Perturbation theory of 2D decagonal quasicrystals

A perturbation method for solving elastic 3D problems for 2D decagonal quasicrystals with point groups 10 mm, 1022. 10m2 and 10/mmm is proposed. We obtain a uniformly valid asymptotic solution of the elastic field by regarding phason field as a perturbation to phonon field and introducing a perturbation parameter epsilon = R/c(11), where c(11) and R are elastic constants of phonon field and phonon-phason coupling, respectively. A general solution for the equations of order zero is given in terms of five "harmonic" functions. As a simple application of the above theory. considering an infinite 2D decagonal quasicrystal of point group 10 mm weakened by a circular crack, A e obtain the uniformly valid asymptotic solutions up to O(epsilon(2)) for the mode I loading. (C) 2002 Published by Elsevier Science B.V.