Analytical and numerical aspects of relaxation and regularization in models of crystal plasticity

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Our project combines analytical and numerical approaches for the study of variational models for finite crystal plasticity. One paradigm is the application of the theory of relaxation to plasticity problems, also in combination with the tools of ¡-convergence. Our project deals both with the derivation of exact analytical results in selected case studies and with the development and implementation of a general algorithm for the efficient numerical determination of the relaxation of a given energy density. The integration of both analytical and numerical relaxation into a finite element code permits to validate and compare with experiment. In parallel, we investigate the role of dislocation line-tension energy. This includes both the derivation of this type of model from discrete and/or continuum models at a smaller scale, by means of ¡-convergence, and the study of the interplay of the energy of geometrically necessary dislocations with relaxation.