2019/12/31 by Michel Fruchart, Vincenzo Vitelli · 30 citations
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Duality (order theory) #Elasticity (physics) #Elasticity and Material Modeling #Force Microscopy Techniques and Applications #Geometry #Homogeneous space #Mathematics #Moduli #Moduli space #Nonlocal and gradient elasticity in micro/nano structures #Physics #Point (geometry) #Pure mathematics #Quantum mechanics #Theoretical physics #Transformation (genetics) #cond-mat.soft
paper · pdf · doi:10.1103/physrevlett.124.248001
published in Physical Review Letters 124(24), 248001 (American Physical Society) · 5 pages, 3 figures + SI
arxiv created 2020/05/19 · openalex publication_date 2020/06/15 · arxiv updated 2020/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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 nonspatial symmetries can occur microscopically in special classes of mechanical structures. Examples of such nonspatial 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 nonspatial 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.