Bone crack inspired pair of Griffith crack opened by forces at crack faces

• Published in: Mechanics of advanced materials and structures 2024-11, Vol.31 (26), p.7957-7966
• Main Authors: Awasthi, A. K., Kaur, Harpreet, Rachna, Ali Siddiqui, Shavej, Emadifar, Homan
• Format: Article
• Language: English
• Subjects: biomechanics; biomedical; bone; components; coupled Fredholm integral equation; Crack opening displacement; Crack tips; cracks; Design criteria; displacement components; Fourier transform; Fourier transforms; Fracture mechanics; Fractures; Fredholm equations; Fredholm integral equations; Griffith crack; Griffith Irwin fracture; Half spaces; healthcare analysis; Integral equations; isotropic medium; orthotropic medium; stress; Triple integral equations
• ISSN: 1537-6494; 1537-6532
• DOI: 10.1080/15376494.2023.2253019

The mathematical theory of elasticity helps in the study of physical quantities in the problem of structures. The structures face the problem of crack's presence, which makes the problem difficult but not impossible to deal. Integral equations are useful in a variety of problems. Integral equations are used to solve problems like fracture mechanics or fracture design. The physical interest in the fracture design criterion is due to stress and crack opening displacement components. We have an accurate form of stress and displacement components for a pair of longitudinal crack propagations in the bone fracture of the human body at the interface of an isotropic and orthotropic half-space that are bounded together in the proposed study. The expression was calculated using the Fourier transform approach near the crack tips, but these components were evaluated using Fredholm integral equations and subsequently reduced to coupled Fredholm integral equations. We employ the Lowengrub and Sneddon problem in this research and reduce it to triple integral equations. The Srivastava and Lowengrub method reduces the solution of these equations to a coupled Fredholm integral equation. The problem is further reduced to a decoupled Fredholm integral equation of the second kind. Triple integral equations are solved, and the problem is reduced to a coupled Fredholm integral equation. The Fredholm integral equation is solved and reduced to a decoupled Fredholm integral equation of the second kind. Stress and crack opening displacement components drive physical interest in fracture design criteria. Finally, the stress and displacement components may be simply calculated in their exact form.