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arXiv · 1912.02384

Simple views on symmetries and dualities in the theory of elasticity

Michel Fruchart·Vincenzo Vitelli
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Abstract

Microscopic symmetries impose strong constraints on the elasticity of a crystalline solid. In addition to the usual spatial symmetries captured by the tensorial character of the elastic tensor, hidden non-spatial symmetries can occur microscopically in special classes of mechanical structures. Examples of such non-spatial symmetries occur in families of mechanical metamaterials where a duality transformation relates pairs of different configurations. We show on general grounds how the existence of non-spatial symmetries further constrains the elastic tensor, reducing the number of independent moduli. In systems exhibiting a duality transformation, the resulting constraints on the number of moduli are particularly stringent at the self-dual point but persist even away from it, in a way reminiscent of critical phenomena.

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Michel Fruchart, Vincenzo Vitelli. 2019-12-05. Simple views on symmetries and dualities in the theory of elasticity. https://doi.org/10.1103/physrevlett.124.248001

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