Single-slip elastoplastic microstructures
Sergio Conti and Florian Theil
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Submission date: 17. Jul. 2003
published in: Archive for rational mechanics and analysis, 178 (2005) 1, p. 125-148
DOI number (of the published article): 10.1007/s00205-005-0371-8
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We consider rate-independent crystal plasticity with constrained elasticity, and state the variational formulation of the incremental problem. For generic boundary data, even the first time increment does not admit a smooth solution, and fine structures are formed. By using the tools of quasiconvexity, we obtain an explicit relaxation of the first incremental problem for the case of a single slip system. Our construction shows that laminates between two different deformation gradients are formed. Plastic deformation concentrates in one of them, the other is a purely elastic strain. For the concrete case of a simple-shear test we also obtain a completly explicit solution.