Non-linear response functions for transversely isotropic elastic membranes

Abstract

For a membrane composed of elastic material with strain energy function per unit volume of the reference configuration, a two-dimensional strain energy function per unit area of the mid-surface is derived by integrating through the thickness. The explicit form of is derived for transversly isotropic materials when the axis of isotropy coincides with the normals to the mid-surface. It is shown that the two-dimensional response of the membranes is isotropic and the structure of resulting constitutive equations are examined in detail. No restrictions are imposed on a particular form of the strain energy function and strains are admitted to be arbitrarily large.