Field distributions in piezoelectric composites with semi-infinite cracks

2020

J. Compos. Sci.

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An analysis for the prediction of the electromechanical field in composite piezoelectric half-planes with attached surface electrode is presented. The composite half-planes are composed of distinct constituents and may include internal defects in various locations. The solution is carried out in a sufficiently large rectangular region, the boundary conditions of which are obtained from the corresponding solution of a homogeneous piezoelectric half-plane. This is followed by the application of the discrete Fourier transform at the domain of which a boundary-value problem is formulated. The solution of this boundary-value problem, followed by the inversion of the Fourier transform, provides, in conjunction with an iterative procedure, the electromechanical field at any point of the rectangular region. Applications are given for a piezoelectric half-plane with defects in the form of a cavity and of short and semi-infinite cracks as well as of a periodically bilayered composite with a crack in one of its layers.

Section: Introductionmentioning

confidence: 68%

“…Following References [12,15], the jumps of the field variables at the opposite sides of the considered rectangular region form the requested boundary conditions that should be imposed in solving the problem of the composite half-plane with internal defects. These jumps are defined as follows:…”

Section: The Boundary Conditionsmentioning

confidence: 99%

The Effect of Defects in Piezoelectric Composite Half-Planes with Surface Electrodes

2020

J. Compos. Sci.

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“…The resulting set of equations in the transform domain and the method of solution have been described by Aboudi (2016) for the piezoelectric case, and the present additional electromagnetic effects do not add essential difficulties. The method of solution is based on discretizing the representative cell into N β and N γ subcells, see Figure 1(e) (for Figure 1(b)’s configuration, the representative cell − d ≤ x 1 ′ ≤ d , − h ≤ x 2 ′ ≤ h is discretized into N α and N β subcells, see Figure 1(f)).…”

Section: Methods Of Solutionmentioning

confidence: 99%

Multiscale analysis for the prediction of the full field in electromagnetoelastic composites with semi-infinite cracks

Journal of Intelligent Material Systems and Structures

2016

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The full field distributions in loaded electromagnetoelastic composites with semi-infinite cracks and other localized defects are predicted by employing micro-to-macroscale analyses. At the micro level, the effective properties of the electromagnetoelastic composite, which consists of piezoelectric and piezomagnetic constituents, are determined by employing a micromechanical analysis which takes into account the detailed interaction between the phases. The subsequent macroscale analysis employs the jumps of the K-field of a crack embedded within a homogeneous electromagnetoelastic medium, computed at the boundaries of a rectangular domain that is sufficiently far away from the localized effects. Then, the double finite Fourier transform is applied and the solution of the problem in the transform domain is derived. Inversion of the Fourier transform provides, in conjunction with an iterative procedure, the resulting electromagnetoelastic field distributions. Both crack fronts perpendicular and parallel to the poling (the axis of symmetry of the composite) are considered. After the verification of the offered approach, results are presented for piezoelectric/piezomagnetic composites with a semi-infinite crack which is interacting with a cavity. In addition, the field distributions in cracked porous electromagnetoelastic materials are presented. A particular emphasis is given to the induced magnetic field caused by the application of electromechanical loading, and to the induced electric field caused by the application of magnetomechanical loading.

“…Extensions of the multiscale analysis for composites with localized damage have been performed by [9] and [23]. The effects of various types of localized damage in 'smart' composites (piezoelectric, electromagneto-elastic and thermo-electro-magneto-elastic) have been investigated by [1], [3], [4], [5] and [6]. Thus far, the described multiscale analysis has been applied to composites with linear constituents, to predict the behavior of linear composites with various types of localized damage.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Micromechanical analysis of hyperelastic composites with localized damage using a new low-memory Broyden-step-based algorithm

Perchikov

2019

Arch Appl Mech

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A multiscale (micro-to-macro) analysis is proposed for the prediction of the finite strain behavior of composites with hyperelastic constituents and embedded localized damage. The composites are assumed to possess periodic microstructure and be subjected to a remote field. At the microscale, finite-strain micromechanical analysis based on the homogenization technique for the (intact) composite is employed for the prediction of the effective deformation. At the macroscale, a procedure, based on the representative cell method and the associated higher-order theory, is developed for the determination of the elastic field in the damaged composite. The periodic composite is discretized into identical cells and then reduced to the problem of a single cell by application of the discrete Fourier transform. The resulting governing equations, interfacial and boundary conditions in the Fourier transform domain, are solved by employing the higher-order theory in conjunction with an iterative procedure to treat the effects of damage and material nonlinearity. The initial conditions for the iterative solution are obtained using the weaklynonlinear material limit and a natural fixed-point iteration. A locally-convergent low-memory Quasi-Newton solver is then employed. A new algorithm for the implementation of the solver is proposed, which allows storing in the memory directly the vector-function history-sequence, which may be advantageous for convergence-control based on specific components of the objective vector-function. The strong-form Fourier transform-based approach employed here, in conjunction with the new solver, enables to extend the application of the method to nonlinear materials and may have computational efficiency comparable or possibly advantageous to that of standard approaches.