  In this work, the so-called Eshelbian or configurational mechanics of
quasicrystals is presented. Quasicrystals are considered as a prototype of
novel materials. Material balance laws for quasicrystalline materials with
dislocations are derived in the framework of generalized incompatible
elasticity theory of quasicrystals. Translations, scaling transformations as
well as rotations are examined; the latter presents particular interest due to
the quasicrystalline structure. This derivation provides important quantities
of the Eshelbian mechanics, as the Eshelby stress tensor, the scaling flux
vector, the angular momentum tensor, the configurational forces (Peach-Koehler
force, Cherepanov force, inhomogeneity force or Eshelby force), the
configurational work and the configurational vector moments for dislocations in
quasicrystals. The corresponding $J$-, $M$-, and $L$-integrals for dislocation
loops and straight dislocations in quasicrystals are derived and discussed.
Moreover, the explicit formulas of the $J$-, $M$-, and $L$-integrals for
parallel screw dislocations in one-dimensional hexagonal quasicrystals are
obtained. Through this derivation, the physical interpretation of the $J$-,
$M$-, and $L$-integrals for dislocations in quasicrystals is revealed and their
connection to the Peach-Koehler force, the interaction energy and the
rotational vector moment (torque) of dislocations in quasicrystals is
established.
