Inclusions and inhomogeneities in strain gradient elasticity with couple stresses and related problems

摘要: Abstract At small length scales and/or in presence of large field gradients, the implicit long wavelength assumption classical elasticity breaks down. Postulating a form second gradient with couple stresses as suitable phenomenological model for small-scale elastic phenomena, we herein extend Eshelby’s formulation inclusions and inhomogeneities. While modified size-dependent tensor hence complete state containing transformation strains or eigenstrains is explicitly derived, corresponding inhomogeneity problem leads to integrals equations which do not appear have closed-form solutions. To that end, equivalent inclusion method extended present framework perturbation series then can be used approximate The scheme inhomogeneities also serves basis establishing expressions effective properties composites stresses. work expected find application towards nano-inclusions certain types addition being subsequent non-linear homogenization schemes.