The dual to the surface stress tensors are the surface strain measures which are represented by two surface fields. The first one is the translation vector of the base surface of the shell while the second field, is the proper orthogonal tensor expressing rotation of the shell cross-section. Since in the case of solids with dislocations there are no displacement vector field. These fields are interpreted as quantities defined on the nonmaterial base surface of the shell.