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Purpose The purpose of this paper is to solve the local problem involving strong contrast heterogeneous conductive material, with application to gas-filled porous media with both perfect and imperfect Kapitza boundary conditions at the bi-material interface. The effective parameters like the dynamic conductivity and the thermal permeability in the acoustics of porous media are also derived from the cell solution. Design/methodology/approach The Fourier transform method is used to solve frequency-dependent heat transfer problems. The periodic Lippmann–Schwinger integral equation in Fourier space with source term is first formulated using discrete Green operators and modified wavevectors, which can then be solved by iteration schemes. Findings Numerical examples show that the schemes converge fast and yield accurate results when compared with analytical solution for benchmark problems. Originality/value The formulation of the method is constructed using static and dynamic Green operators and can be applied to pixelized microstructure issued from tomography images.

In this paper, we present a boundary-volume based Lippmann Schwinger integral equation for numerical homogenization problems of heterogeneous conductive materials with arbitrary contrast ratio and imperfect interface behavior. It is shown that the interior temperature gradient within each homogeneous phase is connected to the material dissimilarity quantities at all boundaries between different phases. The Kapitza interface model can also be included in the formulation. The basic FFT iteration schemes converge fast even for infinite contrast in the case of usual interface conditions. In the case of Kapitza's interface, Conjugate Gradient schemes based on the new formulation converge fast and yield accurate results when compared with standard Finite Element Method.

In the present paper, we propose a new FFT based numerical homogenization method to compute the effective conductivity of fractured media involving insulating and superconductive cracks. The governing Lippmann Schwinger (LS) equations based on temperature jump and heat flux jump distribution localized on crack lines are formulated and the geometry of sharp cracks is described by exact expression of form factors. To solve the LS equations, the bi conjugate gradient stabilized method is used and leads to fast convergence. Numerical examples in 2D and 3D show a good accuracy when compared with standard Finite Element Method solutions.

In this paper, the heat conductivity of two-dimensional (2D) media made of an arbitrarily thermal anisotropic material and containing pores with arbitrary shape and superconductive boundary is considered. In addition to the bulk behavior, the line conduction model is used for the boundary behavior. Such idealized mathematical model can be seen as the limit case of very thin material layer with very high conductivity. The fundamental heterogeneity problem in the micromechanics of a single void embedded in an infinite matrix with both boundary and bulk behavior is then investigated and solved with the complex variable and the Conformal Mapping (CM) techniques. The heterogeneity problem results are then used to obtain the effective heat conductivity of the porous material with different homogenization schemes.

International audience; In this article, we develop an extension of the Fourier transform solution method in order to solve conduction equation with nonperiodic boundary conditions (BC). The periodic Lippmann-Schwinger equation for porous materials is extended to the case of non-periodicity with relevant source terms on the boundary. The method is formulated in Fourier space based on the temperature as unknown, using the exact periodic Green function and form factors to describe the boundaries. Different types of BC: flux, temperature, mixed and combined with periodicity can be treated by the method. Numerical simulations show that the method does not encounter convergence issues due to the infinite contrast and yields accurate results for both local fields and effective conductivity.

International audience; In this paper, the heat conductivity of two-dimensional (2D) material containing arbitrary shape pore with highly conducting pore boundary are considered. To model the distinct heat transfer behavior of the pore boundary, the line conduction model is used. The heterogeneity problem of a single void embedded in an infinite matrix is then investigated and solved with the complex variable and the Conformal Mapping techniques. The results of the latter are then used to obtain the effective heat conductivity of the porous material with different homogenization schemes.

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The effective viscoelastic properties of a rock mass embedding many sets of planar fractures are estimated. The rock matrix is modeled by a standard Zener rheological model, while the linear elastic or a linear non ageing viscoelastic laws is considered to relate the opening displacement of a fracture and the stresses acting on its surfaces. The correspondence principle is considered to transform the problem in hand to an equivalent elastic problem in Laplace-Carson (LC) space. Then, closed form solutions to the creep parameters in time space are derived. For the case of elastic fractures, we show that the presence of the fractures modifies the instantaneous and long term compliances of viscoelastic fractured rocks by the same way as it does for the case of elastic fractured rocks. However, they do not affect the variations versus time of the creep parameters. Unlike the case of elastic fractures, viscoelastic fractures modify the variations versus time of the creep parameters. However for all the situations, we observe that the effective creep properties of a fractured medium made of a Zener solid matrix and Zener fractures can be explicitly expressed by an effective Generalized Maxwell rheology of which the rheological parameters are functions of the viscoelastic parameters of the matrix and the fractures.

Formation of confined tetra-silicene (t-silicene) from the melt is studied by molecular dynamics (MD) simulation. Models containing 6066 atoms interacted via Stillinger-Weber potential are obtained by cooling from 5000 K to 300 K. We find that t-silicene is formed with the broad buckling distribution ranged from 0.60 A to 1.49 A differed from unique buckling of 1.49 A predicted by DFT calculations. Depending on the cooling rate used in simulations one can obtain crystalline or amorphous samples. Crystallization and glass transition temperatures are defined, namely, T X ≈ 1950 K and T g ≈ 1350 K. These temperatures are higher than those found for hexa-silicene. Structural characteristics of models are studied in details via radial distribution functions (RDFs), coordination number, bond-angle, interatomic distance and buckling distributions plus ring statistics. In addition, 2D visualization of atomic configurations plus diffraction pattern of the models at 300 K is done in order to see in more details structure of the models. Main types of structural defects are defined and their role in chemico-physical performance of t-silicene is discussed. Although main structural units are tetragons, both amorphous and crystalline t-silicenes contain many rings differed from tetragons. According to our calculations, the Poisson ratio for the obtained t-silicene is positive. In order to clarify interatomic potential effects on the formation of t-silicene, the same simulation procedure is done with the reactive force field and intensive comparison is given.