Modeling Rate-Dependent Dissipation in Granular Solids via Continuum Thermodynamics

Understanding the multi-scale processes that control the dissipation of energy during high pressure impact and penetration in granular targets is pivotal to many civilian and military applications. This project will advance knowledge in this area by formulating and validating new hypotheses about the interplay between grain-scale energy loss via surface area creation and the consumption of energy in granular systems undergoing simultaneous comminution, frictional shear and volume change. For this purpose, it is proposed to use energy arguments to reconcile the process of time-dependent crack extension at the scale of single particles with the phenomenology of inelastic creep and/or relaxation in granular solids. Such hypothesis will be verified via a set of coordinated tests conducted at both particle and assembly scale, as well as by constitutive modeling tasks relevant for such two scales of analysis. The experiments will test scaling hypotheses linking the energy necessary to initiate grain fracture to that required to comminute an assembly made of the same particles.The validity of such scaling laws will be tested for a range of strain rates and will be used to assess the role of grain-scale attributes (size, shape and mineralogy) on the dissipation capacity of granular cushions. Data from such tests will be used to formulate rate-dependent models of the crack growth process, as well as of the time-dependent deformation of granular packings. The latter case will be addressed via continuum thermodynamics, and it will be conceived by exploiting a one-dimensional loading configuration that is commonly used in high-pressure tests conducted under quasi-static and dynamic conditions. Hence, by bridging the physics of grain-scale fracture with the processes that control compaction and shearing in granular solids, this project will provide new tools to track the different forms of energy dissipation in granular solids subject to extreme levels of pressure and velocity, thus facilitating the reinterpretation of existing evidences about their performance as protective barriers and/or shock absorbers.