Study on compressive mechanical tests and constitutive models of cortical bone under different strain rates
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摘要: 皮质骨作为人体骨骼系统的重要组成部分，能有效分散与吸收外部冲击力，保护内部骨髓腔、周围软组织和器官不受损伤。为研究冲击载荷作用下皮质骨的力学响应，借助万能材料试验机、分离式霍普金森压杆（split Hopkinson pressure bar，SHPB）装置对猪皮质骨开展了不同应变率下的准静态与动态压缩实验。采用超景深三维显微系统和数字图像相关（digital image correlation，DIC）技术观察了皮质骨的压缩形变特征，利用含损伤的黏弹性本构模型对实验数据进行了拟合，确定了模型中的本构参数。结果表明，皮质骨在压缩过程中表现为骨质裂纹的产生与扩展，其力学性能具有明显的应变率相关性，弹性模量、屈服应力和压缩强度随应变率的增加而显著提高。准静态加载时，应力-应变曲线包括弹性变形和塑性变形阶段；高应变率加载时，应力-应变曲线在应变小于0.2%时为弹性，随着压缩量的增加呈现高度的非线性，无显著塑性变形，表现出一定的黏弹性特征。通过实验曲线与本构模型理论曲线的对比，理论值与实验值的误差较小，本构模型能准确描述皮质骨在不同应变率下的压缩力学行为，研究成果为人体冲击伤的救治与防护设计提供理论参考。Abstract: Cortical bone, as a critical component of the human skeletal system, effectively disperses and absorbs external impact forces, protecting the internal medullary cavity, surrounding soft tissues, and organs from damage. To investigate the mechanical response of cortical bone under impact loading, quasi-static and dynamic compression experiments were conducted on porcine cortical bone at varying strain rates using a universal material testing machine and a Split Hopkinson Pressure Bar (SHPB) apparatus. The compression deformation characteristics of cortical bone were observed employing ultra-depth three-dimensional microscopy and Digital Image Correlation (DIC) techniques. A damage-integrated viscoelastic constitutive model was applied to fit the experimental data, and the constitutive parameters of the model were determined. The results demonstrate that the compression process of cortical bone is characterized by the initiation and propagation of microcracks, with its mechanical properties exhibiting significant strain-rate dependence. The elastic modulus, yield stress, and compressive strength increase markedly with higher strain rates. Under quasi-static loading, the stress-strain curve consists of distinct elastic and plastic deformation stages. In contrast, under high-strain-rate loading, the stress-strain response remains purely elastic at strains below 0.2%, but transitions into a highly nonlinear regime with increasing compression. Notably, no significant plastic deformation occurs under dynamic loading, revealing pronounced viscoelastic behavior. Comparison between the experimental data and theoretical curves from the constitutive model shows good agreement, with minimal deviations between predicted and measured values. The model accurately captures the compressive mechanical behavior of cortical bone across different strain rates, validating its reliability for simulating impact scenarios. These findings provide valuable theoretical insights for the treatment of impact-related injuries and the design of protective equipment. The strain-rate-dependent mechanical properties of cortical bone highlight the importance of considering dynamic loading conditions in biomechanical studies. This research contributes to a deeper understanding of bone fracture mechanisms under traumatic impacts and supports advancements in injury prevention strategies.
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Key words:
- cortical bone /
- impulsive load /
- viscoelastic /
- strain rate /
- constitutive model
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图 6 SHPB实验原理示意图
Figure 6. Schematic diagram of Split Hopkinson Pressure Bar experimental setup
图 14 应变率为1 800 s−1时整形后的入射、反射和透射波形
Figure 14. Incident, reflected, and transmitted waveforms after shaping at a strain rate of 1 800 s−1
图 15 应变率为1 800 s−1时的应力平衡图
Figure 15. Stress equilibrium diagram at a strain rate of 1 800 s−1
图 18 应变率为1 800 s−1时皮质骨的变形过程
Figure 18. Deformation process of at a strain rate of 1 800 s−1
图 22 低应变率和高应变率时本构模型示意图
Figure 22. Schematic illustration of the constitutive model at low strain rates and high strain rates
表 1 压杆材料参数
Table 1. Material parameters of the pressure bar
材料 ρ0/(kg·m−3) E0/GPa c0/(m·s−1) I0/(kg·m−2·s−1) LC4硬铝合金 2.7×103 70 5.05×103 1.36×107 
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表 2 含损伤的黏弹性本构模型参数
Table 2. Parameters of the viscoelastic constitutive model with damage
D0 a b E0/MPa ηp/(MPa·s) Em/MPa θm/s En/MPa θn/s m n p 1.2 1.1 0.7 2.3×103 0.001 2.1×103 5.7×10−6 2.0×104 14.8 0.99 1.0 0.99
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表 3 拟合决定系数R2
Table 3. Coefficient of determination R2
$ \dot \varepsilon $/s−1 R2 $ \dot \varepsilon $/s−1 R2 0.001 0.997 450 0.990 0.01 0.999 900 0.984 0.1 0.982 2200 0.998 300 0.996
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