**Comminution of solids caused by kinetic energy of high shear strain rate, with implications for impact, shock, and shale fracturing**

Although there exists a vast literature on the dynamic comminution or fragmentation of rocks, concrete, metals, and ceramics, none of the known models suffices for macroscopic dynamic finite element analysis. This research outlines the basic idea of themacroscopic model. Unlike static fracture, in which the driving force is the release of strain energy, here the essential idea is that the driving force of comminution under high-rate compression is the release of the local kinetic energy of shear strain rate. The density of this energy at strain rates >1,000/s is found to exceed themaximum possible strain energy density by orders of magnitude, making the strain energy irrelevant. It is shown that particle size is proportional to the −2/3 power of the shear strain rate and the 2/3 power of the interface fracture energy or interface shear stress, and that the comminution process is macroscopically equivalent to an apparent shear viscosity that is proportional (at constant interface stress) to the −1/3 power of this rate. A dimensionless indicator of the comminution intensity is formulated. The theory was inspired by noting that the local kinetic energy of shear strain rate plays a role analogous to the local kinetic energy of eddies in turbulent flow.

Example of comminution of material into prismatic hexagonal particles; the velocities are shown as infinitesimal displacements (in which case the gaps at the hexagon corners are second-order small and thus negligible). (A) Undeformed material, (B) sheared material, and (C) comminuted material.

**References:**

Bazant, Z.P., and Caner, F.C. (2014). “Impact comminution of solids due to local kinetic energy of high shear strain rate: I. Continuum theory and turbulence analogy.” J. of the Mechanics and Physics of Solids 64, 223–235 (with Corrigendum, Vol. 67 (2014), p. 14).

Bazant, Z.P., and Caner, F.C. (2014). “Impact comminution of solids due to local kinetic energy of high shear strain rate: II. Microplane model and verification.” J. of the Mechanics and Physics of Solids 64, 236–248.

Bazant, Z.P., and Caner, F.C. (2013). “Comminution of solids caused by kinetic energy of high shear strain rate, with implications for impact, shock and shale fracturing.” Proc., National Academy of Sciences 110 (48), 19291–19294.