Numerical formulation for three-dimensional fracture mechanics problems with a combination of isogeometric and finite element discretizations

• Grant number: 21/06104-9
• Support type: Scholarships in Brazil - Doctorate
• Effective date (Start): October 01, 2021
• Effective date (End): May 31, 2025
• Field of knowledge: Engineering - Civil Engineering - Structural Engineering
• Principal researcher: Rodolfo André Kuche Sanches
• Grantee: Rosicley Júnio Rodrigues Rosa
• Home Institution: Escola de Engenharia de São Carlos (EESC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Isogeometric analysis has been widely applied to structural analysis problems, having as main motivation the integration between computational design and computational mechanics. However, isogeometric discretization presents difficulties in inserting a physical discontinuity. In this sense, we propose the development and computational implementation of a numerical model to analyze the propagation of cracks in three-dimensional structures, constituted by fragile materials and in large displacement regimes, starting from an isogeometric discretization. To enable the representation and propagation of discontinuities while the initial isogeometric discretization is preserved, a domain decompositon method is used, where a local finite element mesh, according to the discontinuity, is superposed on the isogeometric model. Both the global isogeometric model and the local finite element model are based on a positional description that naturally takes into account geometric nonlinearity. Only the local model is reconstructed and remeshed during crack propagation. In order to ensure good efficiency and accuracy of the method, the local model will be enriched, in order to properly represent the stress field at the tips of the cracks, which still allows the direct extraction of stress intensity factors, although the J integral technique must also be implemented for this purpose. The proposed formulation will be evaluated through numerical simulation of several static and dynamic problems that can be described by solid or shell finite elements, and the results will be compared with other results available in the literature. (AU)