Universal Meshes for the Simulation of Brittle Fracture and Moving Boundary Problems

TL;DR

This paper explores the use of universal meshes as an efficient and robust method for simulating brittle fracture and other moving boundary problems, demonstrating their versatility and potential for future applications.

Contribution

It introduces the application of universal meshes to brittle fracture simulation and provides examples including fluid flow past moving obstacles, highlighting their effectiveness.

Findings

Universal meshes enable conforming discretizations for evolving boundaries.

The crack propagation algorithm demonstrates accurate fracture simulation.

Universal meshes are effective for fluid-structure interaction problems.

Abstract

Universal meshes have recently appeared in the literature as a compu- tationally efficient and robust paradigm for the generation of conforming simpli- cial meshes for domains with evolving boundaries. The main idea behind a univer- sal mesh is to immerse the moving boundary in a background mesh (the universal mesh), and to produce a mesh that conforms to the moving boundary at any given time by adjusting a few of elements of the background mesh. In this manuscript we present the application of universal meshes to the simulation of brittle fracturing. To this extent, we provide a high level description of a crack propagation algorithm and showcase its capabilities. Alongside universal meshes for the simulation of brit- tle fracture, we provide other examples for which universal meshes prove to be a powerful tool, namely fluid flow past moving obstacles. Lastly, we conclude the manuscript with some remarks on the current state of universal meshes and future directions.