ON THE SYMMETRIES OF 2D ELASTIC AND HYPERELASTIC TENSORS

A thorough investigation is made of the independent point-group symmet ries and canonical matrix forms that the 2D elastic and hyperelastic t ensors can have. Particular attention is paid to the concepts relevant to the proper definition of the independence of a symmetry from anoth er one. It is shown that the numbers of all independent symmetries for the 2D elastic and hyperelastic tensors are six and four, respectivel y. In passing, a symmetry result useful for the homogenization theory of 2D linear elastic heterogeneous media is derived.