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1
Content available remote Influence of anisotropy induced by microcracks on effective elastic properties
Gambin B, Gałka A., Telega J. J., Tokarzewski S.
Engineering Transactions
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2005
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Vol. 53, iss. 4
363-374
EN
The influence of microcracks distribution on macroscopic elastic properties of composites with a specific structure is studied. The model predicts the properties of laminates made of materials in which fracture process leads to appearance of many microcracks distributed practically uniformly. The method of solution is based on the so-called reiterated homogenization with two different scales of inhomogeneities. The smaller scale is connected with microcracks size. After homogenization performed with the help of FEM an anisotropic homogeneous elastic material is obtained. The anisotropy is implied by directional distribution of microcracks. On the second larger scale, random mixture of two or more different anisotropic elastic materials is considered.
2
Content available remote Investigation and analysis of periodic problem for layered composite structure on periodic foundation by means of non-smooth argument transformation method
Starushenko G., Krulik N., Tokarzewski S.
International Journal of Applied Mechanics and Engineering
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2003
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Vol. 8, no spec.
169-177
EN
The solution of the periodic problem for layered composite structure on the discretely located linear-elastic bearings has been obtained in the paper (Starushenko, 2000). The general case of the problem is considered in this paper. The structure that is located on the combined continuous and discrete elastic foundation is examined. The foundation rigidity is periodically changed in the composite phase limits. The structure is fortified by elastic supports in the component part junction. The problem is solved for general problem statement. It is supposed that physical and geometrical characteristics of the body and elastic foundation can accept any value. The periodic solution of the problem has been obtained in components of displacement function by means of saw-tooth argument transformation method in the paper. Analysis of obtained solution has been carried out. The flexure functions of the elastic foundation depending of the structure rigidity and geometric factors have been found.
3
Content available remote Basic inequalities for multipoint Padé approximants to Stieltjes functions
Tokarzewski S., Telega J. J., Pindor M., Gilewicz J.
Archives of Mechanics
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2002
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Vol. 54, nr 2
141-153
EN
Basic inequalities for diagonal and subdiagonal multipoint Padé approximants to N power series expansions of Stieltjes function f0 at points x1, x2,...,xN are derived. For particular cases the inequalities obtained reduce to those obtained earlier for one-, two- and three-point Padé approximants in [1], [5] and [23], respectively. Numerical examples illustrating the relations achieved are also provided. Our results can be applied to the determination of bounds on the effective moduli of bone subjected to torsion and composites in the case of transport equations.
4
Content available remote Torsional rigidities of cancellous bone filled with marrow : the application of multipoint Padé approximants
Tokarzewski S., Telega J. J., Gałka A.
Engineering Transactions
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2001
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Vol.49, iss.2/3
135-153
EN
An idealized model of prism-like trabecular bone was developed to study its static and dynamic responses under torsional moments. Effects of bone marrow and bone apparent density were investigated. By constructing multipoint Padé approximants [1-2] to the torsional complex modulus, hydraulic stiffening of the prism-like bone due to the presence of bone marrow was predicted. The torsional compliance, creep function and relaxation function were also evaluated.
5
Content available remote Quasifractional approximants for effective conductivity of regular arrays of spheres
Danishevs'kyy V., Andrianov I., Tokarzewski S.
Archives of Mechanics
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2000
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Vol. 52, nr 2
319-327
EN
We study the effective heat conductivity of regular arrays of perfectly conducting spheres embedded in a matrix with the unit conductivity. Quasifractional approximants allow us to derive an approximate analytical solution, valid for all values of the spheres volume fraction phi belongs to [0; phi[max]] (phi[max] is the maximum limiting volume of a sphere). As the bases we use a perturbation approach for phi --> 0 and an asymptotic solution for phi --> phi[max]. Three different types of the spheres space arrangement (simple, body and face-centred cubic arrays) are considered. The obtained results give a good agreement with numerical data.
6
Content available Application of the reiterated homogenization to determination of the effective moduli of compact bone
Telega J.J., Gałka A., Tokarzewski S.
Journal of Theoretical and Applied Mechanics
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1999
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nr 3
687-706
EN
The aim of the paper is twofold. First, the available results of finding the effective macroscopic elastic moduli of a compact bone by using homogenization are surveyed. Secondly, it is shown that the proper framework for studying such organic materials with hierarchical microstructure is that of reiterated homogenization. T-convergance theory is applied to obtain the general formulae for the effective elastic moduli of a material with three structural levels.
PL
Cel pracy jest dwojaki: po pierwsze, przedstawiono podsumowanie dotychczasowych badań dotyczących wyznaczania współczynników sprężystości kości zbitej przy zastosowaniu metod homogenizacji. Po drugie, wykazano, że homogenizacja reiterowana stanowi odpowiednie narzędzie do badania takich materiałów organicznych o hierarchicznej mikrostrukturze. Zastosowano teorię T-zbieżności do wyprowadzenia ogólnych zależności opisujących efektywne współczynniki sprężyste materiału o trzech poziomach strukturalnych.
7
Content available A contibutionto evaluation of effective moduli of trabecular bone with rod-like microstructure
Gałka A., Telega J.J., Tokarzewski S.
Journal of Theoretical and Applied Mechanics
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1999
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nr 3
707-728
EN
The homogenization theory has been applied to evaluation of effective moduli of a network of interconnected elastic rods modelling human cancellous bone. Numerical computations of the Young modulus, Poisson ratio and shear modulus have been carried out. The obtained results compare fevourably with available experimental data.
PL
Teorię homogenizacji zastosowano do wyznaczania efektywnych własności mechanicznych dla regularnej sieci elastycznych prętów modelujących kość gąbczastą. Wyznaczono numerycznie efektywne stałe techniczne: moduł Younga, współczynnik Poissona i moduł ścinania. Wyniki porównano z wynikami ekperymentalnymi uzyskując dobrą zgodność.
8
Content available remote Application of homogenization to evaluation of effective moduli of linear elastic trabecular bone with plate-like structure
Gałka A., Telega J., Tokarzewski S.
Archives of Mechanics
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1999
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Vol. 51, nr 3-4
335-355
EN
Cancellous bone with plate-like architecture is modelled as an elastic cellular solid with regular microstructure. General formulae for the effective moduli are derived. Specific examples concern plate-like cancellous bone with isotropic trabeculae.
9
About representation of theory tasks periodic solutions on basis of non-smooth argument transformation
Starushenko G., Krulik N., Tokarzewski S.
Applied Mechanics and Engineering
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1999
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Vol. 4, no spec.
115-120
EN
The analytical method of solving periodic tasks of elasticity theory for layered composites has been suggested in papers (Starushenko et al., 1998). The method based on introduction of special non-smooth argument transformation so-called saw-tooth transformation (t-transformation). The advantage of saw-tooth argument transformation method is connected with possibility of mathematical description in limits of unanimous approach of different nature functions: continuous, piece continuos, with local specialties. Besides its combination with average theory and a lot of scale decomposition method extends opportunities of t-transformation technique application considerably. Solution of elasticity theory for layered composite massive in case of distributed massif forces has been built in paper (Starushenko et al., 1998). In present paper case of general load (acting of periodic distributed and concentrated load in common) is examined.
10
Content available remote Effective moduli of trabecular bone
Telega J.J., Gałka A., Tokarzewski S.
Acta of Bioengineering and Biomechanics
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1999
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Vol. 1, nr 1
53-57
EN
Cancellous bones with plate-like and rod-like architecture are modelled as linear elastic cellular solid with regular microstructure. General formulae for the effective moduli are derived. Specific examples show plate-like and rod-like cancellous bones with isotropic trabecular.
11
Content available remote Two-point Pade approximants for Stieltjes functions and their application to composite materials
Tokarzewski S., Telega J. J.
Applied Mathematics and Computer Science
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1998
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Vol. 8, no 2
417-434
EN
By employing special continued fractions to asymptotic expansions at zero and infinity, the convergence of the balanced and unbalanced two-point Pade approximants (2PPA) to a Stieltjes function is studied in a real domain. We prove that certain balanced and unbalanced two-point Pade approximants form a monotone sequence of upper and lower bounds uniformly converging to a Stieltjes function. The observed monotone and uniform convergence of 2PPA is exemplified in the evaluation of bounds on the effective transport coefficients of periodic inhomogeneous media.
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