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1
Content available remote Electrokinetics in random piezoelectric porous media
Telega J.J., Wojnar R.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2007
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Vol. 55, nr 1
125-128
EN
Macroscopic coefficients together with a Darcy law are obtained for porous piezoelectric medium wit h random, not necessarily ergodic, distribution of pores in which a two-ionic electrolyte flows. Peculiarities of stochastic porosity are indicated.
2
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.
3
Content available remote Influence of asymptotic corrector on the description of the dynamic behaviour of a circular elastic plate
Sławianowska A., Telega J. J.
Archives of Mechanics
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2004
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Vol. 56, nr 1
19-31
EN
The aim of the present paper is to study an initial-boundary value problem for an isotropic circular plate. General theory was developed by the authors in [12]. The novelty consists in the study of influence of second-order terms (correctors), obtained by variational-asymptotic analysis, on the dynamic solution of plates.
4
Content available remote Miary Younga i ich zastosowania w mikromechanice i optymalizacji. Część I. Podstawy matematyczne
Bielski W., Kruglenko E., Telega J. J.
Matematyka Stosowana : matematyka dla społeczeństwa
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2003
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Nr 4
90-138
5
Content available Optimal design of membrane shells. Homogenization-based relaxation of the two-phase layout problem
Lewiński T, Telega J. J.
Journal of Theoretical and Applied Mechanics
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2003
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Vol. 41 nr 3
545-560
EN
The aim of using shell structures instead of plates is to avoid bending, hence the vital role of the membrane theory. Within this theory the classical optimum design problem is formulated: lay out two isotropic materials such that the shell becomes the stiffest possible. The amount of both the materials is fixed. The aim of the present paper is to reformulate this problem in a form assuring its well-posedness. The membrane approximation can be introduced from the very beginning or be imposed upon the relaxation. In the present paper it is shown that the latter modeling leads to a better formulation. It does not lose its stability even if one material degenerates to a void, thus leading to a well-posed shape design problem.
PL
Odpowiednie kształtowanie konstrukcji powłokowych zezwala na minimalizację efektów zginania. Konstrukcje zaprojektowane idealnie powinny pracować bezmomentowo, co podkreśla szczególną rolę teorii powłok błonowych, czyli powłok nie podlegających zginaniu.W pracy rozpatrujemy klasyczne zadanie optymalizacji rozmieszczenia dwu materiałów izotropowych w powłoce przcującej bezmomentowo w celu maksymalizacji jej sztywności. Ilość obu materiałów jest z góry ustalona. Celem pracy jest przeformułowanie tego zagadnienia do postaci dobrze postawionej. Założenie bezmomentowej pracy powłoki może być narzucone od początku lub przyjęte już po procesie relaksacji (w sensie rachunku wariacyjnego). W tej pracy wykazujemy, że ta ostatnia metoda modelowania jest bardziej korzystna.Otrzymuje się sformułowanie, które zachowuje się stabilnie nawet wtedy, gdy jeden z materiałów degeneruje się do pustek, co zezwala na otrzymanie dobrze sformułowanego zadania optymalizacji kształtu.
6
Content available remote Heat Transfer Problems in Orthopaedics
Stańczyk M., Telega J.J.
Engineering Transactions
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2003
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Vol. 51, iss.2-3
267-306
EN
The present paper presents a comprehensive review of the heat transfer problems in orthopaedics. The emphasis is put on presenting clinically relevant issues along with the purpose and motivation for studying the presented problems. The available experimental methods and results are presented and the modelling approaches are described -- mathematical formulations and numerical results. The first of the problems studied is the bone cement heating during cemented implantations, special attention being paid to modelling the kinetics of the acrylic bone cement polymerisation. Next, the heat production during drilling and sawing of the bone is discussed. Eventually, the results concerning frictional heating of the articulating joints are presented.
7
Content available remote Thermal problems in biomechanics - a review. P. 3 Cryosurgery, cryopreservation and cryotherapy
Stańczyk M., Telega J. J.
Acta of Bioengineering and Biomechanics
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2003
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Vol. 5, nr 2
3-22
EN
The aim of this paper is to review available results pertaining to various heat transfer problems of biomechanics. The present part is concerned with low-temperature phenomena, namely the issues of cryosurgery, cryopreservation and cryotherapy. The description of damage mechanisms is also discussed along with its possible applications.
8
Content available Piezoelectric effects in biological tissues
Telega J. J., Wojnar R
Journal of Theoretical and Applied Mechanics
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2002
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Vol. 40 nr 3
723-759
EN
The aim of this paper is to analyze different contibutions and differents points of view concerning the meaning of the piezoelectric effect in the bone. It is now obvious that this effect is overhelming in dry bone. In wet bone more important are streaming potentials.
PL
Analizujemy różne prace i różne punkty widzenia dotyczące zjawiska piezoelektrycznego w kości i jego znaczenia dla biologii tej tkanki. Zjawisko to obserwowane wyraźnie w kości suchej, odgrywa według ostatnich badań mniejszą niż sądzono początkowo rolę w procesach adaptacyjnych kości żywej. Tym niemniej własności piezoelektryczne są istotne dla różnych procesów biologicznych.
9
Content available remote Stationary thermoelasticity and stochastic homogenization
Gambin B., Telega J. J., Nazarenko L. V.
Archives of Mechanics
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2002
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Vol. 54, nr 4
319-345
EN
The aim of the paper is twofold: first, the stochastic homogenization theorem formulated by Dal Maso and Modica [9, 10] is extended to the case applicable to a class of nonlinear problems of mechanics. Second, this new theorem is applied to determine the effective thermoelastic response of the material body with stochastically periodic microstructure. As a result, one obtains the closed form of effective (homogenized) stored energy function. As a specific case, one-dimensional problem is solved analytically.
10
Content available remote Extremum principles for nonpotential and initial-value problems
Telega J. J.
Archives of Mechanics
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2002
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Vol. 54, nr 5-6
663-690
EN
The aim of this paper is to derive extremum and saddle-point principles for a class of nonpotential and initial-value problems. The procedure used is based on an extension of the procedure primarily used by Brezis and Ekeland [7, 8] to classical parabolic equations. In essence, this approach exploits some fundamental notions of convex analysis.
11
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.
12
Content available remote Modelling of heat transfer in biomechanics - a review. P. 2. Orthopaedics
Stańczyk M., Telega J. J.
Acta of Bioengineering and Biomechanics
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2002
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Vol. 4, nr 2
3-31
EN
The aim of this paper consisting of three parts is to review available results pertaining to various heat transfer problems of biomechanics. The second part covers thermal problems specific to orthopaedics. Three classes of problems are investigated: exothermal bone cement polymerisation in situ, frictional heat generation during articulation of joint implants and frictional heat generation during bone cutting and drilling. The existing results pertaining to modelling and experimental measurements are reviewed. Thermal damage criterion is discussed and various possible means of minimising injuries to tissues are discussed. The first class of problems studied includes also our own results.
13
Content available remote Modelling of heat transfer in biomechanics - a review. P. 1. Soft tissues
Stańczyk M., Telega J. J.
Acta of Bioengineering and Biomechanics
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2002
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Vol. 4, nr 1
31-61
EN
The aim of this paper is to review available results that pertain to various heat transfer problems of biomechanics. The present part covers the issues connected with modelling of the heat exchange in perfused tissues. The results are important for the design of hyperthermic treatment protocols, thermal injury assessment, heat Ioss rate in adverse environments, constructing whole-body or whole-Iimb models of heat transfer, etc. The division into two classes of models is proposed: continuum models and vascular models (cf. also [3]). The shortcomings of the most popular bioheat transfer equations are discussed. The effects of cryogenic temperatures on living tissues are described in the third part of the paper. The effects of cryogenic temperatures on living tissues arę described in the third part of the paper.
14
Content available Modelling contact problems with friction in fault mechanics
Bielski W. R., Telega J. J.
Journal of Theoretical and Applied Mechanics
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2001
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Vol. 39 nr 3
475-505
EN
The aim of this contribution is two-fold. First, we review the friction models applied in geophysics. These models cover: state- and rate-dependent friction, rate-dependent friction and slip-dependent friction. Second, we propose a new description in the spirit of modern contact mechanics, introducing sliding rules which interrelate the contact stresses with the slip velocity. Sliding rules are formulated in a subdifferential form. Initial-boudary value problems are formulated in the strong and variational forms. By applying Green's function, the variational formulation for finding normal and tangential contact stresses is proposed.
PL
Modelowanie zagadnień kontaktowych z tarciem w mechanice uskoków geologicznych. Cel pracy jest dwojaki. Po pierwsze, omówiono modeletarcia stosowane w geofizyce. Modele te obejmują tarcie zależne od strun, prędkości i poślizgu. Po drugie, zaproponowano nowy opis tarcia w języku nowoczesnej mechaniki kontaktu, wprowadzając prawa poślizgu wiążące naprężenie poślizgu z prędkością poślizgu. Prawa poślizgu sformułowano w postaci subróżniczkowej. Zagadnienia początkowo-brzegowe sformułowano w postaci silnej i wariacyjnej. Stosując funkcję Greena zaproponowano sformułowanie wariacyjne pozwalające wyznaczyć normalne i styczne naprężenia kontaktowe.
15
Content available Contact problems with friction, adhesion and wear in orthopaedic biomechanics. Part I - general developments
Rojek J., Telega J. J.
Journal of Theoretical and Applied Mechanics
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2001
|
Vol. 39 nr 3
655-677
EN
The present paper is a continuation of the contribution by Rojek and Telega (1999). An alternative adhesion law is used to the study of the bone-implant interface. Various problems related to the bone-implant interface are discussed.
PL
Zagadnienia kontaktowe z tarciem, adhezją i zużyciem w biomachanice ortopedycznej. Część I - Rozważania ogólne. Niniejsza praca stanowi kontynuację wcześniejszej pracy autorów, por. Rojek i Telega (1999). Zastosowano alternatywny model adhezji dla opisu interfazy kość-implant. Przedyskutowano równierz szereg zagadnień związanych z tą interfazą.
16
Content available Contact problems with frictioh, adhesion and wear in orthopaedic biomechanics. Part II - numerical implementation and application to implanted knee joints
Rojek J., Telega J. J., Stupkiewicz S.
Journal of Theoretical and Applied Mechanics
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2001
|
Vol. 39 nr 3
679-706
EN
The present paper is the second part of the contribution by Rojek and Telega (2001). An alternative adhesion law was used to the study of bone-implant interface. Numerical scheme was developed and applied to the knee joint after arthroplasty. Influence of wear debris on this interface and currently used wear models were investigated.
PL
Zagadnienia kontaktowe z tarciem, adhezją i zużyciem w biomachanice ortopedycznej. Część II - Implementacja numeryczna i zastosowanie do stawów kolanowych po implementacji. Niniejsza praca stanowi część drugą pracy, której autorami są Rojek i Telega (2001). Do analizy interfazy kość-implant zastosowano alternatywny opis adhezji. Opracowano algorytm numeryczny, który zastosowano do analizy stawu kolanowego po endoprotezoplastyce. Zbadano wpływ produktów zużycia na analizowaną interfazę oraz przedstawiono aktualnie stosowane modele zużycia.
17
Content available Augmented lagrangian methods for a class of convex and nonconvex contact problems
Telega J. J., Gałka A., Bielski W.
Journal of Theoretical and Applied Mechanics
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2001
|
Vol. 39 nr 3
741-768
EN
The aim of this contribution is threefold. First, we formulate unilateral contact problems for three models of plates and the Koiter shell model. Contact conditions have been formulated on the face being in contact with an obstacle and not on the mid-plane of the plate or the middle surface of the shell. Such a rigorous approach results in nonconvex minimization problems even in the case of thin, geometrically linear plates. Existence theorems are formulated for each model considered. Second, the Ito and Kunisch (1990, 1995) augmented Lagrangians methods have been extended to nonconvex problems. Third, nonconvex duality theory by Rockafellar and Wets (1998), valid for finite-degree-of-freedom systems has been extended to continuous systems. Specific examples have also been provided.
PL
Metody rozszerzonego lagranżianu dla pewnej klasy wypukłych i niewypukłych zagadnień kontaktowych. Cel pracy jest trojaki. Po pierwsze, sformułowane zostały jednostronne zagadnienia kontaktowe dla trzech modeli płyt oraz liniowego modelu powłok Koitera. Warunki kontaktu zostały sformułowane na powierzchni będące w kontakcie z podłożem, a nie na powierzchni środkowej płyty lub powłoki. Takie ścisłe podejście prowadzi do niewypukłych zadań minimalizacji, nawet w przypadku płyt cienkich. Dla każdego zagadnienia sformułowano twierdzenie o istnieniu rozwiązań. Po drugie, metody rozszerzonego lagranżianu Ito i Kunischa (1990, 1995) uogólnione zostały na przypadek zagadnień niewypukłych. Po trzecie, teoria dualności Rockafellara i Wetsa (1998), opracowana dla skończenie wymiarowych zagadnień niewypukłych, została rozszerzona na przypadek układów ciągłych. Podano również kilka przykładów.
18
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
|
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.
19
Content available remote Modelling electronic and elastic properties of cartilage
Gałka A., Telega J. J., Wojnar R.
Engineering Transactions
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2001
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Vol.49, iss.2/3
283-313
EN
The aim of the paper is to propose a novel approach to modelling the macroscopic electromechanical behaviour of cartilage within the framework of linear response. The cartilage is treated as multiphase material with four constituents: anions, cations, viscous fluid and piezoelectric skeleton. The macroscopic equations were derived by using homogenization methods. Only stationary flow was studied. The elastic macroscopic moduli were determined by assuming, after Broom [60], the honeycomb microstructure of the cartilage. Mathematical developments are preceded by a review of structure and properties of a cartilage.
20
Content available remote Modelling elastic behaviour of soft tissues. P.1. Transverse isotropy
Jemioło S., Telega J. J.
Engineering Transactions
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2001
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Vol.49, iss.2/3
241-281
EN
New constitutive relationships for hyperelastic transversely isotropic materials have been proposed. The well-known isotropic hyperelastic model due to Ogden [I.58] has been extended to transverse isotropy. It has been shown that some models intended to describe the nonlinear elastic behaviour of soft tissues are oversimplified and lead to incorrect results. An overview of soft tissue modelling, being a continuation of the one started in [48], has also been given. .
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