Ballistic limit assessment for concrete slabs using the MHJC concrete model

A modified version of the Holmquist-Johnson-Cook (MHJC) model was developed by the authors to handle impact and penetration problems in concrete. In this modified version a new continuous pressure-shear function is adopted where the influence of the third deviatoric stress invariant is considered; in addition, a new strain-rate sensitivity formulation is included and finally three damage variables describing the tensile cracking, shear cracking and pore compaction mechanisms are introduced. Model parameters are obtained for two concrete qualities and perforation of concrete slabs by pointed projectiles is considered numerically and compared with experimental results from the literature. Ballistic limit assessments with deviations under 8 % when compared to the experiments are obtained. The normalizing parameters are the quasi-static uniaxial compressive strength c f and the reference strain rate 0 ε& . Further, B is the pressure hardening coefficient, N is the pressure hardening exponent, C is the strain rate sensitivity coefficient, and max S is the normalized maximum strength that can be developed. Material degradation is described by the damage variable D , resulting in reduction of the cohesive strength. In the negative pressure regime ( 0 P < ) the normalized hydrostatic tension c T T f ∗ = is introduced with T as the maximum hydrostatic tension the material can withstand. The new functions ( ) * eq F ε& and ( ) , R e θ are defined below. By assuming 1.8 2.0 B ≤ ≤ and 0.60 0.80 N ≤ ≤ the MHJC material model agrees with experimental results for the compressive meridian, reported in the literature (Chen 1982), assuming an undamaged state as illustrated in Figure 1. In a complete damaged state ( 1 D = ) concrete behaves as a granular material and the term ( ) * 1 T D − in Equation 1 van-