A variationally consistent membrane wrinkling model based on spectral decomposition of the strain tensor

We propose a novel variationally consistent membrane wrinkling model for analyzing the mechanical responses of wrinkled thin membranes. The elastic strain energy density is split into tensile and compressive terms via a spectral decomposition of the strain tensor. Tensile and compressive parts of the stress and constitutive tensors are then obtained via consistent variation from the respective strain energies. Considering only the positive part of the strain energy in the variational formulation, we obtain a membrane with zero compressive stiffness. By adding the negative strain energy multiplied with a very small factor, we further obtain a residual compressive stiffness, which improves stability and allows handling also states of slackening. Comparison with results from analytical, numerical and experimental examples from the literature on membrane wrinkling problems demonstrate the great performance and capability of the proposed approach, which is also compatible with commercial finite element software.