Missile Impact with Material Comminution: New Concept - Turbulence Analogy

Despite a vast number of papers and reports and major computer simulation efforts, the predictability of the effects missile impact, explosions and shock waves on concrete structures and armor is still less than satisfactory. Particular difficulties occur in dynamic events in which concrete or armor is subjected to extreme shear or compressive strain rates such as 102/s – 106/s and more. At these rates, the material appears to exhibit a surprisingly high apparent resistance to deformation, called the “dynamic overstress”. Its magnitude is one or more orders of magnitude above what could be computationally predicted with the usual material constitutive laws, even if the visco-elasto-plastic rate effect and the activation energy controlled rate effect of bond breakage at fracture front are carefully taken into account. To overcome this problem, a completely new idea is proposed – the enhanced energy dissipation is caused by material comminution (i.e., fragmentation, pulverization) that is driven by the release of local kinetic energy of shear strain rate field of forming particles which, as it turns out, can exceed the maximum possible strain energy of the particles by orders of magnitude, making the usual fracture mechanics inapplicable. The constitutive laws calibrated by quasi-static tests account only for the dissipation by formation of large fragments of the size of largest material inhomogeneities, but much smaller fragments are known to be produced under impact or shock. The new idea is inspired by analogy with the energy dissipation by eddies in turbulent flow. It rests mathematically on the separation of kinetic energies of global motion and of the local velocity field corresponding to the eddies or to the forming particles. In the proposed new theory, the energy dissipated by interface fracture of forming particles will be simulated by artificial equivalent shear viscosity, analogous to the viscosity enhancement by turbulence, which can easily be implemented in the material subroutine of a finite element program. A dimensionless indicator analogous to Reynold’s number will be introduced to delineate interface fracturing by release of kinetic and strain energies. A number of fundamental questions, dealing with volumetric rate comminution, particle splitting, tensorial viscosity, particle friction after comminution, kinetic configurational forces, micromechanics of kinetic fragmentation, statistical distribution of particle sizes, kinetic energy of ejecta, etc., will be studied and resolved. The resulting model will be implemented in the new microplane model M7 developed under previous ARO grant and introduced as a material subroutine in ABAQUS. A desktop server and NU supercomputer cluster QUEST will be used to simulate various types of impact onto concrete walls, with varying exit velocity or penetration depth. The material model will be calibrated by fitting various published test data and validated by predicting other published test data on missile impact as well as shock (Hopkinson bar tests). Paper(s) presenting the results will be published in a leading mechanics journal and the material subroutine will me made freely available to the US defense laboratories and firms.