An accurate fracture analysis of multi-material V-notched Reissner plates under bending or twisting is performed by a new coupling approach of isogeometric analysis (IGA) and eigenfunction expansion method. In this approach, the overall plate is divided into two regions: a singular region near the notch tip (near field) and a regular region far away from the notch tip (far field). The overall model is discretized by a T-spline-based IGA. Asymptotic solutions of singular stress fields are applied to the near field, and therefore, the large number of fundamental unknowns of control points is reduced into a small set of undetermined coefficients. The unknowns in the far field remain unchanged. Consequently, the computational cost is significantly reduced, and explicit expressions of singular stress components in the vicinity of notch tip are obtained without post processing. Comparisons are presented to demonstrate the accuracy and convergence of the present approach. Effects of key influencing factors on the singularity order and singular items of stresses are investigated also.
Quasicrystals (QCs) are representatives of a novel kind of material exhibiting a large number of remarkable specific properties. However, QCs are usually brittle, and crack propagation inevitably occurs in such materials. Therefore, it is of great significance to study the crack growth behaviors in QCs. In this work, the crack propagation of two-dimensional (2D) decagonal QCs is investigated by a fracture phase field method. In this method, a phase field variable is introduced to evaluate the damage of QCs near the crack. Thus, the crack topology is described by the phase field variable and its gradient. In this manner, it is unnecessary to track the crack tip, and therefore remeshing is avoided during the crack propagation. In the numerical examples, the crack propagation paths of 2D QCs are simulated by the proposed method, and the effects of the phason field on the crack growth behaviors of QCs are studied in detail. Furthermore, the interaction of the double cracks in QCs is also discussed.
In this paper, the fracture behaviors of a piezoelectric-elastic bimaterial with cracks terminating at the interface are investigated by a symplectic approach. In the Hamiltonian system, the Hamiltonian forms of governing equations is derived by the Hamiltonian variational principle and a total unknown vector consisted of generalized displacements and stresses. The interface fracture problem is reduced into a symplectic eigenproblem which can be directly solved by the method of separation of variables. Thus, the total unknown vector is expanded in terms of symplectic eigenfunctions. The unknown coefficients of the symplectic series can be determined from the continuity conditions at the interface and outer boundary conditions. Consequently, exact solutions for the singular electro-elastic fields and explicit expression of electric/elastic intensity factors are obtained simultaneously. Results indicate that the electro-elastic singularities and intensity factors only depend on the first few terms of symplectic eigenfunctions with non-zero eigenvalues. Numerical examples are presented to show the effects of key influencing factors on the singularity orders and intensity factors of such interface cracks. Some new results are given also.
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.
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