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

A plastic crack model for smectic A liquid crystals under longitudinal shear is suggested. The solution of the screw dislocation in smectic A is the key to the correct result that we obtained by overcoming a longstanding puzzle. We further use the dislocation pile-up principle and the singular integral equation method to 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 the parameters relevant to the local stability/instability of materials. Our results may be useful for developing soft-matter mechanics. (condensed matter: structural, mechanical, and thermal properties)