# Energy-dissipation balance of a smooth moving crack

## TL;DR

This paper establishes conditions for energy-dissipation balance in Mode III cracks on smooth paths and characterizes displacement singularities near the crack tip, extending previous straight fracture results.

## Contribution

It provides necessary and sufficient conditions for energy balance and generalizes displacement singularity characterization to curved crack paths.

## Key findings

- Conditions for energy-dissipation balance are derived.
- Displacement singularity near the crack tip is characterized.
- Results extend previous straight fracture analyses.

## Abstract

In this paper we provide necessary and sufficient conditions in order to guarantee the energy-dissipation balance of a Mode III crack, growing on a prescribed smooth path. Moreover, we characterize the singularity of the displacement near the crack tip, generalizing the result in [S.Nicaise, A.M.Sandig - \textit{J. Math. Anal. Appl.} 2007] valid for straight fractures.