Overall properties of particulate composites with periodic microstructure in second strain gradient theory of elasticity

In the context of Mindlin's second strain gradient theory, a homogenization scheme for the determination of the effective overall properties of particulate composites with periodic microstructure is developed in this paper. This homogenization method is based on the direct application of an equivalent inclusion method adapted to second strain gradient theory in such a manner that the consistency conditions, in addition to the stress field, are applied to the double stress and triple stress fields of the representative unit cell of composite and its corresponding inclusion problem. Subsequently, by equating the potential energy of the composite material with that of an equivalent homogeneous material, the effective overall elastic moduli of the composite are determined. Moreover, it is shown that the energy expression of the equivalent homogeneous material includes two additional parameters, namely, the cohesion-mismatch-induced initial stress and the cohesion-mismatch-induced surface tension, both arising from the mismatch in the cohesion moduli of the matrix and the reinforcing particles of the composite. The effects of particle size and particle-matrix interface manifest themselves in the formulations and the obtained results of the paper. (C) 2017 Elsevier Ltd. All rights reserved.