Shock wave in a one-dimensional granular chain under Hertz contact

Area of Science:

• Physics
• Materials Science
• Nonlinear Dynamics

Background:

• Shock waves propagate through various media, including granular materials.
• Understanding granular shock wave dynamics is crucial for material science and engineering applications.
• Previous studies have explored shock wave behavior in one-dimensional granular systems.

Purpose of the Study:

• To numerically investigate the behavior of shock waves in a one-dimensional bead chain.
• To analyze the influence of initial overlap on shock wave characteristics, including bead velocity and shock velocity.
• To refine existing models by examining the crossover in shock velocity dependence on piston velocity and initial overlap.

Main Methods:

• Numerical simulations were employed to model the shock wave propagation.
• Analysis focused on bead velocity oscillations around piston velocity.
• The study examined the structure of the shock front and its solitary wave components.

Main Results:

• The shock front is characterized by multiple solitary waves.
• Maximum bead velocity is limited to twice the piston velocity when initial overlap is zero.
• With non-zero initial overlap, maximum bead velocity is between piston velocity and twice the piston velocity.
• Shock velocity depends on both piston velocity and initial overlap, with a clear crossover observed.

Conclusions:

• The study provides a comprehensive understanding of shock wave propagation in one-dimensional granular chains.
• Initial overlap significantly modifies shock wave behavior, affecting both bead and shock velocities.
• The findings offer an improved description of shock velocity dependence on system parameters, advancing previous research.