This solution is to deal with the elastic anisotropy of Organic-rich shale using a Mori-Tanaka's type (Mori and Tanaka, 1973; Benveniste, 1987) anisotropic homogenization model (Sayers, 2013). The anisotropic Hill's tensor (that is required to compute the Eshelby's tensor and the strain concentration tensor) is computed using the solutions derived by Sevostianov et al. (2005).

References:

Mori, T., & Tanaka, K. (1973). Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta metallurgica, 21(5), 571-574.

Benveniste, Y. (1987). A new approach to the application of Mori-Tanaka's theory in composite materials. Mechanics of materials, 6(2), 147-157.

Sevostianov, I., Yilmaz, N., Kushch, V., & Levin, V. (2005). Effective elastic properties of matrix composites with transversely-isotropic phases. International journal of solids and structures, 42(2), 455-476.

Sayers, C. M. (2013). The effect of kerogen on the elastic anisotropy of organic-rich shales. Geophysics.