Singularities of homogeneous deformations of constrained hyper-elastic materials

Singularity analysis is performed for homogeneous deformations of any hyper-elastic, constrained anisotropic material, under any type of conservative quasi-static loading. Critical conditions for branching of the equilibrium paths are defined and their post-critical behavior is discussed. Classification of the simple (cuspoids) and compound (umbilics) singularities of the total potential energy function is effected. The theory is implemented into an umbilic elliptical singularity of an isotropic and totally inextensible unit cube under normal loading.