A note on the classification of anisotropy of bodies defined by implicit constitutive relations

• The meaning assigned to the terminology “anisotropy” is discussed.
• Material symmetry of bodies defined by implicit constitutive relations, which are of much current interest, is considered.
• The paper will now allow for the development of representations for the response of materials defined by implicit constitutive relations in a systematic manner for different symmetries.

In this note we consider the definition of anisotropy with regard to the response of bodies described by implicit constitutive relations. The class of response relations under considerations in this work is implicit relations between the history of the stress, the history of the density, and the history of the deformation gradient. It is shown that the work of Noll [4] defining the anisotropy of bodies in terms of symmetry groups for Simple Materials can be very easily extended to define the anisotropy in terms of symmetry groups for materials whose response is described by relations between the histories of the stresses and the deformation gradient. While symmetry groups are defined, the more arduous task of developing representation theorems for bodies defined through implicit response relations is an important open task.