A novel Hamiltonian-based isogeometric analysis of one-dimensional hexagonal piezoelectric quasicrystal with mode III electrically permeable/impermeable cracks

[Display omitted] •A new coupling approach based on symplectic method and IGA is proposed.•The formulation of IGA for piezoelectric quasicrystals is developed.•Two idealized electrical assumptions at the crack faces are considered.•Fracture parameters for multi-material piezoelectric quasicrystals a...

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Bibliographic Details
Published in:Theoretical and applied fracture mechanics 2020-06, Vol.107, p.102552, Article 102552
Main Authors: Yang, Zhenting, Yu, Xiong, Xu, Chenghui, Tong, Zhenzhen, Zhou, Zhenhuan, Xu, Xinsheng
Format: Article
Language:English
Subjects:
Crack tips
Dimensional analysis
Electric fields
Electrically impermeable/permeable crack
Exact solutions
Fracture mechanics
Intensity factors/coefficients
Isogeometric analysis
Permeability
Piezoelectric quasicrystal
Piezoelectricity
Quasicrystals
Symplectic method
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Summary:[Display omitted] •A new coupling approach based on symplectic method and IGA is proposed.•The formulation of IGA for piezoelectric quasicrystals is developed.•Two idealized electrical assumptions at the crack faces are considered.•Fracture parameters for multi-material piezoelectric quasicrystals are defined. A novel Hamiltonian-based isogeometric analysis is proposed for mode III fracture analysis of piezoelectric quasicrystals (PQCs) with complicated configurations. Two idealized electrical assumptions, namely electrically permeable and impermeable cracks, are considered. The proposed method has two major steps. Firstly, the formulation of isogeometric analysis (IGA) for PQCs is developed and adopted to discretize the overall cracked body. Secondly, analytical solutions near the crack tip are expanded in terms of symplectic eigensolutions in order to change the unknowns of IGA within this region into a set of undetermined coefficients of symplectic series. Therefore, explicit expressions of phonon, phason and electric fields around the crack tip and intensity factors/coefficients are obtained. In numerical examples, several cracked PQCs including a four-leaf-clover-shaped multi-material piezoelectric quasicrystal junction are provided to show the accuracy and effectiveness of the proposed method.
ISSN:0167-8442
1872-7638
DOI:10.1016/j.tafmec.2020.102552