Eshelbian mechanics of novel materials: Quasicrystals

摘要

In this work, the so-called Eshelbian or configurational mechanics ofquasicrystals is presented. Quasicrystals are considered as a prototype ofnovel materials. Material balance laws for quasicrystalline materials withdislocations are derived in the framework of generalized incompatibleelasticity theory of quasicrystals. Translations, scaling transformations aswell as rotations are examined; the latter presents particular interest due tothe quasicrystalline structure. This derivation provides important quantitiesof the Eshelbian mechanics, as the Eshelby stress tensor, the scaling fluxvector, the angular momentum tensor, the configurational forces (Peach-Koehlerforce, Cherepanov force, inhomogeneity force or Eshelby force), theconfigurational work and the configurational vector moments for dislocations inquasicrystals. The corresponding $J$-, $M$-, and $L$-integrals for dislocationloops and straight dislocations in quasicrystals are derived and discussed.Moreover, the explicit formulas of the $J$-, $M$-, and $L$-integrals forparallel screw dislocations in one-dimensional hexagonal quasicrystals areobtained. Through this derivation, the physical interpretation of the $J$-,$M$-, and $L$-integrals for dislocations in quasicrystals is revealed and theirconnection to the Peach-Koehler force, the interaction energy and therotational vector moment (torque) of dislocations in quasicrystals isestablished.