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Europhys. Lett.
Volume 65, Number 5, March 2004
Page(s) 665 - 670
Section Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics
Published online 01 February 2004
Europhys. Lett., 65 (5) , pp. 665-670 (2004)
DOI: 10.1209/epl/i2003-10175-2

Continuum mesoscale theory inspired by plasticity

J. 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