Brittle fracture in linearly elastic plates

TL;DR

This paper derives a mathematical model for brittle fracture in thin elastic plates using Gamma-convergence, capturing the limit behavior as the plate's thickness approaches zero without restrictions on displacements or fracture geometry.

Contribution

It introduces a new Gamma-convergence-based approach to model brittle fractures in thin plates, resulting in a Kirchhoff-Love type limit structure.

Findings

Derived a limit model for brittle fracture in plates as thickness tends to zero.

No restrictions on displacements or fracture set geometry in the analysis.

Characterized the limit model as a Kirchhoff-Love type structure.

Abstract

In this work we derive by Gamma-convergence techniques a model for brittle fracture linearly elastic plates. Precisely, we start from a brittle linearly elastic thin film with positive thickness $\rho$ and study the limit as $\rho$ tends to 0. The analysis is performed with no a priori restrictions on the admissible displacements and on the geometry of the fracture set. The limit model is characterized by a Kirchhoff-Love type of structure.