Shock-induced solitary waves in granular crystals

Area of Science:

• Physics
• Materials Science
• Nonlinear Dynamics

Background:

• Solitary waves (SWs) are nonlinear waves that maintain their shape during propagation.
• Granular materials exhibit complex behaviors under impact, including wave generation.
• Understanding SW formation in granular systems is crucial for impact mitigation and energy dissipation.

Purpose of the Study:

• To develop analytical models for predicting solitary wave (SW) formation in one-dimensional granular chains.
• To derive expressions for contact forces and the number of involved granules during the transition regime.
• To validate theoretical predictions against numerical simulations.

Main Methods:

• Analytical modeling of wave propagation in a 1D array of spherical granules.
• Derivation of explicit formulas for peak contact forces.
• Estimation of the number of granules participating in the transition regime.
• Numerical integration of equations of motion for validation.

Main Results:

• Explicit analytic expressions for peak compressive contact forces in the transition regime were derived.
• Formulas were provided to estimate the number of granules involved in SW formation.
• The dependence of these parameters on shock properties and granule characteristics was analyzed.
• Theoretical results showed good agreement with numerical simulations.

Conclusions:

• The study successfully provides analytical tools to predict key parameters of solitary wave formation in granular chains.
• The findings offer insights into the transition regime preceding SW generation.
• The validated models can aid in the design of granular systems for specific wave propagation characteristics.