Rigid inclusions: stress singularity, inclusion neutrality and shear bands

Analytical solutions in elasticity predict singularities of stress fields at the corners/tips of rigid polygonal/linear inclusions, similarly to the case of void inclusions. On the other hand, a rigid line inclusion is neutral to homogeneous simple shear since a homogeneous stress state is obtained. We show that: (i) photoelastic experimental investigations validate the rigid inclusion model and therefore the assumptions about infinite stiffness of the inclusion and its complete adhesion with the matrix phase; (ii) when perturbations are superimposed upon a homogeneous pre-stress state, analytical incremental solutions display localization of deformation at the tips of rigid line inclusions and along the shear band directions, confirming experimental observations in ductile and quasi-brittle materials.