A variationally consistent model for wrinkling in hyperelastic membranes using spectral decomposition of the stress tensor

We propose a variationally consistent and computationally efficient modeling approach for hyperelastic membranes undergoing wrinkling. Based on spectral decomposition of the stress tensor, the formulation enables a unified treatment of taut, wrinkled, and slack membrane states within a single expression, eliminating the need for case-specific logic. The plane stress condition is strictly enforced: analytically for incompressible materials and iteratively for compressible ones. The stress formulation builds upon the original hyperelastic stress and introduces a correction term governed mainly by the second principal stress, which yields a compact representation and enhances numerical efficiency. To assess the robustness and applicability of the proposed formulation, extensive numerical benchmark tests are conducted. The results confirm its strong predictive capability and suitability for implementation in both standard finite element and isogeometric analysis frameworks. • A variationally consistent model for wrinkling in hyperelastic membranes. • Unified formulation for three membrane states (taut, wrinkled, slack). • Applicable to arbitrary compressible and incompressible hyperelastic materials. • Comparisons to highly resolved shell models demonstrate accuracy and efficiency.