Assessment of torsional behavior of bone section using meshfree method based on TPS radial basis function

Abstract

The torsional study of bone cross-sections consisting of porous and functionally graded material (FGM) is presented in this paper. The modeling of the bone can be thought of as an FGM. For the modeling of FGM material, a classical power law is used. The strength of the bone is reduced when the microstructure of the bone changes with age. Saint-Venant torsion theory is used to formulate the governing equation. Thin plate spline (TPS) radial basis function-based collocation meshfree method is used for discretization and solution of the governing differential equations. The discretized partial differential equations are solved using MATLAB programming. To assess the effectiveness and accuracy of the current TPS-based meshfree approach, numerical examples for circular and hollow circular sections were used to conduct a convergence and validation test. Finally, the torsional rigidity and shear stress of the FGM and porous bone sections are estimated using an actual cross-section of the bone. After conducting a convergence study, a method is developed to produce fresh findings for the actual bone shape section.