A plastic crack model for smectic A liquid crystals under longitudinal shearis suggested. The solution of screw dislocation in smectic A is the key inwhich the correct result is just obtained by overcoming a longstanding puzzle[19]. We further use the dislocation pile-up principle and the singularintegral 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 cracktip and the crack tip opening (tearing) displacement, which are parametersbeing relevant to the local stability/instability of materials. The results maybe useful in developing soft-matter mechanics.
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