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Kanaun S.,Technological Institute of Higher Education of Monterrey | Levin V.,Mexican Oil Institute
Solid Mechanics and its Applications | Year: 2013

The work is devoted to the effective field method and its application in the theory of heterogenous materials. For many years, various versions of the method have been used for the calculation of effective physical and mechanical properties of composite materials (the homogenization problem). In the historical survey, the most important steps of the development of the method are indicated starting from nineteenth century. The main attention is focused on the combination of the effective field and numerical methods that yields efficient numerical algorithms for the calculation of effective properties and detailed fields in periodic and random composite materials. Examples of the application of the method to prediction of conductive, elastic, and elasto-plastic properties of composites are presented. © Springer Science+Business Media Dordrecht 2013. Source


Levin V.M.,Mexican Institute of Petroleum | Kanaun S.K.,Technological Institute of Higher Education of Monterrey | Markov M.G.,Mexican Institute of Petroleum
Poromechanics V - Proceedings of the 5th Biot Conference on Poromechanics | Year: 2013

The generalized Maxwell's method is developed for the calculation of the static effective parameters of poroelastic medium containing a random set of ellipsoidal anisotropic poroelastic inhomogeneities (poroelastic composite material). It is shown that the Maxwell method leads to the equations for the effective poroelastic constants that coincide with equations obtained by other self-consistent methods. Moreover, the Maxwell method allows deriving the so-called «cross-property relations», i.e. relations between different effective poroelastic constants that were established earlier for some particular cases. © 2013 American Society of Civil Engineers. Source


Kanaun S.,Technological Institute of Higher Education of Monterrey
International Journal of Engineering Science | Year: 2015

Scattering of plane monochromatic acoustic waves on a planar screen of arbitrary shape is considered (direct problem). The 2D-integral equation for the pressure jump on the screen is discretized by Gaussian approximating functions. For such functions, the elements of the matrix of the discretized problem take the form of a standard one-dimensional integral that can be tabulated. For regular grids of approximating nodes, the matrix of the discretized problem has the Toeplitz structure, and the corresponding matrix-vector products can be calculated by the Fast Fourier Transform technique. The latter strongly accelerates the process of iterative solution. Examples for an elliptic screen subjected to incident fields with various wave vectors are presented. The problem of reconstruction of the screen shape from the experimentally measured amplitude of the far field scattered on the screen (inverse problem) is discussed. Screens which boundaries are defined by a finite number of scalar parameters are considered. Solution of the inverse problem is reduced to minimization of functions that characterize deviation of experimental and theoretical amplitudes of the far field scattered on a screen. Local and global minima of these functions with respect to the screen shape parameters are analyzed. Optimal frequencies for efficient solution of the inverse problem are identified. © 2015 Elsevier Ltd. All rights reserved. Source


Kanaun S.,Technological Institute of Higher Education of Monterrey
International Journal of Engineering Science | Year: 2012

The homogenization problem for elasto-plastic media with arrays of isolated inclusions (matrix composite) is considered. A combination of self-consistent and numerical methods is used for calculation of the overall response of such composites under quasi-static loading. Elasto-plastic properties of the medium and the inclusions are described by the equations of the incremental theory of plasticity with isotropic hardening. For the construction of the average stress-strain relations of the composites, the process of external loading is divided into a sequence of small steps, and the problem is linearized at every step. The self-consistent effective field method allows reducing the homogenization problem at every step to the calculation of stresses and elasto-plastic deformations in a composite cell that contains a finite number of inclusions. The linearized problems are formulated in terms of volume integral equations for the stress or elastic strain field increments in the cell. For the numerical solution, these equations are discretized by Gaussian approximating functions concentrated in a set of nodes that cover the composite cell. For such functions, elements of the matrix of the discretized problems are calculated in explicit analytical forms. If the approximating nodes form a regular grid, the matrix of the discretized problem has Toeplitz's properties, and the matrix-vector products of such matrices can be calculated by the fast Fourier transform technique. The latter accelerates substantially the process of iterative solution of the discretized problems. The dependencies of the overall stress-strain curves on the number of inclusions inside the cell are studied in the 2D and 3D cases. The inclusions that are stiffer or softer then the matrix are considered. The predictions of the method are compared with the finite element calculations available in the literature. © 2012 Elsevier Ltd. All rights reserved. Source


Kanaun S.,Technological Institute of Higher Education of Monterrey | Kochekseraii S.B.,Chrysler Group LLC
International Journal of Engineering Science | Year: 2012

The work is devoted to computer simulations of the effective conductive properties of open and closed-cell foam materials. The conductivity of the solid phase of the foam is assumed to be much larger than the one of the filler. For the calculation of the effective conductivity, a complex cell element of the foam that consists of a typical cell and its nearest neighbors is introduced. This element is embedded in the medium with the conductivity of the solid phase. For the calculation of the field and field flux in the complex cell, 3D-integral equations for the fields in heterogenous media are used. The effective conductivity is the coefficient that relates the average field and the field flux in the central part of the complex cell. The method is applied to the calculation of the effective conductivity of open cell foams with various shapes of ligaments. Transition from open to closed-cell foams is considered. Predictions of the method are compared with the experimental data available in the literature. © 2011 Elsevier Ltd. All rights reserved. Source

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