Stretch-Based Hyperelastic Material Formulations for Isogeometric Kirchhoff–Love Shells with Application to Wrinkling. (October 2021) - Verhelst, H.M.; Möller, M.; Den Besten, J.H.; Mantzaflaris, A.; Kaminski, M.L.
Abstract: Modelling nonlinear phenomena in thin rubber shells calls for stretch-based material models, such as the Ogden model which conveniently utilizes eigenvalues of the deformation tensor. Derivation and implementation of such models have been already made in Finite Element Methods. This is, however, still lacking in shell formulations based on Isogeometric Analysis, where higher-order continuity of the spline basis is employed for improved accuracy. This paper fills this gap by presenting formulations of stretch-based material models for isogeometric Kirchhoff–Love shells. We derive general formulations based on explicit treatment in terms of derivatives of the strain energy density functions with respect to principal stretches for (in)compressible material models where determination of eigenvalues as well as the spectral basis transformations is required. Using several numerical benchmarks, we verify our formulations on invariant-based Neo-Hookean and Mooney–Rivlin models and with a stretch-based Ogden model. In addition, the model is applied to simulate collapsing behaviour of a truncated cone and it is used to simulate tension wrinkling of a thin sheet. Graphical abstract: Highlights: Formulations for stretch-based (in)compressible material models for Isogeometric Kirchhoff–Love Shells were presented. Symmetries of the 4th order hyperelastic material tensor reduce transformation costs. The collapsing mechanism of a conical shell was revealed using the model and arc-length methods. A tension wrinkling problem was used to compare with experiments and commercial software.