Comparison between the Material Symmetry Approaches of Gurtin and Noll

The material symmetry condition of Noll is compared with that of Gurtin for elastic solids. (In this paper elastic solids refer to simply elastic solid materials.) We demonstrate that the difference between the two approaches is due to the fact that Gurtin's involves an additional rotation of the configuration. We show that the two ideas of material symmetry are equivalent for elastic solids in the context of finite elasticity theory. However, the procedures for applying these two approaches to classical linear elasticity theory are different. Also, we observe that both methods can be directly applied to the invariant infinitesimal theory of Casey and Naghdi without starting with the case of finite deformations. This revised version was published online in July 2006 with corrections to the Cover Date.