Dynamics of Grain Shape Evolution in Particulate Media Subjected to Impact

Understanding the multi-scale processes that affect the topology and mechanics of granular matter is one of the most remarkable challenges in engineering mechanics. In this project, we address this topic by examining the coupled evolution of grain-scale attributes and macroscopic deformation in anisotropic particle packings subjected to extreme pressure and strain rates. Specifically, we propose a comprehensive examination of the simultaneous evolution of two attributes affecting transmission of forces, propagation of elastic waves, and strain energy dissipation: the size and shape of the brittle particles that constitute the building blocks of this class of materials. To address this problem, we will follow a multidisciplinary strategy based on concepts of continuum mechanics, granular physics, experimental mechanics, digital image analysis, and computational modeling. Our key hypothesis is that, despite the nearly exclusive focus of current scientific research on decoding the role of the particle size distribution, the macroscale behavior of granular systems is crucially affected by the shape of their constituting particles, as well as by their evolution. We thus posit that the particle shape is an essential factor for mechanical modeling and characterization protocols. For this purpose, and in agreement with evidence of extreme fragmentation in nature, we postulate the existence of an ultimate shape for heavily crushed particles and examine whether such geometric attractor is reached in conjunction with well-known power-law size distributions typical of comminution limits for brittle solids. This hypothesis is used for constitutive modeling purposes and multi-scale experiment design. Specifically, we aim to test new hypotheses about the evolution of particle shape of crushable particulate solids by: (i) formulating a high-strain-rate continuum-scale framework treating the statistical distribution of the particle shapes as a state variable evolving upon fracture and affecting the dissipation capacity of the solid; (ii) characterizing with digital imaging and ultrasonic measurements the anisotropic elastic properties of grain packings; (iii) implementing our model into simulation platforms able to explain patterns of impact and penetration, as well as to explore a broad space of variables influential for the mechanical performance of particulate materials. If successful, this project will advance our knowledge in this area of solid mechanics by testing new hypotheses about the interplay between grain-scale microstructure evolution and macroscale energy dissipation. Most notably, by bridging the mechanics of particle shape evolution with the resulting alterations of macroscale mechanical properties, this process can shed new light on the processes that control stress transmission and elastic wave steering in materials with adaptive topology, thus inspiring strategies to engineer the performance of protective barriers and/or shock absorbers.