Geodesic
A numerical method to estimate the effective elastic moduli of rocks from twoand three-dimensional digital images of rock core samples
Numerical methods and programming, Tome 18 (2017) no. 4, pp. 416-433.

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A numerical method to estimate the effective elastic moduli of rocks from two- and three-dimensional digital images of rock core samples is proposed. The method is based on the energy equivalence principle for deformations caused by the homogeneous boundary static conditions that simulate a physical experiment. On this basis, the effective compliance tensor of a representative volume of an inhomogeneous medium is determined. A specific feature of the proposed algorithm is a new scheme for calculating the stress-strain static state of a sample by solving the corresponding problem of dynamic elasticity theory using the relaxation method. The obtained numerical results are discussed. The proposed method is verified using homogeneous samples with specified properties as well as for layered materials with effective parameters obtained according to the Schoenberg method. In conclusion, the effective parameters for a three-dimensional core sample are presented.
Keywords: effective parameters, representative volume, energy equivalence principle, homogeneous boundary conditions, relaxation method. 
@article{VMP_2017_18_4_a7,
     author = {G. V. Reshetova and T. S. Khachkova},
     title = {A numerical method to estimate the effective elastic moduli of rocks from twoand three-dimensional digital images of rock core samples},
     journal = {Numerical methods and programming},
     pages = {416--433},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2017_18_4_a7/}
}
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G. V. Reshetova; T. S. Khachkova. A numerical method to estimate the effective elastic moduli of rocks from twoand three-dimensional digital images of rock core samples. Numerical methods and programming, Tome 18 (2017) no. 4, pp. 416-433. http://geodesic.mathdoc.fr/item/VMP_2017_18_4_a7/