THEORY AND NUMERICS OF DUCTILE MICROPOLAR ELASTOPLASTIC DAMAGE

The aim of this work is to extend an isotropic elastoplastic damage concept for ductile materials within a generalized micropolar continuum framework. The underlying motivation is on the one hand to model softening behaviour by damage evolution and on the other hand to regularize the impending loss of ellipticity which results in strong mesh dependence of localization computations. To this end, the classical displacement field is supplemented by an independent rotation field to yield an enhanced continuum. For the model originally proposed by Lemaitre the damage evolution follows from a dissipation potential and the hypothesis of general associativity. Special emphasis is directed towards the numerical implementation of the constitutive model within the framework of finite element analysis of inelastic boundary value problems. To compare damage evolution and standard strain softening the results are contrasted to the outcome of an analysis with the micropolar version of the classical von Mises model. Thereby, the intriguing correspondence of strain softening and damage evolution is highlighted. Additionally, several planar micropolar finite element formulations are derived within mixed variational principles to enhance the poor performance of the standard bilinear displacement and rotation expansions used so far in the literature. The merits of these new element developments are demonstrated for the example of localization within a compression problem.