Continuum mesoscale theory inspired by plasticityJ. P. Sethna1, M. Rauscher1, 2, 3 and J.-P. Bouchaud4
1 Laboratory of Atomic and Solid State Physics (LASSP) Clark Hall, Cornell University - Ithaca, NY 14853-2501, USA
2 Max-Planck-Institut für Metallforschung Heisenbergstr. 3, 70569 Stuttgart, Germany
3 Institut für Theoretische und Angewandte Physik, Universität Stuttgart 70550 Stuttgart, Germany
4 Service de Physique de l'Etat Condensé, CEA-Saclay 91191 Gif-sur-Yvette, France
(Received 29 August 2003; accepted in final form 5 January 2004)
We present a simple mesoscale field theory inspired by rate-independent plasticity that reflects the symmetry of the deformation process. We parameterize the plastic deformation by a scalar field which evolves with loading. The evolution equation for that field has the form of a Hamilton-Jacobi equation which gives rise to cusp-singularity formation. These cusps introduce irreversibilities analogous to those seen in plastic deformation of real materials: we observe a yield stress, work hardening, reversibility under unloading, and cell boundary formation.
46.35.+z - Viscoelasticity, plasticity, viscoplasticity.
62.20.Fe - Deformation and plasticity (including yield, ductility, and superplasticity).
83.60.La - Viscoplasticity; yield stress.
© EDP Sciences 2004