Send to

Choose Destination
Proc Natl Acad Sci U S A. 2013 Nov 26;110(48):19291-4. doi: 10.1073/pnas.1318739110. Epub 2013 Nov 11.

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

Author information

Department of Civil and Environmental Engineering, Northwestern University, Evanston, IL 60208.


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 paper outlines the basic idea of the macroscopic 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 the maximum 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.


dimensional analysis; dynamic fracture; fracture mechanics; shale gas

[Indexed for MEDLINE]
Free PMC Article

Supplemental Content

Full text links

Icon for HighWire Icon for PubMed Central
Loading ...
Support Center