Abstract
We discuss a homogenized model of a pantographic bar considering flexoelectricity. A pantographic bar consists of relatively stiff small bars connected by small soft flexoelectric pivots. As a result, an elongation of the bar relates almost to the torsion of pivots. Taking into account their flexoelectric properties we find the corresponding electric polarization. As a results, the homogenized pantographic bar demonstrates piezoelectric properties inherited from the flexoelectric properties of pivots. The effective stiffness properties of the homogenized bars are determined by the geometry of the structural elements and shear stiffness whereas the piezoelectric properties follow from the flexoelectric moduli of the pivots.
Citations
-
5 7
CrossRef
-
0
Web of Science
-
5 9
Scopus
Authors (4)
Cite as
Full text
- Publication version
- Accepted or Published Version
- License
- open in new tab
Keywords
Details
- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
-
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
no. 149,
pages 1 - 9,
ISSN: 0020-7225 - Language:
- English
- Publication year:
- 2020
- Bibliographic description:
- Eremeev V., Ganghoffer J., Konopińska-Zmysłowska V., Uglov N.: Flexoelectricity and apparent piezoelectricity of a pantographic micro-bar// INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE -Vol. 149, (2020), s.1-9
- DOI:
- Digital Object Identifier (open in new tab) 10.1016/j.ijengsci.2020.103213
- Bibliography: test
-
- Abdoul-Anziz, H. , & Seppecher, P. (2018). Strain gradient and generalized continua obtained by homogenizing frame lattices. Mathematics and Mechanics of Complex Systems, 6 (3), 213-250 . open in new tab
- Auffray, N. , He, Q. C. , & Quang, H. L. (2019). Complete symmetry classification and compact matrix representations for 3D strain gradient elasticity. Interna- tional Journal of Solids and Structures, 159 , 197-210 . open in new tab
- Cordero, N. M. , Forest, S. , & Busso, E. P. (2016). Second strain gradient elasticity of nano-objects. Journal of Mechanics and Physics of Solids, 97 , 92-124 . open in new tab
- Coutris, N. , Thompson, L. L. , & Kosaraju, S. (2020). Asymptotic homogenization models for pantographic lattices with variable order rotational resistance at pivots. Journal of the Mechanics and Physics of Solids, 134 , 103718 . dell'Isola, F. , Seppecher, P. , Spagnuolo, M. , Barchiesi, E. , Hild, F. , Lekszycki, T. , et al. (2019a). Advances in pantographic structures: design, manufacturing, models, experiments and image analyses. Continuum Mechanics and Thermodynamics, 31 (4), 1231-1282 . open in new tab
- dell'Isola, F. , Turco, E. , Misra, A. , Vangelatos, Z. , Grigoropoulos, C. , & Melissinaki, V. (2019b). Force-displacement relationship in micro-metric pantographs: Experiments and numerical simulations. Comptes Rendus Mécanique, 347 (5), 397-405 . open in new tab
- Deng, Q. , Kammoun, M. , Erturk, A. , & Sharma, P. (2014). Nanoscale flexoelectric energy harvesting. International Journal of Solids and Structures, 51 (18), 3218-3225 . open in new tab
- Eringen, A. C. , & Maugin, G. A. (1990). Electrodynamics of continua . New York: Springer . open in new tab
- Landau, L. D. , & Lifshitz, E. M. (1970). Theory and elasticity. Course of theoretical physics : 7 (2nd Ed). Oxford: Pergamon Press . open in new tab
- Le Quang, H. , & He, Q. C. (2011). The number and types of all possible rotational symmetries for flexoelectric tensors. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 467 (2132), 2369-2386 .
- Lee, D. , & Noh, T. W. (2012). Giant flexoelectric effect through interfacial strain relaxation. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 370 (1977), 4 944-4 957 . open in new tab
- Liu, C. , Wu, H. , & Wang, J. (2016). Giant piezoelectric response in piezoelectric/dielectric superlattices due to flexoelectric effect. Applied Physics Letters, 109 (19), 192901 . open in new tab
- Majdoub, M. S. , Sharma, P. , & Cagin, T. (2008). Enhanced size-dependent piezoelectricity and elasticity in nanostructures due to the flexoelectric effect. Physical Review B, 77 (12), 125424 . open in new tab
- Maugin, G. A. (2017). Non-classical continuum mechanics: A dictionary . Singapore: Springer . open in new tab
- Mindlin, R. D. (1964). Micro-structure in linear elasticity. Archive for Rational Mechanics and Analysis, 16 (1), 51-78 . open in new tab
- Mindlin, R. D. (1968). Polarization gradient in elastic dielectrics. International Journal of Solids and Structures, 4 (6), 637-642 . open in new tab
- Mindlin, R. D. , & Eshel, N. N. (1968). On first strain-gradient theories in linear elasticity. International Journal of Solids and Structures, 4 (1), 109-124 . Neuber, H. (1946). Theory of notch stresses: Principles for exact stress calculation . Ann Arbor, Michigan: JW Edwards . open in new tab
- Nguyen, T. D. , Mao, S. , Yeh, Y.-W. , Purohit, P. K. , & McAlpine, M. C. (2013). Nanoscale flexoelectricity. Advanced Materials, 25 (7), 946-974 . Olive, M. , & Auffray, N. (2014). Symmetry classes for odd-order tensors. ZAMM, 94 (5), 421-447 . open in new tab
- Rahali, Y. , Giorgio, I. , Ganghoffer, J. , & dell'Isola, F. (2015). Homogenization à la Piola produces second gradient continuum models for linear pantographic lattices. International Journal of Engineering Science, 97 , 148-172 . open in new tab
- Scerrato, D. , Zhurba Eremeeva, I. A. , Lekszycki, T. , & Rizzi, N. L. (2016). On the effect of shear stiffness on the plane deformation of linear second gradient pantographic sheets. ZAMM, 96 (11), 1268-1279 . open in new tab
- Sharma, N. D. , Maranganti, R. , & Sharma, P. (2007). On the possibility of piezoelectric nanocomposites without using piezoelectric materials. Journal of the Mechanics and Physics of Solids, 55 (11), 2328-2350 . open in new tab
- Spagnuolo, M. , Peyre, P. , & Dupuy, C. (2019). Phenomenological aspects of quasi-perfect pivots in metallic pantographic structures. Mechanics Research Communications, 101 , 103415 . Timoshenko, S. , & Goodier, J. N. (1951). Theory of elasticity (2nd Ed). New York: McGraw-Hill . open in new tab
- Toupin, R. A. (1962). Elastic materials with couple-stresses. Arch Ration Mech Analysis, 11 (1), 385-414 . open in new tab
- Wang, B. , Gu, Y. , Zhang, S. , & Chen, L.-Q. (2019). Flexoelectricity in solids: Progress, challenges, and perspectives. Progress in Materials Science, 106 , 100570 . Yudin, P. V. , & Tagantsev, A. K. (2013). Fundamentals of flexoelectricity in solids. Nanotechnology, 24 (43), 432001 .
- Yurkov, A. S. , & Tagantsev, A. K. (2016). Strong surface effect on direct bulk flexoelectric response in solids. Applied Physics Letters, 108 (2), 022904 . Zhang, S. , Xu, M. , Liu, K. , & Shen, S. (2015). A flexoelectricity effect-based sensor for direct torque measurement. Journal of Physics D: Applied Physics, 48 (48), 485502 . open in new tab
- Zubko, P. , Catalan, G. , & Tagantsev, A. K. (2013). Flexoelectric effect in solids. Annual Review of Materials Research, 43 (1), 387-421 . open in new tab
- Verified by:
- Gdańsk University of Technology
seen 119 times
Recommended for you
Pantographic metamaterials: an example of mathematically driven design and of its technological challenges
- F. dell'Isola,
- P. Seppecher,
- J. J. Alibert
- + 31 authors
Continuum models for pantographic blocks with second gradient energies which are incomplete
- M. Stiltz,
- F. dell'Isola,
- I. Giorgio
- + 3 authors
On existence and uniqueness of weak solutions for linear pantographic beam lattices models
- V. Eremeev,
- F. S. Alzahrani,
- A. Cazzani
- + 4 authors