A model of crack based on dislocations in smectic A liquid crystals

TL;DR

This paper develops a crack model for smectic A liquid crystals based on dislocation theory, providing insights into crack behavior and stability relevant to soft-matter mechanics.

Contribution

It introduces a novel crack model for smectic A liquid crystals using dislocation solutions and integral equations, addressing a longstanding puzzle.

Findings

Determines the size of the plastic zone at the crack tip

Calculates crack tip opening displacement

Provides parameters for local stability analysis

Abstract

A plastic crack model for smectic A liquid crystals under longitudinal shear is suggested. The solution of screw dislocation in smectic A is the key in which the correct result is just obtained by overcoming a longstanding puzzle [19]. We further use the dislocation pile-up principle and the singular integral equation method, construct the solution of the crack in the phase. From the solution we can determine the size of the plastic zone at the crack tip and the crack tip opening (tearing) displacement, which are parameters being relevant to the local stability/instability of materials. The results may be useful in developing soft-matter mechanics.