A well-conditioned global-local extended/generalized finite element method for three-dimensional fracture mechanics: an approach employing phase-field

• Grant number: 20/14605-5
• 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: Caio Silva Ramos
• 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: 19/00434-7 - Efficient and stable formulation for the generalized finite element method and applications, BP.DR

Abstract

Fracture is the main cause of failure in most engineering structures. However, predicting the initiation and propagation of cracks in materials and structures remains a significant challenge in the mechanics of solids. Applying conventional numerical-computational tools to this class of problems, for example the Finite Element Method (FEM), can prove to be quite challenging or even impossible. In the last two decades, several researches have been addressing the effectiveness of Generalized FEM (GFEM) in solving fracture mechanics problems. However, some difficulties inherent to the FEM bring limitations and practical aspects, in particular, the issue of controlling the numerical conditioning of the system of equations produced by the GFEM. To address this aspect, the research developed in the country focuses on the formulation and 3-D computational implementation of a version of GFEM that uses combinations of special Partitions of Unity (flat-top and trigonometric functions) to build the space of the enriched shape functions. Another important issue is that, although the GFEM allows the representation of strong discontinuities inside finite elements, it is still necessary to trace and discretize the crack surface, in addition to criteria that contemplate the beginning and direction of propagation. Thus, the research that will be carried out during the internship period abroad aims to couple the model of phase-fields for fracture with the GFEM. Such a model adds degrees of freedom that represent the crack, making it possible to treat the topology of discrete cracks as a band of diffuse damage. However, this approach requires very refined finite element meshes, even in two-dimensional problems. Thus, the proposal consists of using the global-local GFEM structure and using the models phase-fields for fracture only in local problems, making the computational cost potentially reduced. Addressing this class of problems in this way simplifies the representation of complex phenomena, such as initiation, propagation, coalescence and cracking, without the need for additional ad-hoc criteria. (AU)