Combinatorics

Image segmentation

Level set method

Finite element method

Brittleness

Level set (data structures)

Topology (electrical circuits)

Mathematics

Structural engineering

Interface (matter)

Engineering

Artificial intelligence

Composite material

Capillary action

Set (abstract data type)

Topology optimization

Materials science

Programming language

Capillary number

Computer science

Brittle fracture

Fracture (geology)

Segmentation

Computer Methods in Applied Mechanics and Engineering

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.

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