The description of material symmetry in materials with memory (Q1083245)

Two forms of the conventional procedure for describing material symmetry are presented in the context of the mechanics of materials with memory, in which the stress matrix at time t is assumed to be a functional of the history of the deformation gradient matrix in the time interval \([t_ 0,t]\). In one of these forms the particle considered is identified by its position at time \(t_ 0\) and in the other by its position at time t. This procedure is contrasted with that proposed by \textit{W. Noll} [Arch. Ration. Mech. Anal. 2, 197-226 (1958; Zbl 0083.393)]. Unlike the conventional procedure, in that of Noll the concepts of material symmetry and material frame indifference are inextricably intertwined. Moreover, it does not have general applicability to areas of continuum physics other than mechanics, as does the conventional procedure.