T-matrix approach to effective nonlinear elastic constants of heterogeneous materials.

Abstract

Multiple scattering theory (MST) has been extensively used to investigate the various physical properties of different types of disordered materials. However, its application to nonlinear physical properties of such materials is still very limited because of the complexities involved. In some of our earlier works [T. R. Middya, A. N. Basu, and S. Sengupta, J. Math. Phys. 27, 2807 (1986)] we have extended MST to develop a strain-field solution in nonlinear heterogeneous media. The field solution was then used to calculate effective third-order elastic constants (TOEC's) and first pressure derivatives (FPD's) of effective second-order elastic constants (SOEC's), for polycrystals with constituents having cubic symmetry. The results obtained [T. K. Ballabh, M. Paul, T. R. Middya, and A. N. Basu, Phys. Rev. B 45, 2761 (1992)] compared well with available experimental observations. But there are many polycrystals whose constituents have noncubic symmetry. The major purpose of the present investigation is to extend the field solution to calculate explicitly the effective TOEC's of polycrystals having constituents with trigonal and hexagonal symmetry, in terms of the second- and third-order elastic constants of the constituents. The formulas developed are applied to calculate the effective TOEC's and FPD's of effective SOEC's for four noncubic polycrystals. The results obtained are compared with available experimental data. \textcopyright{} 1996 The American Physical Society.