Finite-element analysis of hyperelastic thin shells with large strains

The objective of this contribution is the development of theoretical and numerical models applicable to large strain analysis of hyperelastic shells confining particular attention to incompressible materials. The theoretical model is developed on the basis of a quadratic displacement approximation in thickness coordinate by neglecting transverse shear strains. In the case of incompressible materials this leads to a three-parametric theory governed solely by mid-surface displacements. The material incompressiblity is expressed by two equivalent equation sets considered at the element level as subsidiary conditions. For the simulation of nonlinear material behaviour the Mooney-Rivlin model is adopted including neo-Hookean materials as a special case. After transformation of nonlinear relations into incremental formulation doubly curved triangular and quadrilateral elements are developed via the displacement method. Finally, examples are given to demonstrate the ability of these models in dealing with large strain as well as finite rotation shell problems.