Self-consistent assessments for the effective properties of two-phase composites within strain gradient elasticity

Analytical method for the second-order homogenization of two-phase composites within Mindlin–Toupin strain gradient elasticity theory is proposed. Direct approach and self-consistent approximation are used to reduce problem determination averaged Cauchy stresses, double stresses static moments inside inclusions under prescribed quadratic boundary conditions. The ellipsoidal shape orthotropic properties phases assumed. Extended equivalent inclusion with linear eigenstrain proposed derive explicit relations between Eshelby-like tensors corresponding concentration that define field variables inclusions. Obtained analytical solutions allow evaluate effective classical elastic moduli composite materials accounting properties, volume fraction, size Presented solution covers full range fraction correctly predicts absence effects homogeneous medium. Examples calculations spherical given. Micro-scale definition well-known simplified provided. Namely, it shown this phenomenological continuum model isotropic matrix small stiff inclusions, which have same Poisson’s ratio those one phase.