Homogenization of porous piezoelectric materials

Martínez-Ayuso, Germán; Friswell, Michael I.; Adhikari, Sondipon; Khodaparast, Hamed Haddad; Berger, Harald

doi:10.1016/j.ijsolstr.2017.03.003

Cited by 64 publications

(44 citation statements)

References 57 publications

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“…In Mandel notation represented by , where is a matrix and the input (output) field has components, the linear operator in elasticity , conduction (or dielectric) , piezoelectricity , and thermoelectricity become 6 6, 3 3, 9 9, and 6 6 symmetric matrices, respectively. Although most existing studies (Dunn and Taya, 1993;Huang and Kuo, 1996;Odegard, 2004;Duschlbauer et al, 2006;Martinez-Ayuso et al, 2017) utilize the Voigt notation, we adapt the Mandel notation here. For example, if we use the Voigt notation for a piezoelectric case, the linear operator matrix (which corresponds to the material properties) and the Eshelby matrix can be expressed as Eqs.…”

Section: Examples Of Numerical Calculations and Fea Validationmentioning

confidence: 99%

“…As mentioned in the previous chapters, we can obtain the effective properties from the Mori-Tanaka method because the expression is applicable to any arbitrarily anisotropic matrix if the Eshelby tensor is known. The Eshelby tensor for anisotropic medium in various physical problems has been extensively studied in the literature (Mura, 1982;Yu et al, 1994;Huang and Kuo, 1996;Dunn and Wienecke, 1997;Qu and Cherkaoui, 2007;Quang et al, 2011;Martinez-Ayuso et al, 2017;Lee et al, 2018d) and the Eshelby tensors for an ellipsoidal inclusion embedded in an arbitrarily anisotropic medium for elasticity, piezoelectricity, conduction/dielectric phenomena, and thermoelectricity can be obtained numerically from Eqs. (22), (23), (27), and (28), respectively.…”

Section: Effects Of Anisotropy Of the Matrix In Various Physical Probmentioning

confidence: 99%

See 1 more Smart Citation

Micromechanics-based homogenization of the effective physical properties of composites with an anisotropic matrix and interfacial imperfections

Ryu¹,

Lee²,

Jung³

et al. 2018

Preprint

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Micromechanics-based homogenization has been employed extensively to predict the effective properties of technologically important composites. In this review article, we address its application to various physical phenomena, including elasticity, thermal and electrical conduction, electric and magnetic polarization, as well as multi-physics phenomena governed by coupled equations such as piezoelectricity and thermoelectricity. Especially, we introduce several research works published recently from our research group that consider the anisotropy of the matrix and interfacial imperfections in obtaining various effective physical properties. We begin with a brief review of the concept of the Eshelby tensor with regard to the elasticity and mean-field homogenization of the effective stiffness tensor of a composite with a perfect interface between the matrix and inclusions. We then discuss the extension of the theory in two aspects. First, we discuss the mathematical analogy among steady-state equations describing the aforementioned physical phenomena and explain how the Eshelby tensor can be used to obtain various effective properties. Afterwards, we describe how the anisotropy of the matrix and interfacial imperfections, which exist in actual composites, can be accounted for. In the last section, we provide a summary and outlook considering future challenges.

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Section: Examples Of Numerical Calculations and Fea Validationmentioning

confidence: 99%

Section: Effects Of Anisotropy Of the Matrix In Various Physical Probmentioning

confidence: 99%

Micromechanics-based homogenization of the effective physical properties of composites with an anisotropic matrix and interfacial imperfections

Ryu¹,

Lee²,

Jung³

et al. 2018

Preprint

View full text Add to dashboard Cite

show abstract

“…Numerical analyses are performed on a representative volume element (RVE), which contains essential physical geometrical information about the microstructural components represented by the PZT particles in the cement matrix. The computational thermal homogenization, applied to the microscale and mesoscale of concrete sequentially in [12,13] is extended to the PZT-cement based composites. The finite element model of the RVE is developed to solve boundary value problems with different boundary conditions in order to evaluate the effective thermo-electromechanical properties of PZT cement-based composites.…”

Section: Introductionmentioning

confidence: 99%

Computational Homogenization of Cement-Based Porous Piezoelectric Composites with Random Structure

Novák

Peter

Žmindák

2019

Strojnícky Časopis - Journal of Mechanical Engineering

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The finite element method (FEM) is used to characterize the effective thermo-electromechanical material properties of cement-based piezoelectric ceramic composites in this paper. The micromechanics representative volume element (RVE) approach is used with distribution of piezoelectric particles in the porous cement matrix. The effects of the piezoelectric particle volume fraction and pore volume fraction on the effective composite properties are determined using sets of different boundary conditions. Microscale homogenization is carried out through the analysis of particles which are randomly distributed in a homogenized matrix.

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“…For modelling periodically heterogeneous media with piezoelectric components, classical upscaling techniques has been employed. Besides the micromechanics approaches including the Mori-Tanaka and self consistent upscaling schemes, [1], the classical periodic homogenization based on the formal two-scale asymptotic expansion method [2,3], or on the two-scale convergence [4] and the periodic unfolding method [5] has been used. Recently, the homogenization of thermoelectric materials was treated in [6].…”

Section: Introductionmentioning

confidence: 99%

“…Besides the periodic homogenization, in [1], the Mori-Tanaka and the selfconsistent schemes were used for upscaling the drained porous piezoelectric materials. Concerning the fluid saturated porous piezoelectric media, the asymptotic method has been applied in [14] to derive macroscopic constitutive laws accounting for the fluid-structure interaction at the pore level, whereby a simplified model of electrolytes was considered.…”

Section: Introductionmentioning

confidence: 99%

Homogenization of the fluid-saturated piezoelectric porous media

Rohan

Lukeš

2018

International Journal of Solids and Structures

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The paper is devoted to the homogenization of porous piezoelectric materials saturated by electrically inert fluid. The solid part of a representative volume element consists of the piezoelectric skeleton with embedded conductors. The pore fluid in the periodic structure can constitute a single connected domain, or an array of inclusions. Also the conducting parts are represented by several mutually separated connected domains, or by inclusions. Two of four possible arrangements are considered for upscaling by the homogenization method. The macroscopic model of the first type involves coefficients responsible for interactions between the electric field and the pore pressure, or the pore volume. For the second type, the electrodes can be used for controlling the electric field at the pore level, so that the deformation and the pore volume can be influenced locally. Effective constitutive coefficients are computed using characteristic responses of the microstructure. The two-scale modelling procedure is implemented numerically using the finite element method. The macroscopic strain and electric fields are used to reconstruct the corresponding local responses at the pore level. For validation of the models, these are compared with results obtained by direct numerical simulations of the heterogeneous structure; a good agreement is demonstrated, showing relevance of the two-scale numerical modelling approach.

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Homogenization of porous piezoelectric materials

Cited by 64 publications

References 57 publications

Micromechanics-based homogenization of the effective physical properties of composites with an anisotropic matrix and interfacial imperfections

Micromechanics-based homogenization of the effective physical properties of composites with an anisotropic matrix and interfacial imperfections

Computational Homogenization of Cement-Based Porous Piezoelectric Composites with Random Structure

Homogenization of the fluid-saturated piezoelectric porous media

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