Numerical implementation of multiplicative elasto-plasticity into assumed strain elements with application to shells at large strains

Alternative formulations of isotropic large strain elasto-plasticity are pr esented which are especially well suited for the implementation into assume d strain elements. Based on the multiplicative decomposition of the deforma tion gradient into elastic and plastic parts three distinct eigenvalue prob lems related to the reference, intermediate and current configuration are i nvestigated. These eigenvalue problems are connected by similarity transfor mations which preserve the eigenvalues. They play an important role in the subsequent development of alternative constitutive formulations and the cor responding finite element implementation. The developed constitutive proced ures rely on the right Cauchy-Green tensor, or equivalently on the Green-La grangian strain tensor, rather than the deformation gradient. Consequently, they can be applied directly to assumed strain elements. Specifically, we are concerned with efficient low order shell elements for which the assumed strain method has proven to be extremely powerful to overcome spurious loc king effects. (C) 1999 Elsevier Science S.A. All rights reserved.