The purpose of this paper is to evaluate the stress concentration at the tip of a permeable interfacial crack near an eccentric elliptical hole in piezoelectric bi-materials under anti-plane shearing. Fracture analysis is performed by Green’s function method and the conformal mapping method, which are used to solve the boundary conditions problem. The mechanical model of the interfacial crack is constructed by interface-conjunction and crack-deviation techniques so that the crack problem is simplified as solving a series of the first kind of Fredholm’s integral equations, from which the dynamic stress intensity factors (DSIFs) at the inner and the outer crack-tips can be derived. The validity of the present method is verified by comparing with a crack emerging from the edge of a circular hole as a reference. Numerical cases reveal parametric dependence of DSIFs on the geometry of eccentric elliptical holes and interfacial cracks, the characteristics of the incident wave, the equivalent piezoelectric elastic modulus and piezoelectric parameters. The results illustrate that the eccentric distance has a great effect on the stress concentration at the crack tip, which may be harmful to the normal service of piezoelectric devices and materials. In addition, the method proposed in this paper can also deal with non-eccentric problems and has wider applicability.
In this paper, we consider the existence and uniqueness of solutions for a quasilinear elliptic equation with a variable exponent and a reaction term depending on the gradient. Based on the surjectivity result for pseudomonotone operators, we prove the existence of at least one weak solution of such a problem. Furthermore, we obtain the uniqueness of the solution for the above problem under some considerations. Our results generalize and improve the existing results.
The problem of dynamically debonded cylindrical inclusion near the interface of semi-infinite piezoelectric materials was theoretically investigated. The effects of different geometric and physical parameters on the dynamic stress intensity factor (DSIF) of the crack tip are discussed. The theoretical expressions for the crack (debonding) DSIF were obtained using methods that included Green’s function, the complex variable function, and multipolar coordinates, and the numerical results showed that the dynamic characteristics of the debonded structure were more obvious under conditions of low frequency and large piezoelectric characteristic parameters. In addition, the period of the DSIF at the crack tip became shorter as the incident wave number increased. There are, therefore, important theoretical and engineering considerations for the dynamic analysis of piezoelectric materials with debonded cylindrical inclusion.
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