Open AccessEffective elastic modulus of a transverse isotropy solid with aligned inhomogeneity
Author(s) -
Sheng Xu,
Xiaoming Tang,
Su Yuanda
Publication year - 2015
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.64.206201
Subject(s) - transverse isotropy , anisotropy , isotropy , materials science , ellipsoid , elastic modulus , transverse plane , scattering , perpendicular , tensor (intrinsic definition) , condensed matter physics , physics , composite material , optics , geometry , mathematics , structural engineering , astronomy , engineering
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.