Page 153 - 《爆炸与冲击》2026年第2期

第 46 卷 高 矗，等： 剪切增强和应变率效应对混凝土类材料状态方程的影响 第 2 期

behaviors, including the shear-enhanced compaction effect and strain-rate effect. Based on the high-fidelity numerical
simulations described above, a quantitative analysis was conducted to investigate the influence of the shear-enhanced
compaction effect and strain-rate effect on EoS behavior of concrete-like materials, and the challenges associated with
eliminating the shear-enhanced compaction and strain-rate coupling effects in flyer-plate impact tests were systematically
identified. The results demonstrate that the Kong-Fang model, when combined with the SPG algorithm, can accurately simulate
the complex dynamic mechanical behaviors of concrete-like materials, including shear-enhanced compaction effect and strain-
rate effect. To achieve high-precision simulation of dynamic mechanical behaviors of concrete-like materials subjected to blast
and impact loadings across high-medium-low pressure ranges, it is essential to establish an EoS with a wide-range pressure
based on experimental data from EoS behavior tests. However, shear-enhanced compaction and strain-rate coupling effects
should be eliminated when using flyer-plate impact test data to calibrate the EoS parameters. A paradox arises in the
establishment of EoS with wide-range pressure for concrete-like materials, and the application of numerical iteration correction
methodology may represent an effective approach to resolving this challenge. These findings provide a theoretical foundation
for the future development of a numerical iteration correction methodology to eliminate the shear-enhanced compaction effect
and strain-rate effect on the EoS of concrete-like materials, thereby facilitating the establishment of a high-precision EoS with a
wide range of pressure for concrete-like materials subjected to impact and blast loadings.
Keywords: concrete-like material; blast and impact loadings; equation of state; shear-enhanced compaction effect; strain-rate effect

混凝土类材料（普通混凝土、水泥砂浆和超高性能混凝土等材料的统称）广泛用于军用和民用防护
结构中 [1-3] 。在炸药爆炸或弹体侵彻等强动载作用下，混凝土类材料可能发生动态拉伸、剪切和压缩等典
型破坏现象 [4-5] 。对爆炸冲击荷载作用下混凝土类材料中应力波传播衰减和动态损伤破坏的精细化数值
模拟是当前研究的热点和难点 [6-8] 。
在爆炸冲击荷载作用近区，混凝土类材料因受高压和高应变率作用而呈近似流体状态，经典损伤塑
[9]
性模型难以有效描述该状态下的力学行为 。目前普遍采用的爆炸冲击荷载作用下混凝土类材料模型
为流体弹塑性模型，如 Holmquist-Johnson-Cook （HJC）模型 [10] 、Riedel-Hiermaier-Thoma （RHT）模型 [11] 、
Karagozian and Case （K&C）模型 [12] 和 Kong-Fang 模型 [13] 。在流体弹塑性模型中，混凝土类材料因孔隙坍
塌和裂纹扩展引起的力学行为变化分别由状态方程（球量）和强度面（偏量）描述。在爆炸冲击荷载作用
下，动态压缩破坏发生在高静水压力状态，动态剪切破坏发生在较低或中等静水压力状态，而动态拉伸
破坏则通常发生在低静水压力状态 。因此，流体弹塑性模型中的状态方程必须能同时准确描述混凝土
[4]
类材料在高-中-低压下的力学行为，即需要建立混凝土类材料宽广压力范围的状态方程。然而，由于混
凝土类材料的等压屈服特性和剪胀特性 [13-14] ，材料既可在等压受力下因压缩而屈服，也可在剪应力作用
下产生体积变形，体积应变与剪应力有关，剪应变与静水压力有关，即存在应力球量与偏量的耦合作用 [13-16] ，
从而给建立混凝土类材料高精度、宽广压力范围的状态方程带来很大挑战。

状态方程（equation of state，EoS）描述了材料
静水压力、密度和内能三者之间的变化，用 3 个 Pressure
维度的空间曲面（Hugoniot 曲面）来描述，曲面上的 Granular material
任意一点均代表材料的某一特定状态 [15] 。由于
材料的内能变化无法直接测量，因此状态方程通 p lock
常简化为二维平面上的压力和密度（常用体积应 Pore compaction
变描述）关系曲线 [17-18] ，如图 1 所示。对于获取 Unloading
混凝土类材料 EoS 数据的实验方法，最初是在静 p crush Unloading
O
高压条件下，对材料体积应变随静水压力的变化 Linear elasticity Volumetric strain
规律进行实验研究而开始的，对应的实验称为静
图 1 混凝土类材料状态方程示意图 [18]
水压缩实验 [19] 。静水压缩实验通常利用伺服装 Fig. 1 Typical equation of state for concrete-like materials [18]

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