Replacement relations for elastic composite materials having different matrices and related problems

摘要

For the first time, explicit closed form relations between overall elastic properties of two composite materials with the same microstructure and properties of inhomogeneities but different matrices are derived. Based on this result, we developed an innovative methodology that allows evaluation of the elastic properties of small particles-the problem of crucial importance in geophysics, mechanics of nanocomposites, biomechanics, etc. The particles are treated as isolated inhomogeneities in two matrix composites that differ by shear moduli (and the same Poisson's ratio) of their matrices, and inversion of the replacement relations leads to explicit formulas for particles' elastic constants. The theoretical model is verified numerically.