Large strain deformations of elastic shells constitutive modelling and finite element analysis Original Research Article

This paper is concerned with the constitutive modelling of large elastic strains with applications to shells. The shell theory itself is characterized by seven degrees of freedom and enjoys the following features: (1) it circumvents the use of a rotation tensor preserving the Euclidean structure of the configuration space and (2) it is capable to the application of a three-dimensional constitutive law. In addition, an elastic finite strain constitutive law is developed which: (1) covers the whole range of deformation experimentally given by Treloar and (2) is formulated in terms of invariants avoiding the use of principal stretches. The second feature means that the model is generalizable to anisotropic material behaviour, and that it allows for straightforward computations of the tangent operator making the whole theory well suited for large strain computations. In addition to the four-node and nine-node displacement-based finite elements, an enhanced strain finite element is examined. Its efficiency is compared with that of displacement-based element formulations. Different examples of large strain shell deformations are presented. It is shown that the application of the enhanced strain concept in the nonlinear constitutive range limits severely the stability of computation.