Evaluation of electroelastic singularity of finite-size V-notched one-dimensional hexagonal quasicrystalline bimaterials with piezoelectric effect. (April 2019) - Zhou, Zhenhuan; Yang, Zhenting; Xu, Wang; Yu, Xiong; Xu, Chenghui; Xu, Xinsheng
Graphical abstract: We presented a Hamiltonian-based method to find exact solutions and fracture parameters of a V-notched quasicrystalline bimaterial with piezoelectric effects. Highlights: We propose an analytical method to the fracture analysis of V-notched quasicrystals. Exact solutions of V-notched quasicrystalline bimaterials are rationally obtained. We introduce the intensity coefficient to evaluate the singular notch-tip fields. The effects of notch positions on the fracture behaviors of quasicrystal are studied. New results are presented and can be used as benchmarks. Abstract: The Mode-III interface V-shape notch in a finite-size one-dimensional hexagonal quasicrystalline bimaterial with piezoelectric effect is investigated under the framework of Hamiltonian mechanics. The electroelastic intensity coefficients are extended to evaluate the fracture behaviors of the V-notched piezoelectric quasicrystalline bimaterial. In the symplectic space, the higher-order differential governing equations are simplified into a set of lower-order ordinary differential equations so that exact solutions are expanded in terms of symplectic series. The undetermined coefficients in the series can be obtained by a highly accurate finite element discretized symplectic method. Explicit expressions of the electroelastic fields and corresponding intensity coefficients are achieved simultaneously. In numerical examples, comparisons are presented to validate the accuracy and reliability of the present work. The effects of notch positions on the electroelastic intensity coefficients are studied and discussed in detail.