THEORY AND ANALYSIS OF SHELLS UNDERGOING FINITE ELASTIC-PLASTIC STRAINS AND ROTATIONS

In this paper theory and analysis of shells undergoing finite elastic and finite plastic strains and rotations are presented. The shell kine matics are based on a relaxed normality hypothesis allowing transverse normal material fibers to be stretched and bended, whereas shear defo rmations are neglected. Lagrangean logarithmic membrane and logarithmi c bending strain measures are introduced, and it is shown that they ca n be additively decomposed into purely elastic and purely plastic part s for superposed moderately large strains and unrestricted rotations. The logarithmic strain measures are used to formulate thermodynamic-ba sed 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 deformat ions by iterative procedures the application of logarithmic strain mea sures allows to realize load steps with corresponding moderate strains and unrestricted rotations. The moderate strain restriction for super posed deformations can be assured by an appropriate update procedure. Formulae are given to determine exactly the rotational change of the r eference configuration during the update. Finally, the principle of vi rtual work with corresponding elastic-plastic material tensor is formu lated and it is shown that the weak form of the virtual work leads to the Lagrangean equilibrium equations and boundary conditions well-know n from the nonlinear theory of elastic shells.