Abstract The original Holmquist-Johnson-Cook (HJC) model, which can only capture the compressive behaviour but not the tensile behaviour of brittle materials, is modified in this study. First, the Lode-angle function is introduced to the yield strength surface to consider the changes in the substantial shear strength between the tensile and compressive meridians. A hyperbolic function is used to describe the strain rate effect under dynamic tensile loading. An exponential model is introduced to express the tensile softening stage of brittle material and define the tensile damage variable. Then the modified HJC model is implemented in LS-DYNA via user subroutine UMAT. Further the modifications are validated by single element tests and rock mechanical laboratory experiments. The verification results show that the modified HJC model can effectively describe the tensile responses of brittle material under static and dynamic loading. Last, a comparison between a blasting-crater field test and the corresponding numerical prediction by the modified HJC model is carried out. The comparison results demonstrate that the shape and size of the crater predicted by the modified HJC model show a good agreement with the field test data. Therefore, the modified HJC model has the capacity to capture the tensile and compressive behaviours and damage evolution of brittle material.

中文翻译：

---

改进的 HJC 模型用于改进爆破载荷下脆性材料的动态响应

摘要 本研究修改了原始的 Holmquist-Johnson-Cook (HJC) 模型，该模型只能捕捉脆性材料的压缩行为而不能捕捉拉伸行为。首先，将洛德角函数引入屈服强度表面，以考虑拉伸和压缩子午线之间的实质剪切强度的变化。双曲线函数用于描述动态拉伸载荷下的应变率效应。引入指数模型来表达脆性材料的拉伸软化阶段并定义拉伸损伤变量。然后修改后的 HJC 模型通过用户子程序 UMAT 在 LS-DYNA 中实现。进一步的修改通过单元素测试和岩石力学实验室实验得到验证。验证结果表明，改进后的HJC模型能够有效地描述脆性材料在静态和动态载荷下的拉伸响应。最后，进行了爆破坑现场试验与相应的改进HJC模型数值预测的比较。对比结果表明，改进后的HJC模型预测的陨石坑形状和大小与现场试验数据吻合较好。因此，修改后的 HJC 模型能够捕捉脆性材料的拉伸和压缩行为以及损伤演化。对比结果表明，改进后的HJC模型预测的陨石坑形状和大小与现场试验数据吻合较好。因此，修改后的 HJC 模型能够捕捉脆性材料的拉伸和压缩行为以及损伤演化。对比结果表明，改进后的HJC模型预测的陨石坑形状和大小与现场试验数据吻合较好。因此，修改后的 HJC 模型能够捕捉脆性材料的拉伸和压缩行为以及损伤演化。