Problem of a point defect, spatial regularization and intrinsic length scale in second gradient elasticity

We consider a problem of an eigenstrain, induced by a point defect embedded in an isotropic, non-locally elastic crystal, where non-locality originates from the higher gradient of strain. We analyze interaction between the microscopic and macroscopic stress and strain fields and give interpretation of the emerging intrinsic length scale effect. We also discuss particular features of spatial regularization as a direct consequence of incorporating the higher gradient of strain in the resulting set of field equations.