A Continuum Approximation for Particle Flux and Projectile Dynamics in Granular Impact

Author: Michael Nicholas Petrakis

Abstract

This work develops a continuum mathematical model for the interaction between a spherical projectile and a granular medium during impact. The granular surface is approximated by a three-dimensional Gaussian boundary, while the projectile is represented as a time-dependent spherical surface. A surface-flux formulation is introduced to describe the redistribution of granular material and is coupled to the changing submerged geometry of the projectile. The projectile dynamics are modeled using gravity together with an effective quadratic granular-resistance force, producing a coupled differential-algebraic system. The formulation is then generalized to arbitrary projectile radius and granular-surface parameters. Finally, the microscopic structure of quartz and granular jamming are discussed to provide physical context for the effective continuum description.

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