On stability and non-uniqueness of the dilatation states of a compressible isotropic unit cube subjected to dead loading

This paper considers a unit elastic cube, made of compressible isotropic material, with its faces subjected to certain dead-load tractions that produce a possible equilibrium state of non-uniform dilatation. It is seen that, at the considered equilibrium state, the cube material acquires properties of pseudo-transverse isotropy. Conditions are obtained for the stability of such an equilibrium state with respect to superimposed pure homogeneous deformations having principal directions parallel to the cube edges. The problem of non-uniqueness of the cube dilatation states is also addressed, and non-uniqueness is illustrated in an example application dealing with an isotropic cube made of the Blatz–Ko material. The nature and the stability features of these equilibrium states are studied in depth.