Intermediate asymptotics on dynamical impact of solid sphere on militextured surface

Area of Science:

• Physics
• Mechanical Engineering
• Materials Science

Background:

• Complex phenomena often exhibit scale-dependent power-law behaviors.
• Understanding the dynamics of solid sphere impacts on elastic surfaces is crucial for various engineering applications.

Purpose of the Study:

• To describe the global scaling behavior of solid sphere impacts on elastic surfaces.
• To develop a theoretical model for predicting impact dynamics based on fundamental physical properties.

Main Methods:

• Dimensional analysis was applied to identify the fundamental dimensionless function governing the impact.
• Energy conservation principles were used to complement the dimensional analysis.
• Newly defined dimensionless parameters were introduced to summarize key factors.

Main Results:

• The power-law behavior is determined by the interplay between inertial and elastic properties, influenced by the sphere's scale.
• Two intermediate asymptotic regimes were identified within different scale ranges.
• The theoretical model demonstrated good agreement with experimental observations.

Conclusions:

• The study provides a comprehensive model for the dynamical impact of solid spheres on elastic surfaces.
• The findings offer insights into dimensional analysis and the concept of self-similarity in physical phenomena.
• The developed dimensionless parameters effectively capture the scale-dependent behavior of the impact dynamics.