On tailoring fracture resistance of brittle structures: A level set interface-enriched topology optimization approach

Jian Zhang,Fred Van Keulen,Alejandro M Aragón

doi:10.1016/j.cma.2021.114189

Abstract

We propose a fully immersed topology optimization procedure to design structures with tailored fracture resistance under linear elastic fracture mechanics assumptions for brittle materials. We use a level set function discretized by radial basis functions to represent the topology and the Interface-enriched Generalized Finite Element Method (IGFEM) to obtain an accurate structural response. The technique assumes that cracks can nucleate at right angles from the boundary, at the location of enriched nodes that are added to enhance the finite element approximation. Instead of performing multiple finite element analyses to evaluate the energy release rates (ERRs) of all potential cracks—a procedure that would be computationally intractable—we approximate them by means of topological derivatives after a single enriched finite element analysis of the uncracked domain. ERRs are then aggregated to construct the objective function, and the corresponding sensitivity formulation is derived analytically by means of an adjoint formulation. Several numerical examples demonstrate the technique’s ability to tailor fracture resistance, including the well-known benchmark L-shaped bracket and a multiple-loading optimization problem for obtaining a structure with fracture resistance anisotropy.

Highlights

Cracks in engineering structures, which could develop during their manufacturing or service life, may affect adversely the mechanical performance and even lead to catastrophic failure
Instead of performing multiple finite element analyses to evaluate the energy release rates (ERRs) of all potential cracks—a procedure that would be computationally intractable—we approximate them by means of topological derivatives after a single enriched finite element analysis of the uncracked domain
Interface-enriched Generalized Finite Element Method (IGFEM) retains the main feature of X/GFEM, it keeps the attractive properties of standard FEM: Since enrichment functions are constructed with Lagrange shape functions of integration elements, their value is exactly zero at original mesh nodes

Summary

Introduction

Cracks in engineering structures, which could develop during their manufacturing or service life, may affect adversely the mechanical performance and even lead to catastrophic failure ( brittle fracture). Computational tools should be used to obtain designs that have been optimized to reduce the likelihood of fracture or other mechanisms that could compromise structural integrity. One such tool is topology optimization [4,5,6,7], which has become a popular design technique in real-world industrial applications [8,9]. Based on structural failure criteria, topology optimization procedures can be classified into three categories: stress-, damage-, and fracture-based approaches

Methods

Results

Conclusion