On the performance of enhanced strain finite elements in large strain deformations of elastic shells: Comparison of two classes of constitutive models for rubber materials

This paper is concerned with the performance of shell finite elements, well established in locking‐free computations with linear constitutive laws, in the case of non‐linear elastic material behaviour. Specifically enhanced strain elements are focused on. It is shown that the element behaviour depends on the resulting form of the stress tensor. Phenomenological models for highly non‐linear and elastically deforming rubber, like that of Odgen, are compared with the statistical‐based constitutive model developed by Arruda and Boyce. Whereas computations with the Odgen or any equivalent phenomenological model prove unstable, the behaviour of the enhanced elements, when the statistical model is applied, is shown to be superior. The behaviour is attributed to the mathematical form of the resulting stress tensor.