The material-point method for granular materials

Abstract

A model for granular materials is presented that describes both the internal deformation of each granule and the interactions between grains. The model, which is based on the FLIP-material point, particle-in-cell method, solves continuum constitutive models for each grain. Interactions between grains are calculated with a contact algorithm that forbids interpenetration, but allows separation and sliding and rolling with friction. The particle-in-cell method eliminates the need for a separate contact detection step. The use of a common rest frame in the contact model yields a linear scaling of the computational cost with the number of grains. The properties of the model are illustrated by numerical solutions of sliding and rolling contacts, and for granular materials by a shear calculation. The results of numerical calculations demonstrate that contacts are modeled accurately for smooth granules whose shape is resolved by the computation mesh. Ó

Numerical implementation of imperfect interfaces

“…Algorithms for dealing with contact have been developed by allowing multiple velocity fields on the background grid. Previous work models slip, stick, or frictional sliding at material interfaces [6,9] or on crack surfaces [10][11][12]. The multiple velocity fields are for different materials or for two sides of a crack, respectively.…”

“…Second, the nodal values are examined to determine if the two velocity fields are in contact. If there is contact, the nodal velocities are altered to [6,9] …”

“…Here µ is the coefficient of friction and ∆v (iii) Once contact velocities are altered, the MPM algorithm proceeds as usual for each velocity field [9]. The standard tasks include computation of internal forces due to particle stress, f ) and the accelerations in step (iii), however, the update would be wrong.…”

“…The simple non-linearity used here was a bilinear law where D n was different for an opened interface under tension than for a closed interface under compression. Since MPM with contact methods [6,9] already detects separation or contact (in tasks (ii) and (iv) above), the imperfect interface tasks used that information. When the interface is in contact, the compressive D n was used; when the interface is separated, the tensile D n was used.…”

Mesoscale numerical modeling of plastic bonded explosives under shock loading

“…For heterogeneous materials like explosives, MPM is more suitable for solving problems involving contact between colliding objects, cracks, large EPJ Web of Conferences deformations and other high velocity problems. It has an advantage over FEM in that the use of the regular grid eliminates the need for doing costly searches for contact surfaces [10].…”