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 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.