Beyond the ``principle of local symmetry'': derivation of a general crack propagation law

TL;DR

This paper derives a comprehensive crack propagation law for slow brittle cracking in 2D and 3D, extending the principle of local symmetry and identifying new material properties needed for accurate modeling.

Contribution

It provides a generalized derivation of crack growth laws using symmetry and gauge invariance, extending the principle of local symmetry to three dimensions and highlighting new material parameters.

Findings

Extended the principle of local symmetry to 3D crack growth

Identified new material properties beyond fracture toughness and elastic constants

Provided a theoretical framework for crack propagation in complex geometries

Abstract

We derive a general crack propagation law for slow brittle cracking, in two and three dimensions, using symmetry, gauge invariance, and gradient expansions. Our derivation provides explicit justification for the ``principle of local symmetry,'' which has been used extensively to describe two dimensional crack growth, but goes beyond that principle to describe three dimensional crack phenomena as well. We also find that there are new materials properties needed to describe the growth of general cracks in three dimensions, besides the fracture toughness and elastic constants previously used to describe cracking.