### Abstract

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 language | English (US) |
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Article number | 20150535 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 471 |

Issue number | 2182 |

DOIs | |

State | Published - Oct 8 2015 |

### Keywords

- 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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## Cite this

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*,

*471*(2182), [20150535]. https://doi.org/10.1098/rspa.2015.0535