Scalable three‐dimensional hybrid continuum‐discrete multiscale modeling of granular media

Abstract

This study presents a scalable three‐dimensional (3D) multiscale framework for continuum‐discrete modeling of granular materials. The proposed framework features rigorous coupling of a continuum‐based material point method (MPM) and a discrete approach discrete element method (DEM) to enable cross‐scale modeling of boundary value problems pertaining to granular media. It employs MPM to solve the governing equations of a macroscopic continuum domain for a boundary value problem that may undergo large deformation. The required loading‐path‐dependent constitutive responses at each material point of the MPM are provided by a DEM solution based on grain‐scale contact‐based discrete simulations that receive macroscopic information at the specific material point as boundary conditions. This hierarchical coupling enables direct dialogs between the macro and micro scales of granular media while fully harnessing the predictive advantages of both MPM and DEM at the two scales. An effective, scalable parallel scheme is further developed, based on the flat message passing interface (MPI) model, to address the computational cost of the proposed framework for 3D large‐scale simulations. We demonstrate that the proposed parallel scheme may offer up to 32X and 40X speedup in strong and weak scaling tests, respectively, significantly empowering the numerical performance and predictive capability of the proposed framework. The 3D parallelized multiscale framework is validated by an element test and a column collapse problem, before being applied to simulate the intrusion of a solid object. The multiscale simulation successfully captures the characteristic response of intrusion as postulated by the modified Archimedes' law theory. The progressive development of the stagnant zone during the intrusion is further examined from a cross‐scale perspective.