Bodies described by non-monotonic strain-stress constitutive equations containing a crack subject to anti-plane shear stress

In this paper the state of stress and strain close to sharp cracks in bodies subjected to an anti-plane state of stress is studied within the context of a non-monotonic strain-stress relation within the context of a generalization of the Cauchy theory of elasticity, providing an exact analytical solution to the problem. A discussion is provided to highlight the main features of stress and strain distributions, and the implications of the new theory for fracture assessments. In particular, it is proved that the intensity of the complete stress field can be expressed as a function of the Stress Intensity Factor K III , as in the case of conventional linearized elasticity theory, thus promoting a K based-approach to the fracture of elastic solids obeying a constitutive relation wherein the linearized strain is expressed as a non-linear function of the Cauchy stress