Analysis of geometrically nonlinear anisotropic membranes: theory and verification

A new anisotropic constitutive model is introduced to simulate the geometrically nonlinear dynamic behavior of general anisotropic membranes experiencing large deformations. This model relates the second Piola-Kirchhoff stress with the Green-Lagrange strain in a 3-D convected curvilinear coordinate frame. The construction of the anisotropic constitutive law from the predefined principal material coordinate system to the final convected curvilinear coordinate system using coordinate transformations is presented. The proposed theory is implemented into a finite element code and several numerical examples are given for validation. An application problem is described to demonstrate the importance of the new model in real applications.