Asymptotic Homogenization Applied to Flexoelectric Rods

Guinovart-Sanjuán, David; Merodio, J.; López-Realpozo, J.C.; Vajravelu, K.; Rodrı́guez-Ramos, Reinaldo; Guinovart-Dı́az, Raúl; Bravo‐Castillero, Julián; Sabina, Federico J.

doi:10.3390/ma12020232

Cited by 10 publications

(6 citation statements)

References 48 publications

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“…The effective stress tensorσ, effective electric displacementd and effective hyperstress tensorS associated with energy density function (30) are defined as:…”

Section: Effective Piezo-flexoelectric Tensorsmentioning

confidence: 99%

“…Note that the expressions forM andḠ in (30), which are not used in the present paper, can be found in [63]. These tensors are only used if we perform structure calculations using the homogenized model ( 30)-(31) (see e.g.…”

Section: Effective Piezo-flexoelectric Tensorsmentioning

confidence: 99%

“…by embedding fixed charges in the material [28]. Another approach has been to use architected materials comprised of piezoelectric phases [29], where the effective flexoelectric properties of the piezoelectric composites are obtained using homogenization [30,31,32,33,34]. More recently, topology optimization [35,36,37,38,39,40,41,42], which has a lengthy and successful history of determining, using inverse homogenization methods [43] the optimal material distribution to maximize a specific property [44,43,45,46], has been applied to increase the apparent flexoelectricity and energy conversion in piezoelectric structures [47,48,49,50].…”

Section: Introductionmentioning

confidence: 99%

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Topology optimization of flexoelectric composites using computational homogenization

Chen

Yvonnet

Song

et al. 2021

Computer Methods in Applied Mechanics and Engineering

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We present a topology optimization framework to design periodic composites comprised of piezoelectric constituents that exhibit large flexoelectric constants. The novelty of the approach is that it leverages a representative volume element (RVE)-based computational homogenization approach that enables the analysis of periodic composites where the characteristic dimensions of the microstructure are significantly smaller than those of the structure, and as such requires only the optimization of a single RVE rather than that of the entire structure. We utilize this approach to analyze the enhancement in flexoelectric constants that can be achieved in different types of PZT-based composites, including hard-hard (PZT-PZT), and hard-soft (PZT-polymer composite, and porous PZT) structures. In all cases, significant enhancements are observed, with improvements between 2 and 15 times those of a naive guess, with some designs reaching a factor of one order of magnitude larger than BTO. We identify different mechanisms governing the enhanced electromechanical couplings, which can arise either from an enhancement of effective piezoelectricity in the RVE for PZT-PZT composites, or from a more subtle interplay involving the enhancement of effective piezoelectric and dielectric properties coupled with a reduction in mechanical compliance for PZT-polymer and porous PZT RVEs.

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“…The effective stress tensorσ, effective electric displacementd and effective hyperstress tensorS associated with energy density function (30) are defined as:…”

Section: Effective Piezo-flexoelectric Tensorsmentioning

confidence: 99%

Section: Effective Piezo-flexoelectric Tensorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Topology optimization of flexoelectric composites using computational homogenization

Chen

Yvonnet

Song

et al. 2021

Computer Methods in Applied Mechanics and Engineering

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“…It is germane here to mention several relevant papers. Guinovart-Sanjuan et al [41] used a two scale asymptotic homogenization method to derive the homogenized flexoelectric behavior in 1D rods. In [42], the effective flexoelectric and piezoelectric behavior of fiber-reinforced nanocomposites with local flexoelectric fibers was derived using an analytical approach.…”

Section: Introductionmentioning

confidence: 99%

Apparent Flexoelectricity Due to Heterogeneous Piezoelectricity

Yvonnet

Chen

Sharma

2020

Journal of Applied Mechanics

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Recent work has highlighted how the phenomenon of flexoelectricity can masquerade as piezoelectricity. This notion can not only be exploited to create artificial piezoelectric-like materials without using piezoelectric materials, but may also explain measurement artifacts in dielectrics. In this article, we show that the reverse is also possible and potentially advantageous in certain situations (such as energy harvesting). By constructing a computational homogenization approach predicated on the finite element method, we argue that composites made of piezoelectric phases can conspire to endow the material with a distinct overall flexoelectric-like response even though the native flexoelectricity of the constituent materials is negligible. Full finite element procedures for numerical evaluation of the different effective tensors, including the flexoelectric tensor, are provided. Numerical investigations are conducted, showing variation of the effective flexoelectric properties with respect to local geometry and properties of the composite in piezoelectric-piezoelectric and polymer-piezoelectric composites. We find that the flexoelectric response can be tuned to nearly {five times} higher than the constituents.

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“…and satisfy the continuity conditions at the interface given in (B.12) -(B.21) .Solving the LQ (35) -(38) and PR (39) -(42) systems, the local functions are obtained. As a particular case, the LQ and PR problems for one-dimensional flexoelectric rod are deduced in[24] (Eqs. (13)-(20)).…”

mentioning

confidence: 99%

Effective predictions of heterogeneous flexoelectric multilayered composite with generalized periodicity

Guinovart-Sanjuán

Vajravelu

Rodrı́guez-Ramos

et al. 2020

International Journal of Mechanical Sciences

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In this work, the general mathematical statements for flexoelectric heterogeneous equilibrium boundary value problems are reported. A methodology to find the local problems and the effective properties of flexoelectric composites with generalized periodicity is presented, using the two-scales asymptotic homogenization method. The statement of the homogenized boundary values problem is given. A procedure to solve the local problems of stratified multilayered composites with complex geometry and perfect contact at the interface is proposed. Consequently, the analytical expressions of the effective coefficients are obtained. The piezoelectric limit case for rectangular bi-laminated composites is validated. Finally, numerical analysis to illustrate the behavior of the effective properties for rectangular and wavy flexoelectric bi-layered structures are shown.

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Asymptotic Homogenization Applied to Flexoelectric Rods

Cited by 10 publications

References 48 publications

Topology optimization of flexoelectric composites using computational homogenization

Topology optimization of flexoelectric composites using computational homogenization

Apparent Flexoelectricity Due to Heterogeneous Piezoelectricity

Effective predictions of heterogeneous flexoelectric multilayered composite with generalized periodicity

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