Modification and Application of Limestone HJC Constitutive Model under the Impact Load

Abstract When the Holmquist-Johnson-Cook (HJC) constitutive model is used to simulate limestone under the impact load, problems of a compaction stage not being characterised and low dynamic peak stress prediction accuracy are observed. The numerical simulation and experimental results were inconsistent. In this study, we proposed a modified HJC constitutive model and parameter determination method. Based on the characteristics of the dynamic stress-strain curve of limestone and relationship between axial and volumetric strains, the linear elastic phase of the state equation of the original HJC constitutive model was modified, and a new state equation was proposed. The yield surface of the original HJC constitutive model was modified on the basis of the sensitivity analysis method and limit surface theory, and a method for determining the parameters of the modified HJC constitutive model of limestone was proposed. The modified model and parameter determination method were experimentally verified using the split Hopkinson pressure bar (SHPB) and a high-speed camera. The results showed that the state equation curve of limestone under the impact load was divided into compaction, linear elastic, and fully compacted stages. After the introduction of the pressure parameters M, P, and Q, the nonlinear change in the stress-strain curve during the compaction stage was highly consistent with the SHPB results. The strength parameters fc, A, B, and N exhibited the maximum impact on the dynamic strength of limestone. After the strength parameters A, B, and N were modified for the yield surface, the prediction accuracy of limestone dynamic peak stress was over 97%, the prediction error rate decreased by more than 10%, and the reliability of numerical simulation results improved. These results can provide a simple and feasible numerical simulation method for the dynamic analysis of rock materials.