Symmetry groups for arbitrary motions of hyperelastic solids

摘要

Symmetry groups associated with field equations which govern finite motions of a wholly arbitrary, anisotropic and heterogeneous hyperelastic solid are investigated. Determining equations for isovector components, which are none other than infinitesimal generators of symmetry groups, are borrowed from an earlier work concerning quite general balance equations and are specialised to the present case. These equations are then solved in order to obtain isovector components associated with a somewhat more general form of field equations by assuming that the strain energy function ∑ of the material depends directly on the deformation gradient matrix F, whereas ∑ should actually be a function of Green deformation tensor C. Eventually, the latter case is considered and the reduced forms of all relations involved are obtained. Group invariant, namely similarity, solutions are discussed and an example is provided for a special type of homogeneous isotropic material.