Abstract
Coupling effects among different physical fields reflect the conversion of energies from one field into another substantially. For simple physical processes, their governing or constitutive equations all satisfy the law of conservation of energy (LCE). Then, an analysis is extended to the coupling effects. First, for the linear direct and converse piezoelectric and piezomagnetic effects, their constitutive equations guarantee that the total energy is conserved during the process of energy conversion between the elastic and electromagnetic fields. However, the energies are converted via the work terms, (βijkEi),kvj and (γijkHi),kvj, rather than via the energy terms, βijkEiejk and γijkHiejk. Second, for the generalized Villari effects, the electromagnetic energy can be treated as an extra contribution to the generalized elastic energy. Third, for electrostriction and magnetostriction, both effects are induced by the Maxwell stress. Moreover, their energies are purely electromagnetic and thus both have no converse effects. During these processes, the energies can be converted in three different ways, i.e., via the non-potential forces, via the cross-dependence of the energy terms, and directly via the electromagnetic interactions of ions and electrons. In the end, the general coupling processes which involve elastic, electromagnetic fields and diffusion are also analyzed. The advantages of using this energy formulation are that it facilitates discussion of the conversion of energies and provides better physical insights into the mechanisms of these coupling effects.
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References
TICHÝ, J., ERHART, J., KITTINGER, E., and PŘÍVRATSKÁ, J. Fundamentals of Piezoelectric Sensorics, Mechanical, Dielectric, and Thermodynamical Properties of Piezoelectric Materials, Springer, New York (2010)
SUNDAR, V. and NEWNHAM, R. E. Electrostriction and polarization. Ferroelectrics, 135(1), 431–446 (1992)
CURIE, J. and CURIE, P. Contractions and expansions produced by voltages in hemihedral crystals with inclined faces. Comptes rendus de l’Académie des Sciences, 93, 1137–1140 (1881)
BOROVIK-ROMANOV, A. S. Piezomagnetism in the antiferromagnetic fluorides of cobalt and manganese. Soviet Physics, Journal of Experimental and Theoretical Physics, 11, 786–793 (1960)
JOULE, J. P. On a new class of magnetic forces. Annals of Electricity, Magnetism, and Chemistry, 8, 219–224 (1842)
MATTEUCCI, C. Recherches expérimentales sur les phénoménes électromagnétiques développés par la torsion. Annales de Chimie et de Physique, 53, 385–417 (1858)
WIEDEMANN, G. Magnetische Untersuchungen. Annalen der Physik, 193, 193–217 (1862)
VILLARI, E. Ueber die aenderungen des magnetischen moments, welche der zug und das hindurchleiten eines galvanischen stroms in einem stabe von stahl oder eisen hervorbringen. Annalen der Physik, 202, 87–122 (1865)
MEIROVITCH, L. Methods of Analytical Dynamics, McGraw-Hill, New York (1970)
PENROSE, O. and FIFE, P. C. Thermodynamically consistent models of phase-field type for the kinetic of phase transitions. Physica D: Nonlinear Phenomena, 43, 44–62 (1990)
WANG, S. L., SEKERKA, R. F., WHEELER, A. A., MURRAY, B. T., CORIELL, S. R., BRAUN, R. J., and MCFADDEN, G. B. Thermodynamically-consistent phase-field models for solidification. Physica D: Nonlinear Phenomena, 69, 189–200 (1993)
JACKSON, J. D. Classic Electrodynamics, John Wiley & Sons, New York (1999)
LARCHE, F. C. and CAHN, J. W. The interactions of composition and stress in crystalline solids. Acta Metallurgica, 33, 331–357 (1985)
EKREEM, N. B., OLABI, A. G., PRESCOTT, T., RAFFERTY, A., and HASHMI, M. S. J. An overview of magnetostriction, its use and methods to measure these properties. Journal of Materials Processing Technology, 191, 96–101 (2007)
MALYUGIN, D. V. On the theory of Wiedemann effects. Journal of Magnetism and Magnetic Materials, 97, 193–197 (1991)
ZHOU, P. and JOHNSON, W. C. Discussion on the mechanism of electromigration from the perspective of electromagnetism. Journal of Electronic Materials, 39(12), 2583–2587 (2010)
ZHOU, P. Analysis on irreversible processes using the phase-field variational approach with the entropy or energy functional. arXiv:1412.0575 (2014) http://arxiv.org/abs/1412.0575v2
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Citation: ZHOU, P. Coupling effects between elastic and electromagnetic fields from the perspective of conservation of energy. Applied Mathematics and Mechanics (English Edition), 42(11), 1649–1662 (2021) https://doi.org/10.1007/s10483-021-2792-9
Project supported by the National Natural Science Foundation of China (No. 51201049)
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Zhou, P. Coupling effects between elastic and electromagnetic fields from the perspective of conservation of energy. Appl. Math. Mech.-Engl. Ed. 42, 1649–1662 (2021). https://doi.org/10.1007/s10483-021-2792-9
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DOI: https://doi.org/10.1007/s10483-021-2792-9