Reduced algebraic conditions for plane or axial tensorial symmetries
| Autor: | Rodrigue Desmorat, Boris Desmorat, Boris Kolev, Marc Olive |
|---|---|
| Přispěvatelé: | Laboratoire de Mécanique et Technologie (LMT), École normale supérieure - Cachan (ENS Cachan)-Centre National de la Recherche Scientifique (CNRS), Institut Jean le Rond d'Alembert (DALEMBERT), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2020 |
| Předmět: |
Physics
Polynomial Plane (geometry) General Mathematics 02 engineering and technology MSC 2010: 74E10 (74B05 74F15) Elasticity (physics) 021001 nanoscience & nanotechnology Elasticity 020303 mechanical engineering & transports Piezo-magnetism 0203 mechanical engineering [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] Mechanics of Materials [SPI.MECA.MEMA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of materials [physics.class-ph] Homogeneous space Anisotropy Symmetric tensor General Materials Science Algebraic number Symmetry (geometry) 0210 nano-technology Axial symmetry Piezo-electricity Mathematical physics |
| Zdroj: | Mathematics and Mechanics of Solids Mathematics and Mechanics of Solids, SAGE Publications, 2020, 25 (12), pp.2155-2177. ⟨10.1177/1081286520920691⟩ |
| ISSN: | 1741-3028 1081-2865 |
| DOI: | 10.1177/1081286520920691 |
| Popis: | In this article, we formulate necessary and sufficient polynomial equations for the existence of a symmetry plane or an order-two axial symmetry for a totally symmetric tensor of order [Formula: see text]. These conditions are effective and of degree [Formula: see text] (the tensor’s order) in the components of the normal to the plane (or the direction of the axial symmetry). These results are then extended to obtain necessary and sufficient polynomial conditions for the existence of such symmetries for an elasticity tensor, a piezo-electricity tensor or a piezo-magnetism pseudo-tensor. |
| Databáze: | OpenAIRE |
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