Average balance equations, scale dependence, and energy cascade for granular materials

Area of Science:

• Physics
• Mechanical Engineering
• Materials Science

Background:

• Granular materials present challenges in modeling due to the discrete-to-continuum transition.
• Previous averaging methods often suffer from domain-size dependency, leading to significant errors.

Purpose of the Study:

• To develop a new averaging method for granular materials.
• To derive accurate average balance equations for granular flows.
• To address the limitations of existing methods regarding domain-size dependency.

Main Methods:

• Developed a novel averaging method decomposing properties into mean values and fluctuations, incorporating gradient effects.
• Applied a local homogeneity hypothesis to simplify balance equations.
• Utilized discrete particle simulation to generate data for a simple shear flow.

Main Results:

• The new method successfully derives average balance equations for granular materials.
• It resolves the issue of domain-size dependency in macroscopic property calculations.
• The method clearly separates affine and nonaffine fields, providing insights into energy cascades.

Conclusions:

• The developed averaging method offers a robust framework for analyzing granular material behavior.
• It accurately predicts macroscopic properties and clarifies energy dissipation mechanisms.
• This approach enhances the understanding of granular flows, particularly in steady, developed conditions.