# Project Details

### Description

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.

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.

Status | Finished |
---|---|

Effective start/end date | 6/8/15 → 6/7/18 |

### Funding

- Army Research Office (W911NF-15-1-0240-P00003)