Impact force and moment problems on random mass density fields with fractal and Hurst effects

Area of Science:

• Solid Mechanics
• Computational Physics
• Materials Science

Background:

• Lamb-type problems analyze wave dynamics in elastic media.
• Cellular automata offer a discrete method for simulating wave propagation.
• Understanding wave behavior in heterogeneous media is crucial for material characterization.

Purpose of the Study:

• To apply cellular automata for simulating dynamic responses in elastic half-planes under surface loads.
• To investigate the influence of random mass density fields with fractal and Hurst characteristics on wave propagation.
• To compare the impact of different random field parameters and wave types.

Main Methods:

• Utilized cellular automata to model wave propagation in a half-plane.
• Employed Cauchy and Dagum random field models for mass density.
• Verified the cellular automata code against continuum elastodynamic solutions.
• Assessed wave propagation sensitivity across various fractal and Hurst parameters.

Main Results:

• The mean response amplitude was reduced by the random mass density field.
• The Hurst parameter exhibited a stronger influence on wave response than the fractal dimension, particularly for values below 0.2.
• Rayleigh waves were more affected by random field parameters than pressure waves.

Conclusions:

• Cellular automata provide a viable method for studying wave dynamics in complex media.
• Random mass density significantly alters wave propagation characteristics.
• The Hurst parameter is a critical factor in determining wave response in such heterogeneous elastic materials.