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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.

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]

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.