Bridging Dynamic Particle Fracture and High-Strain Rate Comminution of Granular Continua

Understanding the multi-scale processes that control energy dissipation during penetration and impact is pivotal to a wide variety of civilian and military applications. This project will advance knowledge in this area by formulating and validating hypotheses about the interplay between grain-scale dissipation via surface area growth and energy consumption in granular materials undergoing comminution. For this purpose, it is proposed to bridge the mechanics of collective breakage in particulate solids to the physics of dynamic fracture. The goal is to derive a thermodynamic theory able to replicate the wide range of inelastic processes taking place in granular media, as well as to express the dissipative capacity of these materials as a function of their grain scale properties (e.g., size, shape, mineralogy). The primary objective of the project is to explain the role of the strain rate on the proportion of frictional and breakage dissipation in granular targets subjected to rapid loads, as well as to reinterpret their rate-sensitivity in terms of the dynamics of crack growth at the grain-scale. For this purpose, theoretical mechanics, laboratory experiments and advanced computing will be used. Crack growth laws inspired by available solutions of dynamic stress intensity factor will be employed to formulate rate-dependent comminution laws for granular solids. To bridge these length scales, scaling relations connecting the rate of entropy production in assemblies to the dynamic fracture of individual grains will be formulated, while the timescale of macroscopic comminution will be connected to the characteristic time of failure of individual particles. Direct visualization based on X-Ray micro-tomography will be used to facilitate the model formulation and assess the evolution of polydispersity during rapid loading, while numerical analyses will be conducted to test the predictive performance of the theory against evidences of heterogeneous crushing during penetration and impact. By bridging the physics of grain-scale fracture with the processes that control compaction and shearing in packed assemblies this project will provide new tools to track the different terms of energy loss in particulate solids subjected to extreme pressures and velocities. Successful completion of this project will therefore generate new methods to engineer the performance of granular systems deployed as protective barriers and/or shock absorbers, as well as to optimize the wide range of applications involving the multi-scale mechanics of inter-particle interactions.