Growth of Shock-Induced Solitary Waves in Granular Crystals

TL;DR

This paper analyzes how shock loads induce the formation of solitary waves in granular crystals, providing explicit formulas to predict wave characteristics based on material and shock properties, validated by numerical comparisons.

Contribution

It introduces explicit analytical expressions for the peak contact force and the number of granules involved during the transition to solitary wave formation in granular crystals.

Findings

Derived formulas accurately predict the transition regime dynamics.

The number of granules involved depends on shock and material properties.

Theoretical results match numerical simulations closely.

Abstract

Solitary waves (SWs) are generated in monoatomic (homogeneous) lightly contacting spherical granules by an applied input force of any time-variation and intensity. We consider finite duration shock loads and focus on the transition regime that leads to the formation of SWs. Based on geometrical and material properties of the granules and the properties of the input shock, we provide explicit analytic expressions to calculate the peak value of the compressive contact force at each contact point in the transition regime that precedes the formation of a primary solitary wave. We also provide explicit expressions to estimate the number of granules involved in the transition regime and show its dependence on the characteristics of the input shock and material/geometrical properties of the interacting granules. Finally, we assess the accuracy of our theoretical results by comparing them with those obtained through numerical integration of the equations of motion.