<p>Development of the homogenization algorithms for&#160;the heterogeneous periodic and non-periodic materials has applications in different domains and considers different types of upscaling techniques&#160;(Fish, 2008, Bagheri, Settari, 2005, Kachanov et al. 1994, Levin et al. 2003).</p><p>The current&#160;presentation&#160;discusses an algorithm implemented in CAE Fidesys (Levin, Zingerman,&#160;Vershinin 2015, 2017)&#160;for calculating the effective mechanical characteristics of a porous-fractured medium (Myasnikov et al., 2016) at the scale of a&#160;periodicity cell dissected by a group of plane-parallel cracks modeled by elastic bonds with specified stiffnesses in the normal and tangential directions in accordance with the method of modeling cracks based on elastic bonds (Bagheri,&#160;Settari, 2005, 2006) In this case, the relationship between the components of the displacement vector and the force vector (normal&#160;stresses at the fracture&#8217;s boundaries) in the normal and tangential directions will be diagonal, neglecting the effects of dilatancy and shear deformations as a result of normal stresses.<br>The presentation&#160;also considers&#160;the general case of the relationship between displacements and forces along the fracture&#8217;s&#160;boundaries, taking into account shear deformations (which leads to an increase in the effective Young's modulus by 30%), and additionally a&#160;cell&#8217;s geometrical model&#160;is generalized&#160;by the presence of pores in the matrix&#8217;s&#160;material. The results of numerical studies on mesh&#160;convergence, the influence of periodicity cell sizes and fracture&#8217;s&#160;thicknesses on the computed effective properties&#160;are presented. A&#160;comparison between&#160;analytical (Kachanov, Tsukrov 1994, 2000)&#160;and numerical results&#160;obtained in CAE Fidesys for&#160;the effective elastic moduli estimation&#160;for particular cases of geometrical models of the periodicity cell is shown.<br>The developed algorithm is used to evaluate the effective mechanical properties of a digital core model obtained by the results of CT-scan data interpretation. A comparison is made with the results of laboratory physical&#160;core tests.&#160;Additionaly an algorithm implemented in CAE Fidesys&#160;and the&#160;results for the effective thermal conductivity and the effective coefficient of&#160;thermal expansion&#160;estimation are given for the considered test rock specimen.</p><p>The reported study was funded by Russian Science Foundation project &#8470; 19-77-10062.&#160;</p><p>&#160;</p><p>&#160;</p><ol><li>Bagheri, M., Settari, A. Effects of fractures on reservoir deformation and flow modeling // Can. Geotech. J. 43: 574&#8211;586 (2006) doi:10.1139/T06-024</li>
<li>Bagheri, M., Settari, A. Modeling of Geomechanics in Naturally Fractured Reservoirs &#8211; SPE-93083-MS, SPE Reservoir Simulation Symposium, Houston, USA, 2005.</li>
<li>Fish J., Fan R. Mathematical homogenization of nonperiodic heterogeneous media subjected to large deformation transient loading // International Journal for Numerical Methods in Engineering. 2008. V. 76. &#8211; P. 1044&#8211;1064.</li>
<li>Kachanov M., Tsukrov I., Shafiro B. Effective moduli of a solid with holes and cavities of various shapes// Appl. Mech. Reviews. 1994. V. 47, &#8470; 1, Part 2. P. S151-S174.</li>
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