Extended isogeometric boundary element method formulation for the crack growth analysis of three-dimensional structural components

Abstract

This research proposal continues the developments of the ongoing research grant 2019/18795-6 by São Paulo Research Foundation (FAPESP). The focus of this research project involves the development of enriched numerical formulations for the crack growth analysis of three-dimensional engineering components considering the Linear Elastic Fracture Mechanics and high-cycle fatigue. In this context, the Boundary Element Method (BEM), in its dual version, is a suitable approach to deal with crack growth problems since it does not require a domain mesh, a fact that simplifies the remeshing process. In addition, this research proposal utilizes the isogeometric analysis (IGA), in which the interpolation of both geometrical and mechanical fields relies on the same curves used by computer aided design (CAD) software. Then, the integration between the numerical analysis and the geometric definitions becomes straightforward, which is one of the advantages of the IGA scheme. Besides, isogeometric functions, as B-Splines and Non-uniform B-Splines (NURBS), are able to precisely represent complex geometrical entities, such as circles, torus, quadric surfaces, among others. Additionally, CAD modellings often parametrize solely the boundary of the mechanical components, which is exactly the geometrical information required by the BEM. Considering the coupling between IGA and BEM, this research utilizes the isogeometric BEM (IGABEM) to perform the structural analysis. Moreover, this project will utilize enrichment strategies coupled with IGABEM within the crack propagation modelling. This will simplify the obtaining of important parameters to the crack growth description. Particularly, the development of the expansion over the displacement fields by the Williams's solution for the crack surface. This enrichment strategy allows the direct determination of the Stress Intensity Factors (SIFs), which are relevant parameters for the crack growth analysis, and also improves the quality of the displacements along the crack. Also, it will be possible to incorporate the displacement discontinuity generated by the crack when it crosses the external boundary. To achieve this goal, this proposal utilizes as an enrichment technique the Heaviside function. This scheme has been successfully proposed and implemented by the applicant's PhD student and it dismisses the remeshing task, which can be highly demanding for NURBS surfaces once they are wide macro elements over the body boundary. This research proposal intends the extension of this idea to the crack propagation analysis. As a result, it will be obtained a robust and efficient extended isogeometric BEM (XIGABEM) formulation to analyze crack growth problems within linear elastic fracture mechanics. Afterwards, the XIBEM scheme will be applied to high-cycle fatigue problems, in which the focus is to determine the admissible number of cycles that a engineering component can perform safely. It is worth mentioning that Professor Trevelyan's group at Durham University (UK) has a wide experience over these topics since he has worked on isogeometric, enriched and three-dimensional BEM formulations as research themes. Thus, his group's contributions will certainly be valuable for the success of this research proposal. (AU)