A pore-level multiscale method for the elastic deformation of fractured porous media

Pore-scale models are useful for understanding and upscaling the mechanical deformation of fractured porous media. The highest fidelity solutions are obtained by direct numerical simulation (DNS), in which the governing equations are discretized and solved with a fine-grid solver (e.g., finite elements) over a 3D image (e.g., X-ray) of a porous sample. However, the downside of DNS is its high computational cost. We present a pore-level multiscale method (PLMM) that approximates DNS efficiently and with controllable accuracy in modeling the linear elastic response of porous solids with arbitrary microstructure and crack pattern. PLMM decomposes the solid into subdomains, over which local basis and correction functions are built. These functions are then coupled with a global problem to yield an approximate solution, whose errors can be iteratively corrected. A key feature of PLMM is that the decomposition need not conform to the cracks, unlike a previous formulation by the authors. This paves the way towards solving crack nucleation and growth problems in the future without the need to dynamically update the decomposition. We represent cracks diffusely using a phase-field variable and explore three strategies for capturing them through either the basis or correction functions. The implications of each strategy on the convergence rate and computational cost are analyzed.