Stationary straight cracks in quasicrystals
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Stationary straight cracks in quasicrystals in linear elastic setting are under scrutiny. The analysis is developed by using Stroh formalism which is modified to account for a totally degenerate eigenvalue problem: in fact, the fundamental matrix of the governing equations of motion admits a repeated eigenvalue corresponding to a single eigenvector. Cases of a semi-infinite rectilinear crack loaded along its margins and a crack of finite length under remote loading conditions are considered. Standard and phason stresses display square-root singularities at crack tip. The latter stresses represent peculiar microstructural inner actions occurring in quasicrystals and are determined by rearrangements assuring quasi-periodicity of the atomic tiling—modes described by a vector field, called phason field, collecting the local degrees of freedom exploited by the atoms within the material elements. Energy release rate increases with the coupling parameter between displacement and phason fields.
KeywordsFracture Stationary crack Quasicrystals Phonon and phason stresses Stroh formalism Degenerate eigenvalue problem Analytic functions
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