Finite element method for plane problems with cracks in icosahedral quasicrystals

摘要

In all about 200 individual QCs observed to date,icosahedral quasicrystals (QCs) are the mostimportant and stable QCs,whose physical properties including elasticity and defects have beenintensively investigated in experimental and theoretical analyses.Beyond the scope of classicalelasticity,there are phonon field,phason field and phonon-phason coupling field in the elasticenergy theory of the QCs.Through transforming the elastic equilibrium equations of icosahedralQCs into the variation of a kind of general potential function,the finite element method to solvethe plane problems of icosahedral QCs subjected to arbitrary boundary conditions is first presentedin this paper.The energy release rate of icosahedral QCs with cracks is determined by extendingthe conventional path independent J-integral.