Moment theory of electromagnetic effects in anisotropic solids

A method for modeling fluid-solid interactions in saturated porous media is proposed. The main challenge is the combination of the material and spatial descriptions. The deformation of the solid, which serves as a "container" to the fluid, is studied by following the motion of its material particles, i.e., in Lagrangian description. On the other hand, the motion of the fluid is described in spatial form, i.e., by using a Eulerian approach. However, the solid deforms and this implies a certain difference regarding the standard formulation used in spatial description of fluid mechanics where a fixed grid dissects space into elementary volumes. Here the grid is no longer fixed, and the elementary volumes will follow the deformation of the solid. Moreover, for the solid as well as for the fluid the balance equations are formulated in the current configuration, where interaction forces and couples are taken into account. By using Zhilin's approach, entropy and temperature are incorporated in the system of equations. Constitutive equations are constructed for both elastic and inelastic components of force and couple stress tensors and interaction force and couple. The constitutive equations for elastic components are found on the basis of the energy balance equation; the constitutive equations for the inelastic components are proposed in accordance with the second law of thermodynamics. Particular emphasis is placed on the constitutive equations of the interaction force and couple, which result in a symmetric form only because of the "hybrid" approach combining the Lagrangian with the Eulerian description. Three possible examples of application of the theory have been presented. For each example, all required assumptions were first stated and discussed and then the complete set of the corresponding equations was presented.

show abstract

“…Such a type of model is used for various modeling of processes, for example, see [26,[30][31][32][33][34][35][36][37][38][39][40][41].…”

Section: Momentum and Angular Momentum Balance Equationsmentioning

confidence: 99%

“…(35) should be modified to a form allowing to get Cauchy-Green relations. For this purpose, it is necessary to rewrite all quantities involving products between force and couple stress tensors by means of derivatives of generalized deformations, see "Appendix 1, 2":…”

Section: Reduced Energy Balance Equation Cauchy-green Relationsmentioning

confidence: 99%

Saturated porous continua in the frame of hybrid description

Brazgina

Иванова

2016

Continuum Mech. Thermodyn.

View full text Add to dashboard Cite

show abstract

“…At the turn of the 20th/21st centuries, the interest in mechanical models of physical processes began to revive. We can refer to continuum models based on translational degrees of freedom [2][3][4][5][6][7][8], continuum models based on rotational degrees of freedom [2,3,[9][10][11][12][13][14][15][16][17][18][19], micromorphic continuum models have been discussed in Refs. [20][21][22], two-component continuum models [23][24][25][26], and continuum models with microstructure based on rotational degrees of freedom [27][28][29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Modeling of physical fields by means of the Cosserat continuum

Иванова

2022

Z Angew Math Mech

View full text Add to dashboard Cite

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.

show abstract

“…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%

Modeling of electrodynamic processes by means of mechanical analogies

Иванова

2020

Z Angew Math Mech

View full text Add to dashboard Cite

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.

show abstract

Moment theory of electromagnetic effects in anisotropic solids

Cited by 6 publications

References 4 publications

Saturated porous continua in the frame of hybrid description

Saturated porous continua in the frame of hybrid description

Modeling of physical fields by means of the Cosserat continuum

Modeling of electrodynamic processes by means of mechanical analogies

Contact Info

Product

Resources

About