Path Independent Integral and Its Application in Plane Quasicrystals

Aim To establish the path independent integral and its dual form of energy type, and to determine the singularity order of stresses near the crack tip in plane quasicrystals. Methods The basic governing equations of plane quasicrystals and Gauss's theorem were applied in the establishment. Results and Conclusion The path independent integral and its dual form for the static, dynamic and moving cracks were obtained and their path independence was proved. By the given path independent integral, the conclusion that near the tip of crack in plane quasicrystals the stress singularity with the order of -1/2, which is correspondent to the analytic solution, was drawn.