Mathematics

CLC number: O 175.5

Cortical Bone Model with a Microcrack under Tensile Loading

¹ School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, Ningxia, China
² School of Science, Ningxia Medical University, Yinchuan 750004, Ningxia, China

^† To whom correspondence should be addressed. E-mail: wws@nxu.edu.cn
li_x@nxu.edu.cn

Received: 8 April 2022

Abstract

The fracture mechanics of cortical bone has received much attention in biomedical engineering. It is a fundamental question how the material constants and the geometric parameters of the cortical bone affect the fracture behavior of the cortical bone. In this work, the plane problem for cortical bone with a microcrack located in the interstitial tissue under tensile loading was considered. Using the solution for the continuously distributed edge dislocations as Green's functions, the problem was formulated as singular integral equations with Cauchy kernels. The numerical results suggest that a soft osteon promotes microcrack propagation, while a stiff osteon repels it, but the interaction effect between the microcrack and the osteon is limited near the osteon. This study not only sheds light on the fracture mechanics behavior of cortical bone but also offers inspiration for the design of bioinspired materials in biomedical engineering.