Wave Propagation in a Row of Topologically Interlocked Tetrahedra

Abstract

This study is concerned with the mechanics of wave propagation in a
type of architectured, granular, material system. Specifically, we investigate
wave propagation in a topologically interlocked material (TIM)
system. TIM systems are assemblies of polyhedrons in which individual
polyhedrons cannot be removed from the assembly without complete disassembly due to the geometric interlocking of the polyhedrons. The study employs an explicit finite element code to compute phase velocities, amplitude distributions, and wave patterns in a linear assembly of topologically interlocking tetrahedra. Tetrahedra are considered fully 3D linear elastic bodies interacting with neighboring tetrahedra by contact and friction.We demonstrate the propagation of a solitary wave along the row of tetrahedra. The velocity of the wave is found to be independent of amplitude for an idealized contact, but dependent of amplitude for a
realistic asperity contact. In the absence of friction and for contact the wave velocity is determined to be approximately 50% the material wave speed, but increases in the presence of friction to about 80% of the material wave speed. We attribute the wave velocity to wave guiding as set by the geometry of the tetrahedra assembly geometry and a rocking motion of tetrahedra on an axis perpendicular to the wave propagation direction. The degree to which such rocking motion occurs is affected by friction.