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Modeling important engineering problems related to flow-induced damage (inthe context of hydraulic fracturing among others) depends critically oncharacterizing the interaction of porous media and interstitial fluid flow.This work presents a new formulation for incorporating the effects of porepressure in a nonlocal representation of solid mechanics. The result is aframework for modeling fluid-structure interaction problems with thediscontinuity capturing advantages of an integral based formulation. A numberof numerical examples are used to show that the proposed formulation can beapplied to measure the effect of leak-off during hydraulic fracturing as wellas modeling consolidation of fluid saturated rock and surface subsidence causedby fluid extraction from a geologic reservoir. The formulation incorporates theeffect of pore pressure in the constitutive description of the porous materialin a way that is appropriate for nonlinear materials, easily implemented inexisting codes, straightforward in its evaluation (no history dependence), andjustifiable from first principles. A mixture theory approach is used (deviatingonly slightly where necessary) to motivate an alteration to the peridynamicpressure term based on the fluid pore pressure. The resulting formulation has anumber of similarities to the effective stress principle developed by Terzaghiand Biot and close correspondence is shown between the proposed method and theclassical effective stress principle.

A nonlocal model for fluid-structure interaction with applications in hydraulic fracturing