Dynamic crack analysis in piezoelectric solids with non-linear electrical and mechanical boundary conditions by a time-domain BEM

Wünsche, Michael; Zhang, Ch.; García-Sánchez, F.; Sáez, Andrés; Sládek, J.; Sládek, V.

doi:10.1016/j.cma.2011.05.007

Cited by 33 publications

(15 citation statements)

References 31 publications

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“…In terms of modelling and solving for piezoelectric applications with BEM, much research has been devoted to investigating the behaviour of piezoelectric material itself [17,18]. For modelling piezoelectric smart structures in SHM, Leme et al [19] established a static model for the analysis of 2D plates bonded with piezoelectric sensors which are formulated as beams.…”

Section: Introductionmentioning

confidence: 99%

A boundary element model for structural health monitoring using piezoelectric transducers

Zou

Benedetti

Aliabadi

2013

Smart Mater. Struct.

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In this paper, for the first time, the boundary element method (BEM) is used for modelling smart structures instrumented with piezoelectric actuators and sensors. The host structure and its cracks are formulated with the 3D dual boundary element method (DBEM), and the modelling of the piezoelectric transducers implements a 3D semi-analytical finite element approach. The elastodynamic analysis of the structure is performed in the Laplace domain and the time history is obtained by inverse Laplace transform. The sensor signals obtained from BEM simulations show excellent agreement with those from FEM simulations and experiments. This work provides an alternative methodology for modelling smart structures in structural health monitoring (SHM) applications.

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Section: Introductionmentioning

confidence: 99%

A boundary element model for structural health monitoring using piezoelectric transducers

Zou

Benedetti

Aliabadi

2013

Smart Mater. Struct.

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“…The dynamic stress intensity factors (DSIF) are calculated and compared with converged FEM solutions. We have employed the extrapolation method in order to calculate the DSIF as follows [16,49]…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…These materials are widely used in composites in the aerospace and automobile industries [29,26], as sensors and actuators (piezoelectric [10,49] and magnetoelectroelastic [25,48] materials) and more recently have applications in biomechanics [13,34] and even in hydraulic fracturing [14,17], just to mention some of the works. Cracks in composite materials can be responsible for complete failure of the component, resulting in economic losses or even loss of life.…”

Section: Introductionmentioning

confidence: 99%

A non-ordinary state-based peridynamics framework for anisotropic materials

Hattori

Trevelyan

Coombs

2018

Computer Methods in Applied Mechanics and Engineering

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Peridynamics (PD) represents a new approach for modelling fracture mechanics, where a continuum domain is modelled through particles connected via physical bonds. This formulation allows us to model crack initiation, propagation, branching and coalescence without special assumptions. Up to date, anisotropic materials were modelled in the PD framework as different isotropic materials (for instance, fibre and matrix of a composite laminate), where the stiffness of the bond depends on its orientation. A non-ordinary state-based formulation will enable the modelling of generally anisotropic materials, where the material properties are directly embedded in the formulation. Other material models include rocks, concrete and biomaterials such as bones. In this paper, we implemented this model and validated it for anisotropic composite materials. A composite damage criterion has been employed to model the crack propagation behaviour. Several numerical examples have been used to validate the approach, and compared to other benchmark solution from the finite element method (FEM) and experimental results when available.Fracture mechanics have been studied for nearly a century, from the first work of Griffith [15] for brittle materials. Over the years a number of researchers have modelled fracture mechanics analytically [28,36] for simple problems and geometries, and more commonly using numerical frameworks, such as the extended finite element method (XFEM) [4,27] and the extended boundary element method (XBEM) [16], among many others. Nevertheless, these methods suffer when crack branching or coalescence are involved.The phase-field method has been shown to model crack branching behaviour [1,18]. The method consists in describing the crack as an interface directly in the formulation and is used conjointly to the finite element method (FEM) [35]. Nevertheless, the method requires a fine mesh around the crack to model the interface correctly. Another drawback of the method is that it can provide unrealistic results. A novel numerical method entitled peridynamics (PD) [40] has been recently developed, and has shown great potential in fracture mechanics problems involving initiating, propagating, branching and coalescing cracks.The original peridynamics (PD) formulation was proposed by Silling [40], where he redefined the classical approach for continuum mechanics using an integral framework instead of partial derivatives. The main reason for using this approach is that the partial derivatives pose a challenge when dealing with fracture mechanics problems, since the governing partial differential equations in elasticity imply that singularities will appear due to the presence of discontinuities, which is not desirable. Due to the integral form of the formulation, no special assumptions are needed to deal with singularities, such as a crack in the domain.The first PD formulation described a continuum medium through discrete particles, interacting between each other through physical connections entitled bonds. Each bond has a stif...

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“…However, it requires fundamental solutions or the free-space Green functions that are unavailable for three-dimensional (3D) problems in piezoelectric anisotropic materials. The application of BEM to piezoelectricity has also been reported (Ding and Liang, 1999; Lee, 1995) with interesting applications to fracture problems (Pan, 1999; Wünsche et al, 2010, 2011).…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional analysis for functionally graded piezoelectric semiconductors

Young

Sládek

et al. 2016

Journal of Intelligent Material Systems and Structures

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This article presents numerical analyses of functionally graded piezoelectric beam with piezoelectric semiconducting material properties using meshless method. Unlike piezoelectric dielectric materials, electron density and electric current are additionally considered in constitutive equations for piezoelectric semiconductors. Mutual coupling of elastic displacements, electric potentials, and electron density increases the complexity of the analyzed problem. For the solution of the set of partial differential equations with non-constant coefficients, the local radial basis function collocation method is proposed in this work. Approximating the spatial variations of all physical fields in the partial differential equations by the multiquadric radial basis function entails an ensuing system for time-dependent problems solved by the Houbolt finite-difference scheme as a time-stepping method. The presented local radial basis function collocation method is verified using the corresponding results obtained using the finite element method. The influence of material parameter gradation and initial electron density is then investigated, along with transient analyses.

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Dynamic crack analysis in piezoelectric solids with non-linear electrical and mechanical boundary conditions by a time-domain BEM

Cited by 33 publications

References 31 publications

A boundary element model for structural health monitoring using piezoelectric transducers

A boundary element model for structural health monitoring using piezoelectric transducers

A non-ordinary state-based peridynamics framework for anisotropic materials

Three-dimensional analysis for functionally graded piezoelectric semiconductors

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