Finite deformations of a bilayer dielectric nonlinear elastic anisotropic tube under an electric field
DOI:
https://doi.org/10.21638/spbu01.2023.211Abstract
In this paper the problem of finite deformations of a dielectric tube under the action of an electric field is considered. The tube consists of two layers, each spirally reinforced with fibres. The angles of the fibres in each layer are different. On the inner and outer surfaces of the tube and between the layers are flexible electrodes. The electric field is induced by applying voltage to the first or second layer, i. e. either to the electrodes on the inner side surface and between the layers, or to the electrodes between the layers and on the outer side surface. A simple model of an electroactive anisotropic incompressible material is considered in the analysis. The potential energy function is represented by the sum of the energy of the isotropic matrix in Gent form, the simplest electrical component and the energy of the reinforced fibres. Using a semi-inverse method, the static problem of the three-dimensional body is reduced to integral equations with respect to the tube deformation parameters: the radius of the outer layer, the multiplicity of longitudinal elongation and the twist angle. The influence of layer thickness on tube deformation under quasi-static increase of voltage is investigated. The purpose of this work is to determine the thickness of the layers at which the application of voltage to the different layers will cause the tube to twist in different directions.Keywords:
nonlinear electroelasticity, dielectric elastomer, reinforcement, tubular actuators, soft robots
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References
Литература
1. R¨ontgen W. C. Ueber die durch Electricit¨at bewirkten Form- und Volumen¨anderungen von dielectrischen K¨orpern. Annalen der Physik 247 (13), 771-786 (1880).
2. Quincke G. IV. On electrical expansion. The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science 10 (59), 30-39 (1880).
3. Gupta U., Qin L., Wang Y., Godaba H., Zhu J. Soft robots based on dielectric elastomer actuators: A review. Smart Materials and Structures 28 (10), 103002 (2019). https://doi.org/10.1088/1361-665X/AB3A77
4. Lu T., Ma C., Wang T. Mechanics of dielectric elastomer structures: A review. Extreme Mechanics Letters 38, 100752 (2020). https://doi.org/10.1016/j.eml.2020.100752
5. Guo Y., Liu L., Liu Y., Leng J. Review of Dielectric Elastomer Actuators and Their Applications in Soft Robots. Advanced Intelligent Systems 3, 2000282 (2021). https://doi.org/10.1002/aisy.202000282
6. Dorfmann L., Ogden R. W. Nonlinear theory of electroelastic and magnetoelastic interactions. New York, Springer (2014).
7. Melnikov A., Ogden R.W. Finite deformations of an electroelastic circular cylindrical tube. Zeitschrift f¨ur angewandte Mathematik und Physik 67 (6), 140 (2016). https://doi.org/10.1007/s00033-016-0733-0
8. He L., Lou J., Du J. Analytical solutions for inextensible fiber-reinforced dielectric elastomer torsional actuators. Journal of Applied Mechanics 84 (5), 051003 (2017). https://doi.org/10.1115/1.4036193
9. He L., Lou J., Du J., Wu H. Voltage-induced torsion of a fiber-reinforced tubular dielectric elastomer actuator. Composites Science and Technology 140, 106-115 (2017). https://doi.org/10.1016/j.compscitech.2016.12.032
10. Kolesnikov A. M. Finite deformations of a non-linearly elastic electrosensitive tube reinforced by two fiber families. Continuum Mechanics and Thermodynamics 34, 1237-1255 (2022). https://doi.org/10.1007/s00161-022-01118-3
11. Лурье А. И. Нелинейная теория упругости. Москва, Наука (1980).
12. Goriely A., Tabor M. Rotation, inversion and perversion in anisotropic elastic cylindrical tubes and membranes. Proc. R. Soc. A. 469 (2153), 20130011 (2013). https://doi.org/10.1098/rspa.2013.0011
13. Lu T. Q., Suo Z. G. Large conversion of energy in dielectric elastomers by electromechanical phase transition. Acta Mechanica Sinica 28 (4), 1106-1114 (2012). https://doi.org/10.1007/s10409-012-0091-x
14. Bazaev K., Cohen N. Electrically-induced twist in geometrically incompatible dielectric elastomer tubes. International Journal of Solids and Structures, 111707 (2022). https://doi.org/10.1016/j.ijsolstr.2022.111707
References
1. R¨ontgen W. C. Ueber die durch Electricit¨at bewirkten Form- und Volumen¨anderungen von dielectrischen K¨orpern. Annalen der Physik 247 (13), 771-786 (1880).
2. Quincke G. IV. On electrical expansion. The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science 10 (59), 30-39 (1880).
3. Gupta U., Qin L., Wang Y., Godaba H., Zhu J. Soft robots based on dielectric elastomer actuators: A review. Smart Materials and Structures 28 (10), 103002 (2019). https://doi.org/10.1088/1361-665X/AB3A77
4. Lu T., Ma C., Wang T. Mechanics of dielectric elastomer structures: A review. Extreme Mechanics Letters 38, 100752 (2020). https://doi.org/10.1016/j.eml.2020.100752
5. Guo Y., Liu L., Liu Y., Leng J. Review of Dielectric Elastomer Actuators and Their Applications in Soft Robots. Advanced Intelligent Systems 3, 2000282 (2021). https://doi.org/10.1002/aisy.202000282
6. Dorfmann L., Ogden R. W. Nonlinear theory of electroelastic and magnetoelastic interactions. New York, Springer (2014).
7. Melnikov A., Ogden R.W. Finite deformations of an electroelastic circular cylindrical tube. Zeitschrift f¨ur angewandte Mathematik und Physik 67 (6), 140 (2016). https://doi.org/10.1007/s00033-016-0733-0
8. He L., Lou J., Du J. Analytical solutions for inextensible fiber-reinforced dielectric elastomer torsional actuators. Journal of Applied Mechanics 84 (5), 051003 (2017). https://doi.org/10.1115/1.4036193
9. He L., Lou J., Du J., Wu H. Voltage-induced torsion of a fiber-reinforced tubular dielectric elastomer actuator. Composites Science and Technology 140, 106-115 (2017). https://doi.org/10.1016/j.compscitech.2016.12.032
10. Kolesnikov A. M. Finite deformations of a non-linearly elastic electrosensitive tube reinforced by two fiber families. Continuum Mechanics and Thermodynamics 34, 1237-1255 (2022). https://doi.org/10.1007/s00161-022-01118-3
11. Лурье А. И. Нелинейная теория упругости. Москва, Наука (1980).
12. Goriely A., Tabor M. Rotation, inversion and perversion in anisotropic elastic cylindrical tubes and membranes. Proc. R. Soc. A. 469 (2153), 20130011 (2013). https://doi.org/10.1098/rspa.2013.0011
13. Lu T. Q., Suo Z. G. Large conversion of energy in dielectric elastomers by electromechanical phase transition. Acta Mechanica Sinica 28 (4), 1106-1114 (2012). https://doi.org/10.1007/s10409-012-0091-x
14. Bazaev K., Cohen N. Electrically-induced twist in geometrically incompatible dielectric elastomer tubes. International Journal of Solids and Structures, 111707 (2022). https://doi.org/10.1016/j.ijsolstr.2022.111707
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Published
2023-05-10
How to Cite
Kolesnikov, A. M., & Letunova, D. A. (2023). Finite deformations of a bilayer dielectric nonlinear elastic anisotropic tube under an electric field. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 10(2), 305–314. https://doi.org/10.21638/spbu01.2023.211
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Mechanics
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
