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A note on the thermo-mechanics of elastic quasi-crystals

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Abstract

In recent years, many papers have been published concerning the elasticity of quasi-crystals. The present study has for main purpose to replace the proposed formulations into the framework of the modern thermo-mechanics of continua. Two types of modelling are envisaged in small deformations, those inspired by the physical descriptions proposed by Bak on the one hand and by Lubensky and co-workers on the other. While the first one fits well in a traditional variational formulation, the second one seems to be best accommodated in the frame of the thermo-mechanics of internal variables of state, the newly introduced “phason” field being then interpreted as such a vector variable. The inclusion of these two models in the theory of configurational forces—useful for the study of the expansion of defects frequent in such crystals—and the possibilities of including the effects of nonlinear elasticity and plasticity are briefly discussed. Important symmetry conditions are however left aside.

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Notes

  1. The study reported in this work was suggested to the author while being the editor and referee of several papers on the elasticity of quasi-crystals. It results from a specific effort from the author to comprehend the basis elements of this elasticity, as in particular exposed in a recent book by Fan [2], and to replace its two basic formulations in a more familiar thermo-mechanical background as accepted in modern continuum mechanics.

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Authors and Affiliations

  1. Institut Jean le Rond d’Alembert, UMR CNRS 7190, Case 162, Sorbonne Universités, Université Pierre et Marie Curie – Paris 6, Tour 55, 4 Place Jussieu, 75252, Paris Cedex 05, France

    Gérard A. Maugin

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Maugin, G.A. A note on the thermo-mechanics of elastic quasi-crystals. Arch Appl Mech 86, 245–251 (2016). https://doi.org/10.1007/s00419-015-1104-6

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