Class-Jump Phenomenon for Physical Symmetries in Bi-dimensional Space

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 3rd-order tensor. Some tensors of higher orders might occur in theory of generalized continuum, for example, in Mindlin’s strain-gradient elasticity [2], physical state of the material is described in each point using three tensors from 4th-order to 6th-order. Damage could also be modeled by an 8th-order tensor. When a complex behavior is studied the first step is to focus attention on its bi-dimensional version. Taking a complex problem at a lower level helps to better understand the physics of the behavior. But it has to be wondered in which measure the phenomenon studied is independent of the dimension of the working space. In this paper attention will be focused on the issue of symmetry classes of linear constitutive behavior, and it will be shown that, in 2D, anomalies could occur.