Symmetry and equivariance in nonlinear elastostatics. I (Q1118439)

This paper is devoted to the study of a notion of material symmetry in three-dimensional elastostatics that takes into account inhomogeneity as well as the geometric symmetry of the reference configuration of a body. The ``body symmetry group'' thus defined is a subgroup of the Euclidean group. Equivariance of the classical field equations under the action of this group is shown. A reduction procedure is proposed for the study of possible symmetry-breaking solutions corresponding to any subgroup of the body symmetry group. The reduced equations are given in the case of inhomogeneous bodies of revolution with O(2) symmetry. A few features of possible symmetry-breaking solutions having SO(2) symmetry are briefly discussed. The case of discrete subgroups of O(2) is mentioned.