On a micropolar continuum approach to some problems of thermo- and electrodynamics

Иванова, Е. А.

doi:10.1007/s00707-019-2359-8

Cited by 19 publications

(32 citation statements)

References 37 publications

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“…This study continues and develops the research carried out in [3, 4, 18, 28–30, 38, 39]. In these works, the authors develop the Cosserat continuum models of a special type.…”

Section: Introductionmentioning

confidence: 62%

“…It is well known that from Equation () it follows the charge conservation law

\frac{d Q}{d t} + \nabla \cdot bold-scriptJ = 0,

which, in fact, is a condition for the solvability of Equation (). We note that interpretations of the electric current density

J

given in [3, 4, 28] and in [18, 29, 30] differ from each other. We also note that none of [3, 4, 28] or [18, 29, 30] suggest any mechanical analogy for the electric charge density

scriptQ

and provide any mechanical interpretation of Equation ().…”

Section: Introductionmentioning

confidence: 99%

“…The idea of describing electromechanical, magnetomechanical, and purely electromagnetic effects by means of continuum mechanics has been discussed by many authors. For example, continuum models based on translational degrees of freedom have been considered in [3–9], continuum models based on rotational degrees of freedom have been proposed in [3, 4, 10–19], micromorphic continuum models have been discussed in [20–22], two‐component continuum models have been constructed in [23–26], continuum models with microstructure based on rotational degrees of freedom have been suggested in [27–30]. We note that in recent years, various models of electro‐ and magneto‐elasticity with nonlinear constitutive equations have been developed, see, e.g., [31–37].…”

Section: Introductionmentioning

confidence: 99%

“…It is shown that in view of the suggested analogies a part of equations that describe the developed models can be treated as analogies of Maxwell's equations

\nabla \times bold-scriptB = μ μ_{0} bold-scriptJ + ε ε_{0} μ μ_{0} \frac{d bold-scriptE}{d t}, \nabla \times bold-scriptE = - \frac{d bold-scriptB}{d t}, \nabla \cdot bold-scriptE = \frac{scriptQ}{ε ε_{0}}, \nabla \cdot bold-scriptB = 0,

where

J

is the electric current density,

scriptQ

is the electric charge density, ε 0 and μ 0 are the permittivity and permeability of free space, ε and μ are the relative permittivity and the relative permeability of the material. We note that interpretations of vectors

E

and

B

given in [3, 4, 28] and in [18, 29, 30] differ from each other. But both [3, 4, 28] and [18, 29, 30] interpret one of the two first equations in () as the angular momentum balance equation and another of them as a consequence of the constitutive equation.…”

Section: Introductionmentioning

confidence: 99%

“…We note that interpretations of vectors

E

and

B

Section: Introductionmentioning

confidence: 99%

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Modeling of electrodynamic processes by means of mechanical analogies

Иванова

2020

Z Angew Math Mech

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This study continues the line of earlier research in mechanical models of electrodynamic processes suggested in previous works. The basic steps we take to construct these models are: to formulate equations of a special type Cosserat continuum, and then to suggest analogies between quantities characterizing the stress–strain state of the continuum and quantities characterizing electrodynamic processes. In addition to the previously introduced mechanical analogies of the electric field vector and the magnetic induction vector, in this paper we provide mechanical analogies of the magnetic field vector, the electric induction vector, the electric current density and the electric charge density. In the framework of the suggested model, we obtain a set of differential equations that coincide with the first Maxwell's equation (the one with the displacement current term), the Gauss law for electric field and the charge conservation law. As a debatable question, we discuss the possibility of modifying the Maxwell–Faraday equation and the Gauss law for magnetic field.

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“…This study continues and develops the research carried out in [3, 4, 18, 28–30, 38, 39]. In these works, the authors develop the Cosserat continuum models of a special type.…”

Section: Introductionmentioning

confidence: 62%

“…It is well known that from Equation () it follows the charge conservation law

\frac{d Q}{d t} + \nabla \cdot bold-scriptJ = 0,

which, in fact, is a condition for the solvability of Equation (). We note that interpretations of the electric current density

J

given in [3, 4, 28] and in [18, 29, 30] differ from each other. We also note that none of [3, 4, 28] or [18, 29, 30] suggest any mechanical analogy for the electric charge density

scriptQ

and provide any mechanical interpretation of Equation ().…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…It is shown that in view of the suggested analogies a part of equations that describe the developed models can be treated as analogies of Maxwell's equations

\nabla \times bold-scriptB = μ μ_{0} bold-scriptJ + ε ε_{0} μ μ_{0} \frac{d bold-scriptE}{d t}, \nabla \times bold-scriptE = - \frac{d bold-scriptB}{d t}, \nabla \cdot bold-scriptE = \frac{scriptQ}{ε ε_{0}}, \nabla \cdot bold-scriptB = 0,

where

J

is the electric current density,

scriptQ

E

and

B

Section: Introductionmentioning

confidence: 99%

“…We note that interpretations of vectors

E

and

B

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Modeling of electrodynamic processes by means of mechanical analogies

Иванова

2020

Z Angew Math Mech

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Thence the moment of momentum

2020

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Fifty years have passed since Truesdell's seminal paper on the origin and status of the balance for the moment of momentum was published in ZAMM. It is time to take stock: Important new developments in the theory of generalized continua with internal degrees of freedom and some fascinating fundamental applications need to be pointed out. Is there new evidence from classical papers regarding its independence from the balance of linear momentum? Can micropolar theory be used to “explain” electromagnetism? How is the conservation of the moment of momentum viewed in today's physics textbooks? In this paper an attempt is made to answer these and many more interesting questions.

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Modeling of physical fields by means of the Cosserat continuum

Иванова

2022

Z Angew Math Mech

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We consider a special type Cosserat continuum and suggest analogies between quantities characterizing the stress-strain state of the continuum and quantities characterizing physical processes. Such an approach provides us with the ability to derive equations describing electricity, magnetism, and other physical phenomena. This study continues the line of our earlier research. In the present paper, we obtain equations that can be treated as a generalization of Maxwell's equations. The main difference between the proposed equations and classical Maxwell's equations is in the description of magnetic phenomena. In particular, we introduce the concept of a magnetic charge vector and show that this quantity, like the electric charge, satisfies the conservation law and the Gauss law. We are convinced that the magnetic charge vector is the most appropriate physical quantity to characterize the state of a magnetized body. In addition to modeling the electromagnetic field, we make assumptions about how the proposed model can describe the field corresponding to the strong interaction.

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On a micropolar continuum approach to some problems of thermo- and electrodynamics

Cited by 19 publications

References 37 publications

Modeling of electrodynamic processes by means of mechanical analogies

Modeling of electrodynamic processes by means of mechanical analogies

Thence the moment of momentum

Modeling of physical fields by means of the Cosserat continuum

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