Relaxed energy densities for large deformations of membranes

Tension field theory can be incorporated into the ordinary theory of finite deformations of membranes by replacing the strain energy function W with a certain relaxed energy density Wr . If W is a convex function of the strain, Wr is the largest convex and increasing function that does not exceed W , and Wr is a convex function of the deformation gradient. Minimum energy and minimum complementary energy theorems are proved for the theory based on Wr .