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The modelling of the elastoplastic behaviour of single
crystals with infinite latent hardening leads to a nonconvex energy
density, whose minimization produces fine structures. The computation
of the quasiconvex envelope of the energy density involves the solution
of a global nonconvex optimization problem. Previous work based on a
brute-force global optimization algorithm faced huge numerical
difficulties due to the presence of clusters of local minima around the
global one. We present a different approach which exploits the structure
of the problem both to achieve a fundamental understanding on the
optimal microstructure and, in parallel, to design an efficient
numerical relaxation scheme.
This work has been carried out jointly with Carsten Carstensen
(Humboldt-Universitaet zu Berlin) and Sergio Conti (Universitaet
Duisburg-Essen)