Abstract An array of equidistant inclined cracks present in 2-D piezoelectric strip is numerically analyzed using distributed dislocation method (DDM). The piezoelectric strip is a cutout of an infinite domain so that the width-to-crack-length ratio is about 100 times larger than the aspect ratio of height-to-crack-length of the specimen. The inclined equidistant cracks are modeled as a continuous distribution of dislocations, and the problem is thus reduced into simultaneous Cauchy's type singular integral equations, which are then solved by the Gauss–Chebychev quadrature method. The study is carried out with respect to number of cracks, aspect ratio, inclination angle, inter-crack space distance, crack-face electrical boundary conditions and electrical loading. Various numbers of inclined equidistant cracks with different inclination angles under semi-permeable crack-face boundary conditions are examined. To show the accuracy and efficacy of DDM in modeling finite cracked piezoelectric problems, fracture parameters obtained by the DDM are validated against the results of extended finite element method under impermeable crack-face boundary conditions for two particular cases i.e., inclined crack and two unequal collinear cracks. The present results show the significant effects of aspect ratio, distance between cracks, inclination angle, crack face boundary conditions, and electrical loading on fracture parameters. The DDM developed to analyze an array of equidistant inclined cracks in 2-D piezoelectric strip can be extended to inclined periodic cracks in 2-D piezoelectric strip under various electrical boundary conditions.

#1Tinh Quoc Bui(TITech: Tokyo Institute of Technology)H-Index: 54

Abstract Accurate numerical modeling of multifield piezoelectric materials is challenging because of the inherent electro-mechanical coupling effect and material anisotropic behaviors. The modeling becomes even more difficult especially for problems with non-smooth solutions like crack under dynamic loading. We present in this paper an extension of the extended isogeometric analysis (XIGA) for simulation of two-dimensional fracture mechanics problems in piezoelectric materials under dynamic and ...

#2Tinh Quoc Bui(TITech: Tokyo Institute of Technology)H-Index: 54

Last. Sohichi Hirose(TITech: Tokyo Institute of Technology)H-Index: 15

view all 5 authors...

Interfacial dynamic impermeable cracks analysis of dissimilar piezoelectric solids under coupled electromechanical impact loadings by the extended finite element method (X-FEM) is presented. The dynamic X-FEM approach recently developed by the authors is further extended to analyze transient responses of interfacial impermeable cracks in dissimilar piezoelectric structures. The mechanical displacements and electrical potential are approximated by appropriate enrichment functions that are not onl...

Last. Yuri Lapusta(CNRS: Centre national de la recherche scientifique)H-Index: 14

view all 5 authors...

A plane strain problem for a periodic set of the limited electrically and magnetically permeable cracks is considered in this work. The tensile mechanical stress, magnetic induction and electrical displacement are applied at infinity. Using the presentations of electro-magneto-mechanical components via sectionally analytic functions, the formulated problem is reduced to a matrix problem of linear relationships with the associated conditions at infinity. The exact analytical solution of this prob...

From the viewpoint of fracture mechanics, of importance is the near-tip field which can be characterized as field intensity factors. In this paper, the crack-tip field intensity factors of the stress and electric displacement in two dimensional piezoelectric solids are evaluated by using four approaches including the displacement extrapolation, the stress method, the J-integral and the modified crack closure integral method (MCCI) based on a boundary element method (BEM). The strongly singular d...

Last. C.W. Lim(CityU: City University of Hong Kong)H-Index: 63

view all 6 authors...

Transient thermal dynamic analysis of stationary cracks in functionally graded piezoelectric materials (FGPMs) based on the extended finite element method (X-FEM) is presented. Both heating and cooling shocks are considered. The material properties are supposed to vary exponentially along specific direction while the crack-faces are assumed to be adiabatic and electrically impermeable. A dynamic X-FEM model is developed in which both Crank–Nicolson and Newmark time integration methods are used f...

Last. Cenbo Xiong(BIT: Beijing Institute of Technology)H-Index: 3

view all 5 authors...

This paper presents a numerical solution to model multiple cracks in a finite plate of an elastic isotropic material. Both the boundaries and the cracks are modeled by distributed dislocations. This method results in a system of singular integral equations with Cauchy kernels which can be solved by Gauss-Chebyshev quadrature method. Four examples are provided to assess the capability of this method.

#1Sergii Kozinov(Freiberg University of Mining and Technology)H-Index: 5

#2Meinhard Kuna(Freiberg University of Mining and Technology)H-Index: 31

Last. Stephan Roth(Freiberg University of Mining and Technology)H-Index: 6

view all 3 authors...

A numerical fracture analysis of piezoelectric and ferroelectric materials is conducted using an advanced exponential cyclic cohesive zone model. The implemented irreversible cohesive law allows for the damage accumulation during subcritical electromechanical loading. Change in polarization direction (as a result of ferroelectric domain switching) due to applied electromechanical loading is taken into account. A generalized capacitor model representing the permittivity of the grain boundaries or...

#1R. R. Bhargava(IITR: Indian Institute of Technology Roorkee)H-Index: 8

#2Kamlesh Jangid(IITR: Indian Institute of Technology Roorkee)H-Index: 7

The problem of two unequal collinear straight cracks weakening a poled transversely isotropic piezoelectric ceramic is addressed under semi-permeable electric boundary conditions on the crack faces. The plate has been subjected to combined in-plane normal(to the faces of the cracks) mechanical and electric loads. Problem is formulated employing Stroh formalism and solved using complex variable technique. The elastic field, electric field and energy release rate are obtained in closed analytic fo...

An investigation of the generalized dynamic intensity factors (GDIFs) of cracked homogeneous and linear magnetoelectroelastic (MEE) solids using the extended finite element method (X-FEM) is presented. Stationary straight and curved cracks in two-dimensional (2D) MEE solids with impermeable electromagnetic crack-face boundary conditions under coupled electro-magneto-mechanical impact loads are investigated. The effects of various aspects including mesh sensitivity; combined dynamic impact loads;...

Last. Rama Bhargava(IITR: Indian Institute of Technology Roorkee)H-Index: 32

view all 4 authors...

Abstract In this work, a subinterface crack problem in piezoelectric bimaterials is analyzed by the extended finite element method (XFEM). Associated with the level set method, the XFEM enables us to accurately capture the singularities at the crack-tips. The fracture parameters consisting of the mechanical stress intensity factors and the electrical displacement intensity factor are evaluated by using the asymptotic crack-tip fields derived from the generalized Stroh’s formalism and the interac...

Abstract A mathematical strip-saturation model is proposed to analyze the influence of changing poling direction on two hairline electrically semi-permeable collinear cracks embedded in a piezoelectric strip. The remote boundaries of the piezoelectric strip are subjected to anti-plane mechanical and in-plane electrical loads. Fourier series method is applied to transform the model into triple series equations which are then reduced to singular integral equations using the integral equation techn...

Last. Yuri Lapusta(University of Auvergne)H-Index: 3

view all 3 authors...

Abstract An interaction of a tunnel conductive crack and a distant strip electrode situated at the interface between two piezoelectric semi-infinite spaces is studied. The bimaterial is subject by an in-plane electrical field parallel to the interface and by an anti-plane mechanical loading. Using the presentations of electromechanical quantities at the interface via sectionally-analytic functions the problem is reduced to a combined Dirichlet-Riemann boundary value problem. Solution of this pro...

#2Guan-Ting Liu(Inner Mongolia Normal University)H-Index: 1

Based on the Gurtin-Murdoch surface/interface model and complex potential theory, by constructing a new conformal mapping, the electrically permeable boundary condition with surface effect is established, and the antiplane fracture problem of three nanocracks emanating from a hexagonal nanohole in one-dimensional hexagonal piezoelectric quasicrystals with surface effect is studied. The exact solutions of the stress intensity factor of the phonon field and the phason field, the electric displacem...

#1M. Nourazar(ZNU: University of Zanjan)H-Index: 1

#1M. Nourazar(ZNU: University of Zanjan)H-Index: 3

Last. M. Ayatollahi(ZNU: University of Zanjan)H-Index: 11

view all 2 authors...

Abstract In this paper, the mixed mode problem for a magneto-electro-elastic (MEE) material containing multiple cracks under in-plane magneto-electro-mechanical loads is analyzed. First, the solution to an generalized dislocation is obtained in the infinite MEE plane. The Fourier transform is employed to derive closed-form expressions for the stress, electric displacement and magnetic induction components. The solution to the problem is consequently reduced to derive singular integral equations ...

Last. Tinh Quoc Bui(TITech: Tokyo Institute of Technology)H-Index: 54

view all 3 authors...

In this paper, we present new analytical solutions for modified polarization saturation (PS) models for arbitrary polarized and semipermeable 2-D piezoelectric media. The PS model is modified to various other non-linear fracture models by varying the normal electric displacement saturated conditions in place of a constant saturated value. These variations are hereby defined as interpolating linear, quadratic and cubic type’s polynomials into saturated value interpolated on the basis of possible ...

#1R. Bagheri(IAU: Islamic Azad University)H-Index: 10

#1Rafat Bagheri(IAU: Islamic Azad University)H-Index: 15

The distributed dislocation technique is developed for the transient analysis of functionally graded magneto-electro-elastic half-plane where cracks are parallel/perpendicular with respect to the half-plane boundary. Laplace and Fourier transforms are employed to solve the governing equations leading to a system of Cauchy singular integral equations on the Laplace transform domain. The dynamic stress intensity factor history can be calculated by numerical Laplace transform inversion of the solut...

Last. Jian-Guo Wu(HEBUT: Hebei University of Technology)

view all 3 authors...

This article investigates the dynamic non-local stress analysis of two collinear semi-permeable mode-I cracks in a piezoelectric medium under the harmonic waves by using the generalized Almansi the...

Abstract In this paper, an automated numerical simulation of the propagation of multiple cracks in a finite elastic plane by the distributed dislocation method is developed. Firstly, a solution to the problem of a two-dimensional finite elastic plane containing multiple straight cracks and kinked cracks is presented. A serial of distributed dislocations in an infinite plane are used to model all the cracks and the boundary of the finite plane. The mixed-mode stress intensity factors of all the c...

#1R. Bagheri(IAU: Islamic Azad University)H-Index: 10

#2M. Noroozi(IAU: Islamic Azad University)H-Index: 2

Abstract In this work, the steady state problem of multiple Yoffe-type cracks propagating in a piezoelectric half-plane within the framework of linear electroelasticity under in-plane electro-elastic loading is studied. At first, the closed-form solution of the moving electric and Volterra type climb and glide edge dislocations are derived using the complex Fourier transforms to achieve the integral equations of a piezoelectric half-plane with several moving cracks. Then, the integral equations ...