  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 tangent material matrices 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 reduction 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.
