Material symmetry and the evolution of anisotropies in a simple material. I: Change of reference configuration
In this work the authors studied the material symmetry and evolution of anisotropies in a simple material. They started by presenting the basic properties of material symmetry groups. Then they showed that for a material symmetry represented by a group of material symmetry groups (MSG); members of which are related by Noll's rule, Noll's rule allowed the generation of MSG, g, from any of its member. They next defined the apparent MSG of a MSG as its subgroup of orthogonal transformations. They showed that the apparent MSG of one MSG in g imposes a structure on all other MSG's of g. They used this property to identify all apparent MSG's realized in g. Finally, they provided particular results for the cases of an isotropic, orthotropic, and transversely isotropic material. This work might be very useful for those researchers working on the mathematical theory of simple materials.
scientific article; zbMATH DE number 4160208