On applique ici les techniques de décomposition harmonique et de Cartan à la classification des groupes de symétries des solides piézoélectriques. Nous montrons en particulier qu'il faut réduire de 19 à 17 le nombre des classes de symétries correspondant au phénomène piézoélectrique.
We apply here the harmonic and Cartan decomposition techniques to piezoelectric material symmetries classification. We show in particular that we shall reduce from 19 to 17 the number of symmetry classes corresponding to the piezoelectric phenomenon.
Publié le :
Giuseppe Geymonat 1 ; Thibaut Weller 1
@article{CRMATH_2002__335_10_847_0, author = {Giuseppe Geymonat and Thibaut Weller}, title = {Classes de sym\'etrie des solides pi\'ezo\'electriques}, journal = {Comptes Rendus. Math\'ematique}, pages = {847--852}, publisher = {Elsevier}, volume = {335}, number = {10}, year = {2002}, doi = {10.1016/S1631-073X(02)02573-6}, language = {fr}, }
Giuseppe Geymonat; Thibaut Weller. Classes de symétrie des solides piézoélectriques. Comptes Rendus. Mathématique, Volume 335 (2002) no. 10, pp. 847-852. doi : 10.1016/S1631-073X(02)02573-6. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02573-6/
[1] Determination of the symetries of an experimentally determined stiffness tensor: application to acoustic measurements, Int. J. Solids Structures, Volume 35 (1998) no. 31–32, pp. 4091-4106
[2] Symmetry classes for elasticity tensors, J. Elasticity, Volume 43 (1996), pp. 81-108
[3] Symmetry classes and harmonic decomposition for photoelasticity tensors, Int. J. Engrg. Sci, Volume 35 (1997) no. 14, pp. 1317-1326
[4] Singularities and Groups in Bifurcation Theory, Vol. I, Springer, 1985
[5] Electrodynamique des Milieux Continus, Mir, 1969
[6] Ondes élastiques dans les solides, Tome I, Masson, 1996
[7] Tensor Analysis for Physicists, Clarendon Press, 1954
[8] A note on the decomposition of tensors into traceless symmetric tensors, Int. J. Engrg. Sci, Volume 8 (1970), pp. 475-481
[9] The description, classification and reality of material and physical symmetries, Acta Mech, Volume 102 (1994), pp. 73-89
- Computation of minimal covariants bases for 2D coupled constitutive laws, International Journal of Engineering Science, Volume 191 (2023), p. 39 (Id/No 103880) | DOI:10.1016/j.ijengsci.2023.103880 | Zbl:1549.74100
- On exotic linear materials: 2D elasticity and beyond, International Journal of Solids and Structures, Volume 264 (2023), p. 112103 | DOI:10.1016/j.ijsolstr.2022.112103
- A review on octupolar tensors, Journal of Physics A: Mathematical and Theoretical, Volume 56 (2023) no. 36, p. 70 (Id/No 363001) | DOI:10.1088/1751-8121/ace712 | Zbl:1531.81185
- Distance to a constitutive tensor isotropy stratum by the Lasserre polynomial optimization method, Mathematics and Mechanics of Complex Systems, Volume 11 (2023) no. 3, pp. 393-428 | DOI:10.2140/memocs.2023.11.393 | Zbl:1527.90149
- Decomposition of third-order constitutive tensors, Mathematics and Mechanics of Solids, Volume 27 (2022) no. 2, pp. 222-249 | DOI:10.1177/10812865211016530 | Zbl:7590421
- A nonlocal operator method for finite deformation higher-order gradient elasticity, Computer Methods in Applied Mechanics and Engineering, Volume 384 (2021), p. 28 (Id/No 113963) | DOI:10.1016/j.cma.2021.113963 | Zbl:1506.74045
- Symmetry classes in piezoelectricity from second-order symmetries, Mathematics and Mechanics of Complex Systems, Volume 9 (2021) no. 1, pp. 77-105 | DOI:10.2140/memocs.2021.9.77 | Zbl:1508.74015
- On the determination of plane and axial symmetries in linear elasticity and piezo-electricity, Journal of Elasticity, Volume 141 (2020) no. 1, pp. 147-163 | DOI:10.1007/s10659-020-09778-5 | Zbl:1448.74017
- Reduced algebraic conditions for plane or axial tensorial symmetries, Mathematics and Mechanics of Solids, Volume 25 (2020) no. 12, pp. 2155-2177 | DOI:10.1177/1081286520920691 | Zbl:1482.74050
- Effective computation of SO(3) and O(3) linear representation symmetry classes, Mathematics and Mechanics of Complex Systems, Volume 7 (2019) no. 3, p. 203 | DOI:10.2140/memocs.2019.7.203
- Harmonic factorization and reconstruction of the elasticity tensor, Journal of Elasticity, Volume 132 (2018) no. 1, pp. 67-101 | DOI:10.1007/s10659-017-9657-y | Zbl:1393.74025
- Random Fields Related to the Symmetry Classes of Second-Order Symmetric Tensors, Stochastic Processes and Applications, Volume 271 (2018), p. 173 | DOI:10.1007/978-3-030-02825-1_10
- , Volume 1798 (2017), p. 020095 | DOI:10.1063/1.4972687
- Handbook of bi-dimensional tensors: part I: Harmonic decomposition and symmetry classes, Mathematics and Mechanics of Solids, Volume 22 (2017) no. 9, pp. 1847-1865 | DOI:10.1177/1081286516649017 | Zbl:1391.74020
- Mathematical Modelings of Some Smart Materials and Structures, Applied Mechanics and Materials, Volume 749 (2015), p. 13 | DOI:10.4028/www.scientific.net/amm.749.13
- Symmetry classes for odd-order tensors, ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik, Volume 94 (2014) no. 5, pp. 421-447 | DOI:10.1002/zamm.201200225 | Zbl:1302.15030
- Symmetry classes for even-order tensors, Mathematics and Mechanics of Complex Systems, Volume 1 (2013) no. 2, p. 177 | DOI:10.2140/memocs.2013.1.177
- Symmetry types of the piezoelectric tensor and their identification, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 469 (2013) no. 2155, p. 20120755 | DOI:10.1098/rspa.2012.0755
- Guide to the Literature of Piezoelectricity and Pyroelectricity. 23, Ferroelectrics, Volume 321 (2005) no. 1, p. 91 | DOI:10.1080/00150190500259707
Cité par 19 documents. Sources : Crossref, zbMATH
Commentaires - Politique