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The paper develops a complex approach to accounting for imperfect contacts (IC) when determining effective properties of various nature. The IC are assumed to be caused by various factors (microstructure features, process’s specifity and so on). To obtain macroscopic properties, we seek a solution of the homogenization problem for the material containing isolated ellipsoidal inhomogeneities when fields are discontinuous at the interphase boundaries. The paper considers, generalizes and compares two existing approaches to accounting for the IC, namely, an approach where IC is modeled by means of a field jump specified in terms of a ratio of field values on the outer and inner sides of the inhomogeneity boundary, and approach, which introduces inhomogeneity with a surface effect. To take into account IC, we have considered an equivalent inhomogeneity with ideal contacts at the boundary. Working the problem on determining the effective diffusional permeability of material provided an example.

This paper is devoted to the analytical calculation of the contribution and opening displacement tensors of an arbitrarily oriented crack in a transformed transversely isotropic (TraTI) matrix. It generalizes a recent work considering elliptically orthotropic (EO) symmetry, as EO is a particular case of TraTI. The latter allows to explore a wider range of symmetries, including non-orthotropic symmetries. The approach is based on the linear transformation between boundary value problems with TraTI and transversely isotropic (TI) bodies. A detailed analysis shows that TraTI fourth-order tensors are described by a set of 11 parameters (5 material parameters and 6 angles defining the transformation). This is a significant enrichment beyond the set of EO tensors which depends on 7 parameters (4 material parameters and 3 angles). New analytical results are obtained for elliptical and circular cracks embedded, respectively, in TraTI, orthotropic TraTI and monoclinic TraTI matrices. It is shown that the most general case leading to analytical derivations of crack contribution and opening displacement tensors is that of a TraTI matrix with a specific restriction: the initial crack must be aligned along the isotropy plane of the TI matrix. To the best of our knowledge, this corresponds to the current largest space of matrix anisotropy allowing analytical derivation of the compliance of a single elliptical crack embedded in an infinite matrix as well as an extension of analytical 3D results showing a coupling between opening and shear modes. Numerical results are presented to illustrate potential applications of the method for the case of an arbitrarily oriented elliptical crack in an infinite uniform matrix of stiffness of arbitrary anisotropy. The best-fit problem investigated in previous papers is revisited and a new algorithm providing the closest stiffness tensor for which there exists an analytical solution to the crack opening displacement tensor is developed. Numerical applications to real TI materials are finally presented. [ABSTRACT FROM AUTHOR]

The paper deals with the calculation of polycrystalline material effective diffusion coefficients. The polycrystalline material has been simulated by two-phase composite consisting of matrix and spheroidal inhomogeneities. The Mori – Tanaka scheme was used to account interactions between inhomogeneities. The proposed simulation took into account the effect of segregation as well. The paper put forward two models to describe the polycrystalline material. The former considered grains to be inhomogeneities, and grain boundaries to be a material matrix. The latter, in contrast, did the grain boundaries to be inhomogeneities, and the grains to be a material matrix. The simulation results were compared with experimental data. The importance of taking into account the segregation parameter when calculating effective diffusion coefficients of polycrystalline material was shown.

In this work, the diffusion equation for the gas-solid system is revised to describe the non-uniform distribution of hydrogen in steels. The first attempt to build a theoretical and general model and to describe the diffusion process as driven by a chemical potential gradient is made. A linear elastic solid body and ideal gas, diffusing into it, are considered. At this stage, we neglect any traps and non-linear effects. The coupled diffusion-elastic boundary problem is solved for the case of the cylinder under the tensile loads. The obtained results correspond to the experimental ones. Based on them, the assumptions about the correctness of the model and its further improvement are suggested.

This paper proposes a mathematical model that can be used to quantify the effects of a polarized electric field on the mechanical properties of a polar dielectric in the framework of mechanics of deformable solids. The physical essence of the phenomenon is known. However, its direct use in practical calculations may cause difficulties due to the complexity of the composition and structure of materials used in the design and manufacture of specific products whose operation regimes are based on polarization effects. A continuum description of the polarization phenomenon makes it possible to circumvent these difficulties. The basis of the generalized model is a micropolar linearly elastic medium. The generalization consists in taking into account the initial stress state of the material, as well as cross effects under the mutual influence of translational and rotational deformations, the possibility to calculate the characteristics of micropolar material properties based on a special nonlocal model of micropolar media with internal nonlocal potential interactions. It takes into account translational and rotational potential interactions of particles of a continuous medium at finite distances. The kinematic characteristics of the material are the same as those used by the traditional model of a micropolar elastic medium ‐ the gradients of translational displacements of the medium's particles, their rotations independent of the medium's rotation and rotations of the particles relative to the medium. Generalized forces performing work on these generalized displacements are volumetrically and surface‐distributed forces and moments. To determine the values of the parameters of the interparticle potentials of the nonlocal model, a method is proposed using data from experiments to determine the material constants of isotropic linearly elastic materials and the dispersion law for plane acoustic waves of high frequency. The paper considers and quantifies the effects of anisotropy in an initially isotropic material, as well as anharmonic effects that cause dielectric heating by a periodically changing polarizing field. The results are compared qualitatively and quantitatively with known experimental data and physical notions of the phenomena in question. [ABSTRACT FROM AUTHOR]

This paper wants to draw attention to several issues in electrodynamic field theory and to make way for a rational continuum approach to the subject. The starting point are the balances for magnetic flux and electric charge, both in a very general formulation for volumes and for open surfaces, all of which can deform and be immaterial or material. The spatial point‐of‐view for the description of fields is favored and its advantages in comparison to the concept of material particles is explained. A straightforward answer to the question of how to choose units for the electromagnetic fields most suitably is also presented. The transformation properties of the electromagnetic fields are addressed by rewriting the balances in space–time notation. Special attention is paid to the connection between the two sets of electromagnetic fields through the so‐called Maxwell–Lorentz–æther relations. The paper ends with an outlook into constitutive theory of matter under the influence of electromagnetic fields and a discussion on curious developments in context with Maxwell's equations. [ABSTRACT FROM AUTHOR]

The paper continues and summarizes our previous investigation on a description of the local increase of hydrogen in the vicinity of the border of a metal specimen after hydrogenation. The local increase is observed after artificial saturation of metal specimens and after operation of metal details in corrosive environments. It can worsen significantly the material properties and its behavior at the macro‐level. A stress‐induced diffusion process in a cylinder is modeled. The paper accounts for the inner stresses and strains by means of chemical potential and by means of the dependence of the diffusion coefficient on elastic strain energy. The stress–strain state is determined within the micropolar theory of elasticity, the results are compared with the ones obtained within the classical theory. Nonuniform fields of stresses and strains result in a nonuniform distribution of hydrogen. Accounting for the couple stress interactions between continuum particles results in a faster saturation of the boundary layer with hydrogen. [ABSTRACT FROM AUTHOR]

A model is proposed for the description of a highly inhomogeneous distribution of hydrogen within a saturated metal specimen (the so-called skin effect due to hydrogen saturation). The model is based on the micropolar continuum approach and results in a nonuniform stress–strain state of a cylindrical metal specimen due to distributed couples or microrotations. The dependence of the diffusion coefficient on the strain energy is considered in order to model stress-induced diffusion. Accumulation of hydrogen within a thin boundary layer results in a highly nonuniform distribution of hydrogen across the specimen. The mutual influence of the stress–strain state and hydrogen accumulation is taken into account. The estimated thickness of the surface layer containing hydrogen is comparable to the thickness observed in experiments. The predicted average concentration coincides with experimental data. [ABSTRACT FROM AUTHOR]

The paper focuses on the modeling of the stress‐affected localized chemical reaction in particles embedded in a matrix material. The self‐consistent field method is used to account for the interaction between particles and to calculate the effective stress field acting on a separate particle. The kinetics of chemical reaction front is governed by the chemical affinity tensor that depends on the stress‐strain state at the reaction front. The influence of the matrix elastic properties and the particle volume fraction on the reaction front kinetics is studied in detail. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper foundations are laid for a future solution of a fully coupled flow problem for the micropolar medium undergoing structural change in a funnel-shaped crusher. Initially the fundamental equations of micropolar media are revisited and the problem of structural changes of micropolar media moving in a crusher is explained. Then a review of the current state-of-the-art is presented and a necessary extension of the problem is motivated. The need for using numerical methods of fluid mechanics is emphasized. As a prerequisite for the study of the fully coupled initial boundary value 2D-flow problem of a micropolar fluid the funnel flow of a Navier-Stokes fluid is investigated based on an implicit finite difference scheme using the Thomas algorithm. Numerical results for velocities, stresses, and for the pressure dependence of the funnel flow are presented. The correctness of the algorithm is checked by specializing to the case of a flow through a tunnel of constant cross-section under the influence of gravity, for which an analytical solution is available. [ABSTRACT FROM AUTHOR]

In order to model the flow of nematic crystals, the theoretical framework according to Ericksen and Leslie is applied. The essentials of the theory are compiled and then specialized to Couette flow. The profiles for linear velocity and orientation angle will be computed and, in particular, we shall also study the rise in temperature due to viscous dissipation, which is frequently ignored by mechanicians. Analytical and numerical solutions for the fields are derived for different boundary conditions and will subsequently be discussed. [ABSTRACT FROM AUTHOR]

At present information about viscous properties of the eye's sclera is scarce, the main reason being that direct measurements cause technical problems. Nevertheless, coefficients of the sclera viscosity are of paramount interest for biomechanics and ophthalmologists. This paper investigates a method for determining the shear viscosity of the sclera based on a comparison of results from mathematical modeling with estimated experimental data from measurements of the IntraOcular Pressure (IOP) over a long time after an intravitreal injection (injection into the vitreous body of the eyeball) into enucleated eyes. In order to model the IOP behavior we consider a viscoelastic spherical layer subjected to a centrally symmetric load as follows. The excess pressure is considered, hence, the external pressure is absent and a displacement of the inner boundary is specified in order to take the intravitreal injection volume into account. We assume that during the experiment the volume of the eyeball remains constant and that the material of the sclera obeys linear transversely isotropic elasticity. The function for the IOP, which is based on fitted experimental data presented in the literature, decreases up to a limit value. As a result, we obtain a value for the shear viscosity of the sclera corresponding to the best adjustment between experimental data and theoretical prediction. [ABSTRACT FROM AUTHOR]

This work presents a thermodynamic analysis of the ballistic heat equation from two viewpoints: classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT). A formula for calculating the entropy within the framework of EIT for the ballistic heat equation is derived. The entropy is calculated for a sinusoidal initial temperature perturbation by using both approaches. The results obtained from CIT show that the entropy is a non-monotonic function and that the entropy production can be negative. The results obtained for EIT show that the entropy is a monotonic function and that the entropy production is nonnegative. A comparison between the entropy behaviors predicted for the ballistic, for the ordinary Fourier-based, and for the hyperbolic heat equation is made. A crucial difference of the asymptotic behavior of the entropy for the ballistic heat equation is shown. It is argued that mathematical time reversibility of the partial differential ballistic heat equation is not consistent with its physical irreversibility. The processes described by the ballistic heat equation are irreversible because of the entropy increase. [ABSTRACT FROM AUTHOR]