The fracture of a physically non-linear inhomogeneous medium under stress-relaxation conditions in inclusions

An isotropic elastic plane is considered which contains different elliptic inclusions remote from one another and which exhibit the properties of non-linear creep. The corresponding constitutive equations contain a damage parameter which varies from zero (in the undeformed state) to unity (at the instant of fracture). Loads which are constant in time act at infinity which cause the relaxation of stresses in the inclusions. The conditions are obtained under which: (a) fracture of inclusions occurs, and (b) fracture is impossible. The results are generalized to the case of a finite domain with a non-linear inclusion of arbitrary form which is under relaxation conditions in a homogeneous stress-strain state.