Strain-rate-dependent microplane model for high-rate comminution of concrete under impact based on kinetic energy release theory

Kedar Kirane, Yewang Su, Zdeněk P. Bažant*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


The apparent increase of strength of concrete at very high strain rates experienced in projectile impact (10 s-1 to 106 s-1), called 'dynamic overstress', has recently been explained by the theory of release of local kinetic energy of shear strain rate in finite size particles about to form. This theory gives the particle size and the additional kinetic energy density that must be dissipated in finite-element codes. In previous research, it was dissipated by additional viscosity, in a model partly analogous to turbulence theory. Here it is dissipated by scaling up the material strength. Microplane model M7 is used and its stress-strain boundaries are scaled up by factors proportional to the-4/3rd power of the effective deviatoric strain rate and its time derivative. The crack band model with a random tetrahedral mesh is used and all the artificial damping is eliminated. The scaled M7 model is seen to predict the crater shapes and exit velocities of projectiles penetrating concrete walls of different thicknesses as closely as the previousmodels. The choice of the finite strain threshold for element deletion criterion, which can have a big effect, is also studied. It is proposed to use the highest threshold above which a further increase has a negligible effect.

Original languageEnglish (US)
Article number20150535
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2182
StatePublished - Oct 8 2015


  • Crack band model
  • Dynamic overstress
  • Finite-element simulation
  • Material fragmentation
  • Projectile impact
  • Strain-rate effects

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)


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