A Large Deformation Elastic-Viscoplastic Analysis of a Thick-Walled Spherical Shell

TLDR

The study formulates a large‑deformation elastic‑viscoplastic theory that accounts for elastic and inelastic deformations throughout loading and unloading. The theory links essential parameters to state variables using dislocation‑dynamics‑motivated constitutive relations and is implemented via a numerical scheme applied to a thick‑walled spherical shell under internal pressure. The theory eliminates the need for a yield criterion or prior loading state determination, and numerical examples demonstrate its application.

Abstract

A large deformation elastic-viscoplastic theory is formulated which considers both elastic and inelastic deformations to be present at all stages of loading and unloading. The theory does not require the assumption of a yield criterion or the prior determination of whether the material is loading or unloading. The theory is based on relating the essential parameters to state variables; the particular constitutive relations are motivated by the equations of “dislocation dynamics.” In the present formulation, thermal effects and properties representing the worked state of the material such as strain hardening are not considered. A numerical scheme for calculating deformations is developed and applied to a thick-walled spherical shell under internal pressure. Various numerical examples are presented.