A modified coherent potential approximation: Grain-contact moduli and coordination-number effect

We modified the self-consistent coherent potential approximation (CPA) for modeling properties of granular composite materials so that it takes into consideration the grain coordination number and distinctive elastic moduli for grain-contact zones. The original CPA was reasonably accurate for low-porosity consolidated sandstones but used only inclusion (pore or grain) shape and did not take into account morphological parameters such as coordination number and contact area or contact moduli. In our modified model, the grain inclusion was represented as a "grain with contact area"; therefore, scattering of elastic waves by contacts was incorporated. The modified CPA has been used to calculate data for 3D digital models of sintered quartz bead samples and Fontainebleau sandstones. Reduction of local elastic moduli for contact zones of specified area and thickness reduced effective overall moduli of the bulk sample. The modified theory predicted this weakening accurately, as compared to finite-element simulations.