Contact model for elastically anisotropic bodies and efficient implementation into the discrete-element method

TL;DR

This paper presents a simplified, accurate contact law for elastically anisotropic bodies that integrates into discrete element methods, enabling efficient simulations and demonstrating effects of anisotropy on macroscopic behavior and vibrational properties.

Contribution

It introduces a Hertz-like contact law for anisotropic materials with orientation-dependent contact modulus and an efficient implementation method for discrete element simulations.

Findings

The contact law accurately models anisotropic elastic contacts across various geometries.

Efficient precomputation enables practical simulation of anisotropic particles.

Anisotropy can be exploited to engineer tunable vibrational band gaps.

Abstract

We introduce a contact law for the normal force generated between two contacting, elastically anisotropic bodies of arbitrary geometry. The only requirement is that their surfaces be smooth and frictionless. This anisotropic contact law is obtained from a simplification of the exact solution to the continuum elasticity problem and takes the familiar form of Hertz' contact law, with the only difference being the orientation-dependence of the material-specific contact modulus. The contact law is remarkably accurate when compared with the exact solution, for a wide range of materials and surface geometries. We describe a computationally efficient implementation of the contact law into a discrete element method code, taking advantage of the precomputation of the contact modulus over all possible orientations. Finally, we showcase two application examples based on real materials where elastic anisotropy of the particles induces noticeable effects on macroscopic behavior. Notably, the second example demonstrates the ability to engineer tunable vibrational band gaps in a one-dimensional granular crystal by mere rotation of the constituent spherical particles.