Strain-rate effects associated with the HJC concrete model

The Holmquist-Johnson-Cook (HJC) model for concrete was presented in 1993 and has been used extensively since that time. Since then a third invariant effect has been added and the shear modulus has been revised to vary such that Poisson's ratio is held constant. It has always been diffcult, however, to determine the appropriate constant for the strain-rate effect as most of the published data are for the net stress as a function of the strain rate. Because concrete is both pressure dependent and strain-rate dependent, it is necessary to separate the individual effects. Recently strain-rate data for three concrete materials were presented by Piotrowska and others [1, 2], where the data are presented as equivalent stress versus confining pressure for a high strain rate and a quasi-static strain rate. This is the form necessary to determine the appropriate strain-rate effect, and the data show that the strain-rate effect is larger than used in the initial publication of the HJC model, and also that the strain-rate effect is a function of the confining pressure. For lower pressures the strain-rate effect is a factor to be applied to the quasi-static data (which is the effect represented in the original HJC model), but for higher pressures the strain rate effect is better represented by an additive term. With the addition of an another HJC constant (the pressure at which the strain rate effect transitions from a multiplied factor to an additive term) it is possible to more accurately represent the response of concrete under high pressures and high strain rates, and it is possible to compute more accurate results for projectile penetration into concrete targets. The paper presents the modified form of the HJC model, an analysis of the strain-rate effects, and results of penetration computations that are compared to experimental data in the literature.