Theory and analysis of shells undergoing finite elastic-plastic strains and rotations

Abstract

In this paper theory and analysis of shells undergoing finite elastic and finite plastic strains and rotations are presented. The shell kinematics are based on a relaxed normality hypothesis allowing transverse normal material fibers to be stretched and bended, whereas shear deformations are neglected. Lagrangean logarithmic membrane and logarithmic bending strain measures are introduced, and it is shown that they can be additively decomposed into purely elastic and purely plastic parts for superposed moderately large strains and unrestricted rotations. The logarithmic strain measures are used to formulate thermodynamic-based constitutive equations for isotropic elastic and plastic material behavior with isotropic and kinematic hardening induced by continuous plastic flow. To analyse path-dependent elastic-plastic shell deformations by iterative procedures the application of logarithmic strain measures allows to realize load steps with corresponding moderate strains and unrestricted rotations. The moderate strain restriction for superposed deformations can be assured by an appropriate update procedure. Formulae are given to determine exactly the rotational change of the reference configuration during the update. Finally, the principle of virtual work with corresponding elastic-plastic material tensor is formulated and it is shown that the weak form of the virtual work leads to the Lagrangean equilibrium equations and boundary conditions well-known from the nonlinear theory of elastic shells.