Conservation integrals of any quasicrystal and application

摘要

By using direct calculation of the gradient and divergence of the Lagrangian of any quasicrystal, its dynamic conservation integrals are derived. These conservation integrals can be reduced to J- and M-integrals for plane and antiplane problems, which are calculated around the tip of an interfacial crack of antiplane sliding mode between a crystal and a quasicrystal.