New developments to the hp-adaptive global-local generalized FEM and applications to 3-D fracture mechanics problems

• Grant number: 20/14463-6
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: August 01, 2021
• End date: July 31, 2022
• Field of knowledge: Engineering - Civil Engineering - Structural Engineering
• Principal Investigator: Sergio Persival Baroncini Proenca
• Grantee: Murilo Henrique Campana Bento
• Supervisor: Carlos Armando Magalhães Duarte
• Host Institution: Escola de Engenharia de São Carlos (EESC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: University of Illinois at Urbana-Champaign, United States
• Associated to the scholarship: 19/00435-3 - Hp-adaptive formulation for the global-local generalized finite element method and applications, BP.DR

Abstract

This research project is part of the main PhD grant (FAPESP process number 2019/00435-3), and it is related to the tasks and activities to be developed by the PhD student during the internship period at UIUC (University of Illinois at Urbana-Champaign - USA), under the supervision of Prof. C. Armando Duarte. Three-dimensional (3-D) simulations are often required to solve complex problems in structural engineering that cannot be simplified to two-dimensional (2-D) models without losing important information about their solutions. The main objective of this project is to originally expand the already performed 2-D implementations of the adaptive techniques for the global-local Generalized FEM (GFEM-gl) to 3-D problems. However, it is already expected that these new developments may not be simple and straightforward because of several geometrical difficulties that arise in 3-D simulations. The outstanding expertise of Prof. Duarte and his research group in both this type of simulations and GFEM-gl will contribute to properly guide the computational implementation of these new developments. Initially, the ZZ-BD error estimator and some adaptive techniques will be used to solve 3-D Fracture Mechanics problems using a single-scale (conventional) GFEM approach. Once a good understanding and accuracy of these analyses are obtained, the coupling between the ZZ-BD and the adaptive techniques with the GFEM-gl will be carried out. All of these implementations will be performed so that they can combine the different tools properly. The contributions that this one-year internship program at UIUC will bring to the main PhD project will be essential to complete the 3-D applications proposed in the main research project. In addition, the comprehension of 3-D simulations and the generation of an adaptive tool to solve problems in Fracture Mechanics will certainly expand the range of original results that can arise in this PhD. Finally, the internship will also provide extremely important contributions to the student's professional and scientific training. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BENTO, MURILO H. C.; PROENCA, SERGIO P. B.; DUARTE, C. ARMANDO. Recovery strategies, a posteriori error estimation, and local error indication for second-order G/XFEM and FEM. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, v. 124, n. 13, p. 38-pg., 2023-03-23. (19/00435-3, 20/14463-6)

BENTO, M. H. C.; PROENCA, S. P. B.; DUARTE, C. A.. Well-conditioned and optimally convergent second-order Generalized/eXtended FEM formulations for linear elastic fracture mechanics. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, v. 394, p. 24-pg., 2022-05-01. (19/00435-3, 20/14463-6)