横向各向同性固体材料中含定向非均匀体的有效弹性模量

Effective elastic modulus of a transverse isotropy solid with aligned inhomogeneity

针对含定向非均匀体的横向各向同性复合材料(即TI介质),采用球形有效体散射等效的方法,根据TI材料下的D,N_(ij)表达式,对横向各向同性条件下Eshelby张量的积分通用表达式进行化简,推导出了复合材料的具有横向各向同性特性的有效弹性模量的表达式,并依此进行了数值分析.计算结果表明:利用本方法计算的有效模量随非均匀体含量的增大而减小;定向排列的非均匀体影响横向各向同性介质的固有各向异性,水平指向的非均匀体会增大材料的横向各向同性,模拟结果对评价含非均匀体各向异性介质的特征具有指导意义.

The effective modulus of transversely isotropic compound material containing aligned ellipsoidal inhomogeneity is derived using the method of sphere-equivalency of effective scattering.Based on this approach,we derive the integral solution of the Eshelby tensor for the anisotropic medium,allowing for numerically evaluating the effects of anisotropy for the solution.The numerical results show that the effective modulus of the medium decreases monotonically with increasing the concentration of the inhomogeneties.The anisotropy increases if the inhomogeneity alignment direction is perpendicular to the TI symmetry axis of the background medium.By reducing the numbers of matrix elastic modulus from 5 to 2,we calculate the slowness surfaces for the three modes of propagation in an isotropic medium containing aligned ellipsoidal inhomogeneity.The results are the same as the existing ones,which validates the exactness of our theory.The modeling results can be used to evaluate elastic property of an anisotropic medium with aligned inclusions,such as earth formation shale rocks containing aligned cracks.