楕円体強化基材を含む複合材料の巨視的損失係数のマイクロメカニックス解析

摘要

線形常微分方程式で表される線形粘弾性体の構成式rnは，定常入力・定常応答の際には振幅に関する代数方rn程式に帰着し，線形弾性体の構成式と形式的に一致すrnるという特性を有している．%Macroscopic loss factors are derived for a composite material containing many ellipsoidal reinforcements whose semi-axes are different from each other by using the equivalent inclusion method combined with the Mori-Tanaka theorem. Eshelby tensor rearranged as a function of Poisson's ratio of the matrix multiplied by the geometrical factor is used for the reinforcement in the analysis. Since all reinforcements are assumed to align along the same direction in the modeling, the composite material has three perpendicular two fold rotational symmetries and hence nine components of the macroscopic loss factor of the composite can be expressed in terms of the geometrical factors. Moreover, it can be seen that the imaginally part of the complex Poisson's ratio of the constituent must be equal to zero from the condision that the magnitude of the macroscopic loss factor of a porous material must be equal to that of the matrix.