Nonlinear Theory of Elastic Directed Surfaces

Abstract

The present paper develops a nonlinear theory for the deformation of an elastic directed surface by assuming the existence of a strain energy function and postulating a principle of virtual work which governs its mechanical behavior. The equations of equilibrium and the boundary conditions are shown to involve both the classical stress as well as the double stress. Constitutive equations are derived which give the stress and double stress as functions of a complete set of strain measures which describe the deformation of directed surfaces.