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

Betsch P., Stein E.

Alternative formulations of isotropic large strain elasto-plasticity are presented which are especially well suited for the implementation into assumed strain elements. Based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts three distinct eigenvalue problems related to the reference, intermediate and current configuration are investigated. These eigenvalue problems arc connected by similarity transformations which preserve the eigenvalues. They play an important role in the subsequent development of alternative constitutive formulations and the corresponding finite element implementation. The developed constitutive procedures rely on the right Cauchy-Green tensor, or equivalently on the Green-Lagrangian 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 locking effects.