A theoretical and computational model for isotropic elastoplastic stress analysis in shells at large strains Original Research Article

The article presents new aspects of large-strain isotropic elastoplastic analysis of shells. On the shell theory side, we consider several possible continuum based parametrizations of the shell deformation and investigate their applicability with respect to the implementation of general three-dimensional local constitutive models. As an aspect of computational shell analysis we then discuss in detail the numerical implementation of a shell based on the parametrization of the top and bottom surface in terms of a new 8-node brick-type mixed finite shell element on the basis of assumed strain and enhanced strain variational approaches. On the side of plasticity theory we adopt a recently proposed intermediate-configuration-free formulation of large-strain plasticity based on the notion of a plastic metric and consider its representation with respect to the parameter manifold of the shell. This frame is formulated in terms of principal strains and principal stresses with respect to dual co- and contra-variant eigenvector triads associated with a mixed-variant elastic strain tensor. The new aspect of computational plasticity is the development of a stress update algorithm for the plasticity model mentioned above which includes a general return mapping in the eigenvalue space. The algorithm can be applied to general coordinate charts and is particularly convenient when formulated with respect to the space of the curvilinear coordinates of the shell parametrization. We demonstrate the performance of the finite element formulation and constitutive algorithms by means of several numerical examples.