A nonlocal multiscale discrete-continuum digital rock physics model at pendular regime

Abstract:

We propose a nonlocal multiscale framework that couples grain-scale micro-structural simulations of porous media with a macroscopic continuum-based finite element model at pendular regime. The upshot of this nonlocal coupling model is that it retains the simplicity and efficiency of the continuum-based finite element model, while possessing the original length scale of the microstructure. In particular, the collective mechanical responses of grains at material points are homogenized via a staggered nonlocal operator applied on local regions such that the multiscale simulations exhibit no pathological mesh dependence. Since granular materials may appear to be incompressible at critical state, we employ a one-point quadrature integration rule to relax the solution, while using hourglass control to eliminate the zero-energy modes. Numerical examples are used to analyze the onset and propagation of shear bands in granular materials. Finally, the robustness and accuracy of the proposed multiscale model are verified in comparisons with single-scale benchmark microstructural simulations. The nonlocal multiscale coupling scheme is able to capture the plastic dilatancy and pressure-sensitive frictional responses commonly observed inside dilatant shear bands, and replicate the anisotropy induced by the liquid-bridge and contact fabrics, without employing any phenomenological plasticity model or water-retention curve at macroscopic level.