Bifurcation and stability of homogeneous deformations of an elastic body under dead load tractions with \(Z_ 2\) symmetry (Q1179712)

The author studies the bifurcation and stability of the homogeneous deformation of a homogeneous, isotropic, incompressible elastic body subject to three perpendicular sets of dead-load surface tractions of which two have equal magnitude. The stability problem is formulated as the minimization problem of a certain potential energy. A theorem on the existence of minima is given. The tools to study the bifurcation problem are singularity and group theory. Finally a body made of a Moony-Rivlin material is treated as an example.