Based on the fundamental equations of magnetoelectroelastic material and the analytic theory, and using the Muskhelishvili-introduced well-known elastic techniques combined with the superposition principle, the closed form solution of the generalized stress field of the interaction between many parallel screw dislocations and a semi-infinite crack in an infinite magnetoelectroelastic solid is obtained, on the assumption that the surface of the crack is impermeable electrically and magnetically. Besides, the Peach–Koehler formula of n parallel screw dislocations is given. Numerical examples show that the generalized stress varies with the position of point z and is related to the material constants. The results indicate that the stress concentration occurs at the dislocation core and the tip of the crack. The result of interaction makes the system stay in a lower energy state.
Quasicrystals(QCs) are sensitive to the piezoelectric(PE) effect. This paper studies static deformation of a multilayered one-dimensional(1 D) hexagonal QC plate with the PE effect. The exact closed-form solutions of the extended displacement and traction for a homogeneous piezoelectric quasicrystal(PQC) plate are derived from an eigensystem. The general solutions for multilayered PQC plates are then obtained using the propagator matrix method when mechanical and electrical loads are applied on the top surface of the plate. Numerical examples for several sandwich plates made up of PQC, PE, and QC materials are provided to show the effect of stacking sequence on phonon, phason, and electric fields under mechanical and electrical loads, which is useful in designing new composites for engineering structures.
A cylindrical system of vector functions, the stiffness matrix method and the corresponding recursive algorithm are proposed to investigate the static response of transversely isotropic,layered magneto-electro-elastic(MEE) structures over a homogeneous half-space substrate subjected to circular surface loading. In terms of the system of vector functions, we expand the extended displacements and stresses, and deduce two sets of ordinary differential equations, which are related to the expansion coeficients. The solution to one of the two sets of these ordinary differential equations can be evaluated by using the stiffness matrix method and the corresponding recursive algorithm. These expansion coeficients are then integrated by adaptive Gaussian quadrature to obtain the displacements and stresses in the physical domain. Two types of surface loads, mechanical pressure and electric loading,are considered in the numerical examples. The calculated results show that the proposed technique is stable and effective in analyzing the layered half-space MEE structures under surface loading.
A three-phase confocal elliptical cylinder model is proposed to analyze micromechanics of one-dimensional hexagonal piezoelectric quasicrystal(PQC) composites.Exact solutions of the phonon,phason,and electric fields are obtained by using the conformal mapping combined with the Laurent expansion technique when the model is subject to far-field anti-plane mechanical and in-plane electric loadings.The effective electroelastic constants of several different composites made up of PQC,quasicrystal(QC),and piezoelectric(PE) materials are predicted by the generalized self-consistent method.Numerical examples are conducted to show the effects of the volume fraction and the cross-sectional shape of inclusion(or fiber) on the effective electroelastic constants of these composites.Compared with other micromechanical methods,the generalized selfconsistent and Mori-Tanaka methods can predict the effective electroelastic constants of the composites consistently.
Based on the fundamental equations of piezoelasticity of quasicrystal material,we investigated the interaction between a screw dislocation and a wedge-shaped crack in the piezoelectricity of one-dimensional hexagonal quasicrystals.Explicit analytical solutions are obtained for stress and electric displacement intensity factors of the crack,as well as the force on dislocation.The derivation is based on the conformal mapping method and the perturbation technique.The influences of the wedge angle and dislocation location on the image force are also discussed.The results obtained in this paper can be fully reduced to some special cases already available or deriving new ones.
By means of analytic function theory, the problems of interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are studied. The analytic solutions of stress fields of the interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are obtained. They indicate that the stress concentration occurs at the dislocation source and the tip of the crack, and the value of the stress increases with the number of the dislocations increasing. These results are the development of interaction among the finitely many defects of quasicrystals, which possesses an important reference value for studying the interaction problems of infinitely many defects in fracture mechanics of quasicrystal.
