Ductile damage analysis of elasto-plastic shells at large inelastic strains

The objective of this contribution is to model ductile damage phenomena under consideration of large inelastic strains, to couple the corresponding constitutive law with a multi-layer shell kinematics and to give nally an adequate nite element formulation. An elastic{plastic constitutive law is formulated by using a spatial hyperelasto-plastic formulation based on the multiplicative decomposition of the deformation gradient. To include isotropic ductile damage the continuum damage model of Rousselier is modi ed so as to consider large strains and additionally extended by various void nucleation and macro-crack criteria. In order to achieve numerical e ciency, elastic strains are supposed to be su ciently small providing a numerical e ective integration based on the backward Euler rule. Finite element formulation is enriched by means of the enhanced strain concept. Thus the well-known de ciencies due to incompressible deformations and the inclusion of transverse strains are avoided. Several examples are given to demonstrate the performance of the algorithms developed concerning large inelastic strains of shells and ductile damage phenomena