Viscoplastic shells. Theory and numerical analysis

Abstract

The paper is intended as a review of the work carried out at the institute to which the authors belong, regarding the theory of viscoplastic shells in both versions of small and finite strains. Within the first version, the kinematics incorporated is assumed to be linear allowing for an additive decomposition of the strain rate. For the axisymmetric case, a hybrid strain-based functional is presented. Contrasting this, in the finite strain case, the shell kinematics is considered as geometrically exact. Here, the shell theory itself is seven-parametric and allows for the application of a three-dimensional constitutive law. The constitutive law used is that of Bodner & Partom which falls within the class of unified constitutive models. The multiplicative decomposition of the deformation gradient is employed, but no use is made of the so-called intermediate configuration. The elastic constitutive law is of a logarithmic type. An enhanced strain finite element formulation is developed and several examples of finite deformations of various shell geometries are presented.