A new membrane wrinkling theory based on the concept of a relaxed strain energy function is introduced. The theory is derived as a specific case of the saturated elasticity theory. The anisotropy is imported by means of a material metric tensor. The corresponding formulations for Neo-Hookean material, including the impending wrinkling surface are presented. The theory is then implemented into a finite element code, and several examples are studied by using the finite element code. Results of those examples are presented to show the effectiveness of the new theory for predicting wrinkling in anisotropic membranes. A membrane wrinkle pattern test is also carried out to verify the new theory.
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