Abstract
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.
Highlights
Concrete is a material that is difficult to model accurately under the conditions of large strains, high strain rates and high pressures
Concrete is often defined by its unconfined compressive strength, there are wide ranges of behavior for different concrete materials with similar unconfined compressive strengths
Experimental strain-rate data have been presented for several different concrete materials [1, 2], and the data are for a range of pressures. These data are exactly what are needed to determine an improved description of the strain-rate effect in concrete. They show that the strain-rate effect is greater than previously determined for the original HJC model, and that for lower pressures the strain-rate effect is a factor to be applied to the quasi-static data, but for higher pressures the strain rate effect is better represented by an additive term
Summary
Concrete is a material that is difficult to model accurately under the conditions of large strains, high strain rates and high pressures. The Holmquist-Johnson-Cook (HJC) computational model for concrete was presented in 1993 [3] and it has been used extensively since It is a relative simple model, it represents the strength as a function of the pressure, damage and strain rate; the damage as a function of the pressure, the equivalent plastic strain and the volumetric plastic strain; and the pressure as a function of the. Experimental strain-rate data have been presented for several different concrete materials [1, 2], and the data are for a range of pressures. These data are exactly what are needed to determine an improved description of the strain-rate effect in concrete. The remainder of this article briefly describes the original and modified HJC models; it provides an analysis of the strain-rate data presented by Piotrowska et al [2]; it determines the appropriate strain-rate parameters for a 48 MPa concrete provided by Hanchak et al [7]; it provides computed results for the response of penetrators impacting concrete targets; and it provides comparisons of these results to test data that are presented by Hanchak et al
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