Class-jump phenomenon for physical symmetries in bi-dimensional space.

Nicolas Auffray (1) , R. Bouchet (1) , Y. Bréchet (2)

1 ONERA - The French Aerospace Lab [Châtillon]
2 SIMaP - Science et Ingénierie des Matériaux et Procédés

In condensed matter physics tensors are used to model physical properties of materials. Some well known examples are elasticity which is modeled by a 4th-order tensor or piezoelectricity by a 3rdorder tensor. Some tensors of higher order might occur in theory of generalized continuum, for example in Mindlin's strain-gradient elasticity [2] in which the physical state of the material is described in each point using three tensors from 4th-order to 6th-order one. Damage could also be modeled by an 8th-order tensor. When ones studying such complex models the first step is to focus attention in its bi-dimensional version. Taking a complex problem at a lower level help to better understand the physics of the behavior. But we have to wonder in which measure the phenomenon we study is independent of the dimension of the space we are working in. In this paper we will focus our attention on the issue of symmetry classes of linear constitutive behavior, and show that in a two dimension anomalies could occur.

Mots clés: Tensor algebra; symetry classes

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

Nicolas Auffray, R. Bouchet, Y. Bréchet. Class-jump phenomenon for physical symmetries in bi-dimensional space.. Lecture Notes in Applied and Computational Mechanics, 46, Springer, pp.1-11, 2009, ⟨10.1007/978-3-642-00911-2_1⟩. ⟨hal-00338839⟩