Finite element and asymptotic homogenization methods applied to smart composite materials

Berger, Harald; Gabbert, Ulrich; Köppe, H.; Rodrı́guez-Ramos, Reinaldo; Bravo‐Castillero, Julián; Guinovart-Dı́az, Raúl; Otero, José A.; Maugin, Gérard A.

doi:10.1007/s00466-003-0500-x

Cited by 57 publications

(28 citation statements)

References 23 publications

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“…For the general case of a solid RVE with random fibers distribution, see For the evaluation of the effective properties, suitable boundary conditions have to be applied to the unit cell in such a way that, apart from one component of the strain/electric field vector, all other components are equal to zero [14,15]. Then each effective coefficient can be easily determined by multiplying the corresponding row of the material matrix by the strain/electric field vector.…”

Section: Resultsmentioning

confidence: 99%

“…Several analytical and computational multiscale approaches have been developed in order to predict the macroscale properties of heterogeneous materials at the lower scale(s), [6][7][8][9][10][11]. Although most of these efforts have been devoted to continuum mechanics [12,13], some applications to multiphysics problems are also available [14,15]. A few of these concern electromechanically coupled problems such as in the case of piezoelectricity [16].…”

Section: Introductionmentioning

confidence: 99%

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Numerical homogenization of piezoelectric textiles with electrospun fibers for energy harvesting

Maruccio

Lorenzis

2014

Frattura Ed Integrità Strutturale

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ABSTRACT. Piezoelectric effects are exploited in an increasing number of micro-and nano-electro-mechanical systems. In particular, energy harvesting devices convert ambient energy (i.e. mechanical pressure) into electrical energy and their study is nowadays a very important and challenging field of research. In this paper, the attention is focused on piezoelectric textiles. Due to the importance of computational modeling to understand the influence that micro-scale geometry and constitutive variables have on the macroscopic behavior, a homogenization strategy is developed. The macroscopic structure behaviour is obtained defining a reference volume element (RVE) at the micro-scale. The geometry of the RVE is based on the microstructural properties of the material under consideration and consists in piezoelectric polymeric nano-fibers subjected to electromechanical contact constraints. This paper outlines theory and numerical implementation issues for the homogenization procedure. Moreover, within this approach the average response resulting from the analysis of different fiber configurations at the microscale is determined providing a multiphysics constitutive model for the macro-scale.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical homogenization of piezoelectric textiles with electrospun fibers for energy harvesting

Maruccio

Lorenzis

2014

Frattura Ed Integrità Strutturale

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“…All curves are monotone increasing. The self-consistent effective field (SCEF) solution and finite-element method (FEM) [5][6][7][8][9] lie on top of the lower bound. The asymptotic homogenization method (AHM) also lies on top of the lower bound.…”

Section: Long Cylindrical Fibersmentioning

confidence: 99%

Variational bounds for anisotropic elastic multiphase composites with different shapes of inclusions

et al. 2008

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In the present work, unified formulae for the overall elastic bounds for multiphase transversely isotropic composites with different geometrical types of inclusions embedded in a matrix are calculated, including the spherical and long or short continuous cylindrical fiber cases. The influence of the different geometrical configurations of the inclusions on the composites is studied. The transversely isotropic effective bounds are obtained by applying the variational formulation for anisotropic composites developed by Willis, which relies on expressions for the static transversely isotropic Green's function. Some numerical calculations and comparisons with the effective coefficients derived from the self-consistent approach, asymptotic homogenization method, and finite element method (FEM) are shown for different aspect ratio values, exhibiting good agreement.

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“…Asymptotic homogenization has long been developed to treat the effective properties of composite with large amount of inhomogeneities. [20] For periodic piezoelectric composites where the electroelastic coupling equation with rapidly oscillating coefficients can be established, the asymptotic homogenization plus FEM [21][22][23] has been adopted to find the effective properties. In this study, the effective electromechanical properties of cellular piezoelectret film are analyzed by means of the asymptotic homogenization implemented by FEM.…”

Section: Introductionmentioning

confidence: 99%

“…[20][21][22][23] In this study, the local analysis is carried out in ANSYS. The SOLID5 element, which is 8-node hexahedron isoparametric coupling element, is used here to mesh the RVE.…”

mentioning

confidence: 99%

Numerical modeling of the effective electromechanical properties of cellular piezoelectret film by asymptotic homogenization

Wan

Fan

2013

Advanced Composite Materials

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Cellular piezoelectret film is actually the voided charged polymer foam that, macroscopically, shows significant quasi-piezoelectricity in the thickness direction. In this study, cellular piezoelectret film is viewed as a periodic composite, where the charged microvoids are taken as piezoelectric inclusions scattered periodically in the host polymer matrix. Based on the asymptotic homogenization for piezoelectric composite implemented by finite element method, the effective electromechanical properties of cellular piezoelectret film are numerically modeled. Dependence of the overall electromechanical properties on various material parameters and geometric variables of voids is explored. The inflation experiments of cellular piezoelectret film published in the literature can also be numerically simulated. It is shown that the overall properties of cellular piezoelectret film can be effectively simulated by the asymptotic homogenization based on finite element analysis. This approach can be an efficient mean for the numerical simulation of the overall properties in the optimization design of cellular piezoelectret film with complex microvoid structures.

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Finite element and asymptotic homogenization methods applied to smart composite materials

Cited by 57 publications

References 23 publications

Numerical homogenization of piezoelectric textiles with electrospun fibers for energy harvesting

Numerical homogenization of piezoelectric textiles with electrospun fibers for energy harvesting

Variational bounds for anisotropic elastic multiphase composites with different shapes of inclusions

Numerical modeling of the effective electromechanical properties of cellular piezoelectret film by asymptotic homogenization

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