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Pseudo-plasticity and Pseudo-inhomogeneity Effects in Materials Mechanics

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Abstract

It is shown that a large variety of physical effects such as continuously distributed defects, heat conduction, anelasticity (plasticity in finite-strains, growth), phase transitions and more generally shock-waves, can be viewed as pseudo-material inhomogeneities when continuum thermomechanics is completely projected onto the material manifold itself. Main ingredients in this approach are the notions of local structural rearrangements (Epstein and Maugin) and of its thermodynamical dual, the Eshelby material stress tensor. An outcome of this is the unification of the theories of inhomogeneity of Eshelby on the one hand, and of Kroener-Noll-Wang, on the other hand. The notion of configurational forces as understood nowadays in solid-state physics and engineering mechanics follows necessarily from these developments. They are driving forces acting on sets of material points that correspond to strongly localized fields and, in the limit, singularities, which are also viewed as pseudo-inhomogeneities. The second law of thermodynamics then is a constraint imposed on the time evolution of these pseudo-inhomogeneities (e.g., plastic evolution, volumetric growth, progress of a crack, advancement of a phase-transition front, etc.). This has very powerful implications in numerical schemes drawn directly on the material manifold (e.g., thermodynamically admissible volume-element scheme for the simulation of phase-transformation evolution).

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  1. Laboratoire de Modélisation en Mécanique, UMR CNRS 7607, Université Pierre et Marie Curie (Paris 6), Case 162, 4 place Jussieu, 5252, Paris, Cedex 05, France

    Gerard A. Maugin

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Maugin, G.A. Pseudo-plasticity and Pseudo-inhomogeneity Effects in Materials Mechanics. Journal of Elasticity 71, 81–103 (2003). https://doi.org/10.1023/B:ELAS.0000005634.81007.11

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