The elastic moduli estimation of the solid-water mixture

Conceptually, the undrained elastic constants estimated by the poroelasticity theory should be identical to the effective moduli of the two-phase composite of a porous material saturated with pore water. Here we show numerically that the undrained elastic constants determined by an effective moduli estimate are almost identical with those calculated by poroelasticity theory, and if pore shapes are not exactly known and the porosity is around 50%, estimating the elastic constant as the average value of its Voigt and Reuss bounds is reasonably accurate. This is the situation in bone and dentin, the materials that are our primary intended application. This result will hold for situations in which the totally enclosed water phase is constrained to small deformations by virtue of its confinement. Importantly, in this work we assume that water is an isotropic elastic solid with a shear modulus that is 10−4 times the bulk modulus of the water. Note that it is compressible, but almost incompressible with a Poisson’s ratio of 0.4999.