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Indexed by:Journal Papers

Date of Publication:2019-12-01

Journal:MATHEMATICS AND MECHANICS OF SOLIDS

Included Journals:SCIE、EI

Volume:24

Issue:12

Page Number:4032-4050

ISSN No.:1081-2865

Key Words:Piezoelectric quasicrystal; multi-material junction; electrically permeable; impermeable crack; intensity coefficient; singularity order; symplectic method

Abstract:An accurate fracture analysis of a multi-material junction of one-dimensional hexagonal quasicrystals with piezoelectric effect is performed by using Hamiltonian mechanics incorporated in the finite element method. Two idealized electrical assumptions, including electrically permeable and impermeable crack-face conditions, are considered. In the Hamiltonian system, the analytical solutions to the multi-material piezoelectric quasicrystal around the crack tip (singular domain) are obtained and expressed in terms of symplectic eigensolutions. Therefore, the large number of nodal unknowns in the singular domain is reduced into a small set of undetermined coefficients of the symplectic series. The unknowns in the non-singular domain remain unchanged. Explicit expressions of phonon stresses, phason stresses, and electric displacement in the singular domain and newly defined fracture parameters are achieved simultaneously. Comparisons are presented to verify the proposed approach and very good agreement is reported. The key influencing parameters of the crack are discussed in detail. The effects of electrical assumptions and positions of the crack on the fracture parameters are discussed in detail.