A hybrid material‐point spheropolygon‐element method for solid and granular material interaction

Abstract

Capturing the interaction between objects that have an extreme difference in Young's modulus or geometrical scale is a highly challenging topic for numerical simulation. One of the fundamental questions is how to build an accurate multi-scale method with optimal computational efficiency. In this work, we develop a material-point-spheropolygon discrete element method (MPM-SDEM). Our approach fully couples the material point method (MPM) and the spheropolygon discrete element method (SDEM) through the exchange of contact force information. It combines the advantage of MPM for accurately simulating elastoplastic continuum materials and the high efficiency of DEM for calculating the Newtonian dynamics of discrete near-rigid objects. The MPM-SDEM framework is demonstrated with an explicit time integration scheme. Its accuracy and efficiency are further analysed against the analytical and experimental data. Results demonstrate this method could accurately capture the contact force and momentum exchange between materials while maintaining favourable computational stability and efficiency. Our framework exhibits great potential in the analysis of multi-scale, multi-physics phenomena.

Hybrid continuum-discrete simulation of granular impact dynamics

“…where ∆t crit is the critical time step size, α ∈ [0, 1] is a safety factor for stability, h is the grid spacing, and c is the acoustic velocity of the continuum. We note that unlike the stability condition in the original MP-DEM [27], Eq. ( 24) uses the mass of material point m p to account for potential gasification which makes m p very small.…”

“…The existing MP-DEM framework [27] calculates the contact force magnitude using a linear spring model f = k N δ, where k N is the contact normal stiffness. However, the linear contact model does not guarantee satisfaction of the non-penetration condition, δ ≤ r p , because it cannot prevent the force magnitude from becoming greater than k N r p .…”

“…Note that unlike the original barrier function in Li et al [29], Eq. ( 22) does not have the free parameter for accuracy control (denoted by d therein), because the barrier thickness has been prescribed to be r p to be consistent with MP-DEM [27]. Then, based on thermodynamic conjugacy, the contact force magnitude f is derived from the barrier function as…”

“…The coupling force is then augmented to each of the MPM and DEM calculations. In doing so, we modify the original MP-DEM [27] to account for gasification of the MPM-discretized continuum. Recall that the trans-phase constitutive relation (10) uses the mass density to detect gasification.…”

“…A promising alternative to the existing approaches is a hybrid continuum-discrete approach that describes a granular material as a continuum and a solid intruder as a discrete entity. One of such hybrid schemes is the material-point and discrete-element method (MP-DEM) [27], whereby MPM and DEM are coupled by exchanging contact force information at their interface. The MP-DEM approach has a high potential to simulate a variety of solid-granular interactions with far greater robustness and efficiency compared with pure continuum or discrete methods.…”