Numerical Modeling For Fracture Mechanics Problems Using The Open-source Fenics Platform

Abstract

Fracture mechanics is the mechanical approach to fracture processes, which emerged due to limitations in the application of traditional concepts of Mechanics of Materials to predict the behavior of cracked materials. Analytical problem solutions with this approach may be unattainable, which allows the use of numerical modeling, such as the finite element method. However, the use of more advanced software that solves engineering problems numerically is limited by its high cost. FEniCS is an open source computational platform that solves partial differential equations by the finite element method. Thus, from a tutorial for this computational platform, this work proposes to reproduce a classic problem of linear elastic fracture mechanics, based on the validation of a comparison of a linear elastic problem with the commercial software ANSYS ®. With the help of the provided tutorial, an code was built to model a three-point bending test. Implemented with the aid of Gmsh and Paraview, it was possible to obtain satisfactory results, and to show that FeniCS is a powerful and accessible tool for solving fracture mechanics problems.