3D fracture study of cracked functionally graded biological materials by XIGA approach using Bézier extraction of NURBS. (April 2023) - Mishra, Ranjan
Abstract: Functionally graded material (FGM) offers many varied engineering applications especially in biomedical implants and also used as biomaterials in orthopaedic implants such as hip & knee replacement and joint replacements and orthodontic applications. High risks are involved with revision surgery as orthopaedic prostheses suffer from limited lifetime. Commonly used bio materials consist of uniform and single constituent are vulnerable for their fabrication. Therefore, FGMs are developed to fabricate hybrid bio-material for overcoming these shortcomings. A long service life and safety of these hybrid bio-materials used in biomedical applications are one of the most important objective for their safe design and fabrications. In this paper, three-dimensional (3D) fracture problems in elastically graded biological materials by extended isogeometric analysis (XIGA) using Bézier extraction of NURBS are numerically simulated to understand the fracture behaviour. Bézier extraction of NURBS-based basis functions are implemented in discretization of domain for approximating both unknown field solution and geometries. The Bézier extraction operation decomposes the NURBS basis functions into a set of linear combination of Bernstein polynomials and a set of C 0 –continuity Bézier elements. For FGMs, exponential law has been implemented for grading the material property from left region (Material-A) to right region (Material-B). Few test cases based on penny-shaped crack problems have been solved to calculate fracture parameters, Von-Mises stress contours and deformation contours. Highlights: Investigation of three-dimensional fracture behaviours in functionally graded biomaterial plate containing 3D penny shaped and semi-circular crack under mechanical loading environment is done by XIGA approach using Bézier extraction of NURBS. Fracture parameter i.e., SIFs based on modified interaction integral phenomenon under mechanical tensile loads are calculated. Deformation contours, Von-Mises stress contours and mode-I, mode-II, mode-III SIFs are achieved for few elastically graded biological material (FGBM) systems containing 3D penny shape crack. Studies on the effect of material gradation directions, different FGM system of materials, semi-circular crack, and mechanical tensile loads in elastic field on SIFs are don.