THE DESCRIPTION, CLASSIFICATION, AND REALITY OF MATERIAL AND PHYSICALSYMMETRIES

We reconsider the definitions of both material symmetries and physical symmetries which are described in terms of point groups, i.e. subgrou ps of the full orthogonal group, because these two concepts are often confused and the classical descriptions of physical symmetry for inela stic behaviour of materials are impracticable. All two- and three-dime nsional point groups are classified into two types: compact and non-co mpact. The reality of every compact point group in the description of a material or a physical symmetry is justified in four aspects, that i s: (i) point groups characterized by a finite set of tensors, (ii) Hil bert's theorem for integrity bases, (iii) correlation between integrit y bases and function bases (generalization of Wineman and Pipkin's the orem), and (iv) physical reality. The unreality of any non-compact poi nt group in the description of a material or a physical symmetry is pr oposed as a new principle of continuum physics. As applications, the c omplete sets of all classes of two- and three-dimensional point groups which describe physical symmetries for linear physical properties (su ch as thermal expansion, piezoelectricity, elasticity, etc.) and for m ore general mechanical constitutive laws are given.