A novel Hamiltonian-based isogeometric analysis of one-dimensional hexagonal piezoelectric quasicrystal with mode III electrically permeable/impermeable cracks. (June 2020) - Yang, Zhenting; Yu, Xiong; Xu, Chenghui; Tong, Zhenzhen; Zhou, Zhenhuan; Xu, Xinsheng
Graphical abstract: Highlights: 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. Abstract: 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.