Mechanical Model of Cortical Bone with Radial Microcrack in Osteon Under Uniaxial Tensile Load

WANG Yulin; HAN Huili; YAN Jie

doi:10.20176/j.cnki.nxdz.20260203

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Mechanical Model of Cortical Bone with Radial Microcrack in Osteon Under Uniaxial Tensile Load

Mathematical and Physical Sciences | 更新时间：2026-04-22

- Mechanical Model of Cortical Bone with Radial Microcrack in Osteon Under Uniaxial Tensile Load
- Journal of Ningxia University (Natural Science Edition in Chinese and English) Vol. 47, Issue 2, Pages: 97-103(2026)
- 作者机构：
  
  1.宁夏师范大学数学与计算机科学学院，宁夏固原 756099
  2.宁夏大学数学统计学院，宁夏银川 750021
- 作者简介：
- 基金信息：
- DOI：10.20176/j.cnki.nxdz.20260203
  CLC：
- Received：26 September 2025，
  
  Published：15 March 2026
- 稿件说明：
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王玉林，韩惠丽，闫洁.单轴拉伸载荷下骨单位含径向微裂纹的密质骨力学模型［J］.宁夏大学学报（自然科学版中英文），2026，47（2）：97-103.

WANG Yulin，HAN Huili，YAN Jie.Mechanical Model of Cortical Bone with Radial Microcrack in Osteon Under Uniaxial Tensile Load［J］.Journal of Ningxia University （Natural Science Edition in Chinese and English）2026，47（2）：97-103.
王玉林，韩惠丽，闫洁.单轴拉伸载荷下骨单位含径向微裂纹的密质骨力学模型［J］.宁夏大学学报（自然科学版中英文），2026，47（2）：97-103. DOI： 10.20176/j.cnki.nxdz.20260203.

WANG Yulin，HAN Huili，YAN Jie.Mechanical Model of Cortical Bone with Radial Microcrack in Osteon Under Uniaxial Tensile Load［J］.Journal of Ningxia University （Natural Science Edition in Chinese and English）2026，47（2）：97-103. DOI： 10.20176/j.cnki.nxdz.20260203.

摘要

针对Haversian密质骨的力学行为，建立含有单条径向微裂纹的密质骨平面力学模型。基于线弹性断裂力学理论和位错方法，推导出骨单位应力场的数学表达式，并构建与应力强度因子相关的奇异积分方程组。数值结果表明，增大骨单位与间质骨间的剪切模量比是抑制裂纹扩展的关键，且当裂纹趋近黏合线时，该抑制效果会因几何屏蔽效应而进一步增强。研究结果可为生物医学工程中仿生材料的设计提供理论依据。

Abstract

This paper investigates the mechanical behavior of Haversian cortical bone by establishing a plane mechanical model of cortical bone containing a single radial microcrack. Based on linear elastic fracture mechanics and crystal dislocation theory， the mathematical expression of the stress field in the osteon is derived， and a set of singular integral equations related to the stress intensity factor is constructed. Through numerical examples， the influence of osteon size， shear modulus ratio， and the location and length of the microcrack on the stress intensity factor at the microcrack tip is systematically studied. The numerical results indicate that increasing the shear modulus ratio between the osteon and the interstitial bone is key to inhibiting crack propagation. Moreover， as the crack approaches the cement line， this inhibitory effect is further enhanced due to the geometric shielding effect. This study provides a theoretical basis for the design of biomimetic materials in biomedical engineering.

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references

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