Stress field in an isotropic elastic solid containing a circular hard or soft inclusion under uniaxial tensile stress

An inclusion generates a stress concentration and it plays a crucial role both damage evolution and mechanical response of materials. In the current work, the stress fields around hard and soft circular inclusions are analytically determined within the framework of the linear theory of elasticity. The Kirsch's solution is here modified for the case of a hard or a soft inclusion, by applying both the theory of superposition and equi-energy stress partition criterion. The presented approach is validated by finite element simulations by considering with six different hard and soft inclusions.