Fundamentals of Magnetoelasticity

Bardzokas, D.; Filshtinsky, Michael L.; Filshtinsky, Leonid A.

doi:10.1007/3-540-71031-0_9

Cited by 5 publications

(11 citation statements)

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“…These methods were developed by Lekhnitskii [50], by Mikhlin [51], by Grigolyuk and Filshtinsky [28] and by many others. They were developed in modern books [5,16,17,29,30,46,56,65,68,74,75] and papers cited therein. However, the books [16,[28][29][30]47] were not translated into English including the third edition of Gakhov's book [24] from 1977.…”

Section: Surveymentioning

confidence: 99%

Mathematical Models of Elastic and Piezoelectric Fields in Two-Dimensional Composites

Filshtinsky

Mityushev

2014

Mathematics Without Boundaries

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This paper is devoted to boundary value problems for harmonic and biharmonic equations which arise in modeling of elastic and piezoelectric fields in two-dimensional composites. All the problems are investigated by the method of complex potentials. The considered boundary value problems for analytic functions are reduced to integral equations. We discuss methods based on the integral equations for multiply connected domains and in the double periodic statement. Relations to the alternating scheme of Schwarz and to the method of perturbations are considered. Applications to calculation of the effective properties tensor are discussed. This paper also contains results published from 1964 in Russian and not known in English literature.

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Section: Surveymentioning

confidence: 99%

Mathematical Models of Elastic and Piezoelectric Fields in Two-Dimensional Composites

Filshtinsky

Mityushev

2014

Mathematics Without Boundaries

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“…The combined effect of the anti-plane deformation and the electric fields in each section of the fiber composite is locally described by the coupled equations [19] σ i3 = c 44…”

Section: Local Equations and Complex Potentialsmentioning

confidence: 99%

“…The functions ϕ 1 (z) and ϕ 2 (z) are analytic in G ± and continuously differentiable in the closures of the considered domains. The following representations take place [19] …”

Section: Local Equations and Complex Potentialsmentioning

confidence: 99%

“…This problem in the theory of composites provides the following standard method to compute the effective piezoelectric constants [19]. First, the averaged values σ 3 and D ( = 1, 2) are fixed.…”

Section: Double Periodic Statementmentioning

confidence: 99%

“…The theory of the self-consistent methods was systematically discussed by Kanaun and Levin [17]; its limitations were analyzed in [18]. A method of integral equations for doubly periodic problems including anisotropic piezoelectric composites was developed in [19][20][21]. A rigorous mathematical study of the piezoelectric boundary value problems based on the theory of singular integral equations was presented in [22,23].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Effective anti-plane properties of piezoelectric fibrous composites

Rylko

2013

Acta Mech

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Anti-plane shear of piezoelectric fibrous composites is theoretically investigated. The geometry of composites is described by the 2-dimensional geometry in a section perpendicular to the unidirectional fibers. The previous constructive results obtained for scalar conductivity problems are extended to piezoelectric antiplane problems. First, the piezoelectric problem is written in the form of the vector-matrix R-linear problem in a class of double periodic functions. In particular, application of the zeroth-order solution to the R-linear problem yields a vector-matrix extension of the famous Clausius-Mossotti approximation. The vector-matrix problem is decomposed into two scalar R-linear problems. This reduction allows us to directly apply all the known exact and approximate analytical results for scalar problems to establish high-order formulae for the effective piezoelectric constants. Special attention is paid to non-overlapping disks embedded in a two-dimensional background.

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On the possibility of classical vacuum polarization and magnetization

Fumeron

Moraes

Berche

2023

Class. Quantum Grav.

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It is common practice to take for granted the equality (up to the constant $\varepsilon_0$) of the electric displacement ($\bf{D}$) and electric ($\bf{E}$) field vectors in vacuum. The same happens with the magnetic field ($\bf{H}$) and the magnetic flux density ($\bf{B}$) vectors (up to the constant $\mu_0^{-1}$). The fact that gravity may change this by effectively inducing dielectric or magnetic responses to the primary fields is commonly overlooked. It is the purpose of this communication to call attention to classical polarization or magnetization of the vacuum due to the concomitant presence of gravitational and electromagnetic sources. The formalism of differential forms (exterior calculus) is used since it provides a clear-cut way to achieve this. This work offers new routes for possible detection of various spacetime geometries via their electromagnetic manifestations and the way they influence light propagation.

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Fundamentals of Magnetoelasticity

Cited by 5 publications

References 0 publications

Mathematical Models of Elastic and Piezoelectric Fields in Two-Dimensional Composites

Mathematical Models of Elastic and Piezoelectric Fields in Two-Dimensional Composites

Effective anti-plane properties of piezoelectric fibrous composites

On the possibility of classical vacuum polarization and magnetization

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