Yang Liu, WaiChing Sun*, Zifeng Yuan, Jacob Fish
Department of Civil Engineering and Engineering Mechanics
* Email: email@example.com
A three-dimensional multiscale model has been developed and used to analyze the evolutions of microstructural attributes and hydraulic properties inside dilatant shear bands. In the proposed multiscale coupled scheme, we establish links between the discrete element method, which explicitly replicates granular motion of individual particles, and a finite element continuum model, which captures the homogenized responses of the granular assemblies. A spatial homogenization is performed to obtain the stress measure from representative elementary volume of discrete element simulations for macroscopic explicit dynamics finite element simulations. We demonstrate that the multiscale coupling scheme is able to capture the plastic dilatancy and pressure-sensitive frictional responses commonly observed inside dilatant shear bands, and replicate the induced anisotropy of the elasto-plastic responses, without employing any phenomenological plasticity model at macroscopic level. To improve cost-efficiency and prevent shear locking, a one-point quadrature rule is used along with an hour-glass control algorithm. Since discrete element simulations in each representatively elementary volume (Gauss point) requires no direct communication with its neighbors, the multiscale code can be programmed as a perfectly parallel problem, which is well suited to large scale distributed platforms and does not suffer parallel slowdown.
The resultant multiscale continuum-discrete coupling method retains the simplicity and efficiency of a continuum-based finite element model while naturally introducing length-scale to cure mesh pathology. In addition, internal variables, such as plastic dilatancy and plastic flow direction, are now obtained directly from granular physics, without introducing unnecessary empirical relations and phenomenology. Microstructural information, such as force chain length, coordination numbers and pore size distribution are compared with permeability inferred from lattice Boltzmann flow simulations to explain the mechanism that leads to the formation of flow conduit during strain localization.
Keywords: multiscale; FEM-DEM model; granular materials; dynamics shear band; anisotropy