Long Wavelength Scattering Approximations for the Effective Elastic Parameters of Spherical Inclusion Problems

장파장 산란 근사를 이용한 구형 개재물 문제의 유효 탄성적 성질

The effective elastic properties of materials containing spherical inclusions were calculated by the elastic wave scattering theory. In the formulation additional scattering fields by the presence of random multiple scatterers that affects the effective properties were found by the single scattering approximation. In calculating the scattering fields the ensemble average on the displacements and strains inside the scatterer was found from the static approximation at long wavelength limit. The displacements were assumed to be equal to the incident field, while the strains were calculated by Eshelby's equivalent inclusion principle on the single inclusion problem. Four different models were considered and they reflected different degrees of multiple scattering effects based on the approximation introduced in the process of embedding the inclusion in the matrix. The expressions for the effective elastic constants were given in each model, and their relations to the results obtained from other scattering theory and elasticity theory were discussed. The theoretical predictions were compared with experimental results on the epoxy matrix composites containing tungsten particles of different sizes and volume fractions