Abstract
While most granular materials in nature and technology consist of non-convex particles, the majority of discrete element (DEM) codes are still only able to cope with convex particles, due to the complexity of the computational geometry and the occurrence of multiple contacts. We have reengineered a code for convex polygonal particles to model non-convex particles as rigidly connected clusters. Constricting non-convex particles along the symmetry axes by 30% leads to an increase of the materials strength of up to 50%.
Highlights
IntroductionMost discrete element methods use convex particles: Tangential forces are taken up only by (dry, Coulomb-) friction forces
Most discrete element methods use convex particles: Tangential forces are taken up only by friction forces
For an increase of the non-convexity for the same elongation, the material strength increases up to 50The effect comes from the tangential forces which for non-convex particles are picked up and deflected by the interlocking surface geometries via the elastic normal forces
Summary
Most discrete element methods use convex particles: Tangential forces are taken up only by (dry, Coulomb-) friction forces. We use the Cundall-Strack-model [7] for Coulomb friction where the tangential friction force between two particles is incremented proportional to their relative sliding distance, and a cutoff μN is introduced proportional to the normal force N = Fel + Fdiss We implement rigid clusters where the the equations of motion (including rotation) act on the center of mass of the (rigid) cluster, while the interaction laws (forces, torques) between monomers of different clusters are the ones above for convex polygons, as layed out in Ref. Different from clusters of round particles [1], polygonal monomers of the same particle (see Fig. 4) don’t overlap, so there is no local variation of the Young’s modulus due to multiple overlaps, with unforseeable consequences for the stability.
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