Architected cellular piezoelectric metamaterials: Thermo-electro-mechanical properties

Abstract Advances in additive manufacturing have recently made possible the manufacturing of smart materials with arbitrary microarchitectures, which leads to developing lightweight smart metamaterials with unprecedented multifunctional properties. In this paper, asymptotic homogenization (AH) method is developed for predicting the effective thermo-electro-mechanical properties of architected cellular piezoelectric metamaterials. The effect of pore microarchitecture (relative density and cell topology) and polarization direction on elastic, dielectric, piezoelectric, pyroelectric and thermal properties of periodic cellular piezoelectric metamaterials is explored. The pore topology is determined by Fourier series expansion. Alternative pore microarchitectures are considered by tailoring shape parameters, scaling factor, and rotation angle of the constitutive pore. Smart cellular metamaterials made of both single-phase (BaTiO3) and bi-phase (BaTiO3-expoy) piezoelectric materials are considered. Apart from effective thermo-electro-mechanical properties, a series of figures of merit for the cellular piezoelectric metamaterials, i.e. piezoelectric coupling constant, acoustic impedance, piezoelectric charge coefficient, hydrostatic figure of merit, current responsivity, voltage responsivity and pyroelectric energy harvesting figures of merit, are presented and the reason for difference between the figures of merit of different types of piezoelectric metamaterials is discussed. The figures of merit shed lights on the effect of microarchitecture on optimizing the multifunctional performance of smart cellular metamaterials for applications as structurally efficient multifunctional energy harvesters. It is found that the piezoelectric and pyroelectric figures of merit of cellular piezoelectric metamaterials can be significantly improved compared to the commonly used honeycomb cellular materials and composite materials with solid circular inclusion if an appropriate microarchitecture is selected for the pore. For example, piezoelectric charge coefficient ( d h ) for a transversely polarized single-phase cellular piezoelectric metamaterial with a solid volume fraction of 0.4 can be 350% higher than the corresponding figures of merit of honeycomb piezoelectric material; voltage responsivity of transversely polarized bi-phase cellular piezoelectric metamaterials with an inclusion volume fraction of 0.3 can be also 249% higher than the corresponding value of composite materials with a solid circular inclusion.

[1]  M. Babaei,et al.  THERMOPIEZOELECTRIC ANALYSIS OF A FUNCTIONALLY GRADED PIEZOELECTRIC MEDIUM , 2011 .

[2]  V. Veselago The Electrodynamics of Substances with Simultaneously Negative Values of ∊ and μ , 1968 .

[3]  Daniel Therriault,et al.  One-Step Solvent Evaporation-Assisted 3D Printing of Piezoelectric PVDF Nanocomposite Structures. , 2017, ACS applied materials & interfaces.

[4]  Johannes T. B. Overvelde,et al.  Relating pore shape to the non-linear response of periodic elastomeric structures , 2014 .

[5]  A. Kalamkarov,et al.  Asymptotic Homogenization of Composite Materials and Structures , 2009 .

[6]  Tungyang Chen Piezoelectric properties of multiphase fibrous composites: Some theoretical results , 1993 .

[7]  David R. Smith,et al.  Metamaterials and Negative Refractive Index , 2004, Science.

[8]  Johannes T. B. Overvelde,et al.  Compaction Through Buckling in 2D Periodic, Soft and Porous Structures: Effect of Pore Shape , 2012, Advanced materials.

[9]  R. Kar-Gupta,et al.  Electromechanical response of piezoelectric composites : Effects of geometric connectivity and grain size , 2008 .

[10]  Le Van Lich,et al.  Polar and toroidal electromechanical properties designed by ferroelectric nano-metamaterials , 2016 .

[11]  Jinho Oh,et al.  Higher order zig-zag theory for fully coupled thermo-electric–mechanical smart composite plates , 2004 .

[12]  Maen Alkhader,et al.  Electromechanical Response of Piezoelectric Honeycomb Foam Structures , 2014 .

[13]  V. Shalaev Optical negative-index metamaterials , 2007 .

[14]  T. A. Venkatesh,et al.  Electromechanical response of (3–0, 3–1) particulate, fibrous, and porous piezoelectric composites with anisotropic constituents: A model based on the homogenization method , 2014 .

[15]  Sergei A. Tretyakov,et al.  Resonance Properties of Bi-Helix Media at Microwaves , 1997 .

[16]  U. Chettiar,et al.  Negative index of refraction in optical metamaterials. , 2005, Optics letters.

[17]  T. A. Venkatesh,et al.  Electromechanical response of piezoelectric foams , 2012 .

[18]  M. C. Dökmeci,et al.  Vibrations of piezoelectric crystals , 1980 .

[19]  Wang Biao,et al.  Three-dimensional analysis of an ellipsoidal inclusion in a piezoelectric material , 1992 .

[20]  U. Gabbert,et al.  Numerical Evaluation of Effective Material Properties of Transversely Randomly Distributed Unidirectional Piezoelectric Fiber Composites , 2007 .

[21]  Julián Bravo-Castillero,et al.  Numerical and analytical analyses for active fiber composite piezoelectric composite materials , 2015 .

[22]  Changchun Wu,et al.  A study of three-dimensional four-step braided piezo-ceramic composites by the homogenization method , 2001 .

[23]  Glaucio H. Paulino,et al.  Design of functionally graded piezocomposites using topology optimization and homogenization - Toward effective energy harvesting materials , 2013 .

[24]  Martin Maldovan,et al.  Sound and heat revolutions in phononics , 2013, Nature.

[25]  Alexander L. Kalamkarov,et al.  An asymptotic homogenization model for smart 3D grid-reinforced composite structures with generally orthotropic constituents , 2009 .

[26]  R. Kar-Gupta,et al.  Electromechanical response of 1–3 piezoelectric composites: Effect of fiber shape , 2008 .

[27]  Andrea Bacigalupo,et al.  Multi-field asymptotic homogenization of thermo-piezoelectric materials with periodic microstructure , 2017, 1701.03361.

[28]  Jongmin Shim,et al.  3D Soft Metamaterials with Negative Poisson's Ratio , 2013, Advanced materials.

[29]  J. D. Eshelby The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[30]  Martin L. Dunn,et al.  Micromechanics predictions of the effective electroelastic moduli of piezoelectric composites , 1993 .

[31]  R. Kar-Gupta,et al.  Electromechanical response of porous piezoelectric materials , 2006 .

[32]  Roderic S. Lakes,et al.  Cellular solid structures with unbounded thermal expansion , 1996 .

[33]  Takahiro Shimada,et al.  Hierarchical ferroelectric and ferrotoroidic polarizations coexistent in nano-metamaterials , 2015, Scientific Reports.

[34]  R. Kar-Gupta,et al.  Electromechanical response of porous piezoelectric materials: Effects of porosity distribution , 2007 .

[35]  Yuki Sato,et al.  Heat flux manipulation with engineered thermal materials. , 2012, Physical review letters.

[36]  T. A. Venkatesh,et al.  Electromechanical behavior of auxetic piezoelectric cellular solids , 2015 .

[37]  Erasmo Carrera,et al.  Multi-coating inhomogeneities approach for the effective thermo-electro-elastic properties of piezoelectric composite materials , 2010 .

[38]  M. Dunn Micromechanics of coupled electroelastic composites: Effective thermal expansion and pyroelectric coefficients , 1993 .

[39]  C. Della,et al.  The performance of 1-3 piezoelectric composites with a porous non-piezoelectric matrix , 2008 .

[40]  U. Gabbert,et al.  An analytical and numerical approach for calculating effective material coefficients of piezoelectric fiber composites , 2005 .

[41]  J. Bravo-Castillero,et al.  Analytical formulae for electromechanical effective properties of 3–1 longitudinally porous piezoelectric materials , 2009 .

[42]  T. A. Venkatesh,et al.  Electromechanical response of 1-3 piezoelectric composites with hollow fibers , 2008 .

[43]  T. A. Venkatesh,et al.  Electromechanical response of (3-0) porous piezoelectric materials: Effects of porosity shape , 2011 .

[44]  Jensen Li,et al.  Double-negative acoustic metamaterial. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[45]  T. A. Venkatesh,et al.  Effects of foam shape and porosity aspect ratio on the electromechanical properties of 3-3 piezoelectric foams , 2012 .

[46]  A. Akbarzadeh,et al.  Thermal wave: from nonlocal continuum to molecular dynamics , 2017 .

[47]  Huanyang Chen,et al.  Acoustic cloaking in three dimensions using acoustic metamaterials , 2007 .

[48]  Damiano Pasini,et al.  Snapping mechanical metamaterials under tension. , 2015, Advanced materials.

[49]  Damiano Pasini,et al.  Mechanical properties of lattice materials via asymptotic homogenization and comparison with alternative homogenization methods , 2013 .

[50]  J. Aboudi,et al.  Piezoresistive fiber-reinforced composites: A coupled nonlinear micromechanical–microelectrical modeling approach , 2014 .

[51]  Christopher S. Lynch,et al.  Purified and porous poly(vinylidene fluoride-trifluoroethylene) thin films for pyroelectric infrared sensing and energy harvesting , 2010, Smart Materials and Structures.

[52]  A. Deraemaeker,et al.  Numerical evaluation of the equivalent properties of Macro Fiber Composite (MFC) transducers using periodic homogenization , 2010 .

[53]  George M. Whitesides,et al.  A three-dimensional actuated origami-inspired transformable metamaterial with multiple degrees of freedom , 2016, Nature Communications.

[54]  D. Pasini,et al.  Multiphysics of Multilayered and Functionally Graded Cylinders Under Prescribed Hygrothermomagnetoelectromechanical Loading , 2014 .

[55]  M. Babaei,et al.  Coupled thermopiezoelectric behaviour of a one-dimensional functionally graded piezoelectric medium based on C–T theory , 2011 .

[56]  Jeong Woo Lee,et al.  Mechanical analyses of “Shellular”, an ultralow-density material , 2016 .

[57]  Yan Zhang,et al.  Enhanced pyroelectric and piezoelectric properties of PZT with aligned porosity for energy harvesting applications† †Electronic supplementary information (ESI) available. See DOI: 10.1039/c7ta00967d Click here for additional data file. , 2017, Journal of materials chemistry. A.

[58]  Steve Dunn,et al.  Piezoelectric nanogenerators – a review of nanostructured piezoelectric energy harvesters , 2015 .

[59]  T. A. Venkatesh,et al.  On the relationships between cellular structure, deformation modes and electromechanical properties of piezoelectric cellular solids , 2016 .

[60]  J. Bravo-Castillero,et al.  Effective properties of piezoelectric composites with parallelogram periodic cells , 2012 .

[61]  Yi He,et al.  Heat capacity, thermal conductivity, and thermal expansion of barium titanate-based ceramics , 2004 .