# International Journal of Engineering Science

Published by Elsevier

Online ISSN: 0020-7225

Published by Elsevier

Online ISSN: 0020-7225

Publications

Article

We present a three-dimensional mathematical framework for modeling the evolving geometry, structure, and mechanical properties of a representative straight cylindrical artery subjected to changes in mean blood pressure and flow. We show that numerical predictions recover prior findings from a validated two-dimensional framework, but extend those findings by allowing effects of transmural gradients in wall constituents and vasoactive molecules to be simulated directly. Of particular note, we show that the predicted evolution of the residual stress related opening angle in response to an abrupt, sustained increase in blood pressure is qualitatively similar to measured changes when one accounts for a nonlinear transmural distribution of pre-stretched elastin. We submit that continuum-based constrained mixture models of arterial adaptation hold significant promise for deepening our basic understanding of arterial mechanobiology and thus for designing improved clinical interventions to treat many different types of arterial disease and injury.

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Article

Computational prediction of blood damage has become a crucial tool for evaluating blood-wetted medical devices and pathological hemodynamics. A difficulty arises in predicting blood damage under turbulent flow conditions because the total stress is indeterminate. Common practice uses the Reynolds stress as an estimation of the total stress causing damage to the blood cells. This study investigates the error introduced by making this substitution, and further shows that energy dissipation is a more appropriate metric of blood trauma.

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Article

Vascular mechanics has been studied in depth since the early 1970s mainly following classical concepts from continuum mechanics. Yet, an important distinction of blood vessels, in contrast to typical engineering materials, is the continuous degradation and deposition of material in these living tissues. In this paper we examine mechanical consequences of such mass turnover. Motivated by Lyapunov's stability theory, we introduce the new concepts of mechanobiological equilibrium and stability and demonstrate that blood vessels can maintain their structure and function under physiological conditions only if new material is deposited at a certain prestress and the vessels are both mechanically and mechanobiologically stable. Moreover, we introduce the concept of mechanobiological adaptivity as a third corner stone to understand vascular behavior on a continuum level. We demonstrate that adaptivity represents a key difference between the stability of mechanobiological and typical human-made systems. Based on these ideas, we suggest a change of paradigm that can be illustrated by considering a common arterial pathology. We suggest that aneurysms can be interpreted as mechanobiological instabilities and that predictions of their rupture risk should not only consider the maximal diameter or wall stress, but also the mechanobiological stability. A mathematical analysis of the impact of the different model parameters on the so-called mechanobiological stability margin, a single scalar used to characterize mechanobiological stability, reveals that this stability increases with the characteristic time constant of mass turnover, material stiffness, and capacity for stress-dependent changes in mass production. As each of these parameters may be modified by appropriate drugs, the theory developed in this paper may guide both prognosis and the development of new therapies for arterial pathologies such as aneurysms.

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Article

We consider the effect of an elastic modulus that decreases with depth on the load-displacement relation for indentation of a graded half space by a rigid indenter. A closed-form approximation incorporating features of the plate on an elastic substrate and the Hertzian contact theory is compared with finite element results for the case of a uniform stiff layer on a homogeneous substrate. Some general results are presented for the case where the grading has inverse power-law form and the effects of truncation to a finite surface value are investigated numerically. Finally, a more practical error-function grading is considered. In all cases, the load-displacement relation is closer to linear than in the homogeneous case. We conclude that the experimental data can be used to determine parameters in a predetermined form of grading, but that comparative insensitivity to the exact form of the grading would make it difficult to distincguish experimentally between different models based on indentation experiments alone.

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Article

The airways and parenchyma of lung experience large deformations during normal respiration. Spatially accurate predictions of airflow patterns and aerosol transport therefore require respiration to be modeled as a fluid-structure interaction problem. Such computational models in turn require constitutive models for the parencyhma that are both accurate and efficient. Herein, an implicit theory of elasticity is derived from thermodynamics to meet this need, leading to a generic template for strain-energy that is shown to be an exact analogue for the well-known Fung model that is the root of modern constitutive theory of tissues. To support this theory, we also propose a novel definition of Lagrangian strain rate. Unlike the classic definition of Lagrangian strain rate, this new definition is separable into volumetric and deviatoric terms, a separation that is both mathematically and physically justified. Within this framework, a novel material model capable of describing the elastic contribution of the nonlinear response of parenchyma is constructed and characterized against published data.

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Article

In a series of papers commencing in 1988, Rogers and Spencer and their co-authors developed a procedure for deriving exact solutions to the equations of elasticity for materials that are isotropic but are inhomogeneous along a specified direction, so that the elastic constants may be taken as functions of a single space variable. In the case of a thick plate we will suppose the elastic moduli are known functions of the coordinate normal to the plane of the plate, so that laminated plates and functionally-graded plates are covered by this analysis. In the case of a plate with traction-free upper and lower surfaces, England and Spencer [A.H. England, A.J.M. Spencer, Complex variable solutions for inhomogeneous and laminated elastic plates, Math. Mech. Solids 10 (2005) 503–539] have derived general solutions which may be expressed in terms of four analytic functions of the complex variable in the mid-plane of the plate. These solutions are generalisations of the Kolosov–Muskhelishvili solutions for plane-strain elasticity. This analysis has been extended to cover the case of a pressure field applied to one face of the plate. In general the bending and extensional behaviour of the plate is coupled. The intention in this paper is to illustrate these solutions and to derive some stiffness coefficients for general inhomogeneous circular plates of this type.

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Article

A significant mathematical error is identified and corrected in a recent
highly-cited paper on oscillatory flows of second-grade fluids [Fetecau &
Fetecau (2005). Int. J. Eng. Sci., 43, 781--789]. The corrected solutions are
shown to agree identically with numerical ones generated by a finite-difference
scheme, while the original ones of Fetecau & Fetecau do not. A list of other
recent papers in the literature that commit the error corrected in this Comment
is compiled. Finally, a summary of related erroneous papers in this journal is
presented as an Appendix.

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Article

The following problem is considered in this paper: Let xt be a solution to the stochastic differential equation: dxt = m[xt, t] dt+ σ[xt, t] dyt where yt is the Brownian motion process. Let xt(n) be the solution to the ordinary differential equation which is obtained from the stochastic differential equation by replacing yt with yt(n) where yt(n) is a continuous piecewise linear approximation to the Brownian motion and yt(n) converges to yt as n → ∞. If xt is the solution to the stochastic differential equation (in the sense of Ito) does the sequence of the solutions xt(n) converge to xt? It is shown that the answer is in general negative. It is however, shown that xt(n) converges in the mean to the solution of another stochastic differential equation which is: .RésuméL'auteur étudie le problème suivant: xt est une solution de l'équation différentielle stochastique dxt = m(xt, t)dt + σ (xt, t)dyt où yt représente le mouvement Brownien. Soit xt(n), une solution de l'équation différentielle ordinaire, obtenue en partant de l'équation différentielle stochastique en remplacant yt par yt(n), oü yt(n) est une approximation linéaire continue du mouvement Brownien, convergeant vers yt lorsque n → ∞.Si xt est la solution de l'équation différentielle stochastique (prise dans le sens de Ito), la séquence des solutions xt(n) peut elle converger vers xt ? L'auteur montre que la réponse à cette question est en général négative. Il montre, cependant, que xt(n) converge, en moyenne, vers la solution d'une autre équation différentielle stochastique qui s'exprime par .ZusammenfassungDieser Beitrag befasst sich mit dem folgenden Problem: xt sei eine Lösung der stochastischeri Differentialgleichung: dxt = m(xt, t) dt + σ(xt, t) dyt, wo yt der Brownsche Bewegungsprozess ist. xt(n) sei die Lösung der gewöhnlichen Differentialgleichung, und zwar erhält man diese von der stochastischen Differentialgleichung, indem man yt durch yt(n) ersetzt, wo yt(n) sich in kontinuierlichen Stücken und linear der Brownschen Bewegung annähert, und wo yt(n) auf yt konvergiert, wenn n gegen ∞ geht. Es erhebt sich die Frage: Konvergiert die Lösungsfolge xt(n) auf xt, ween xt die Lösung der stochastischen Differentialgleichung ist ? Es wird gezeigt, dass die Antwort im allgemeinen negativ ist. Es wird jedoch nachgewiesen, dass xt(n) im Mittelwert auf die Lösung einer anderen stochastischen Differentialgleichung konvergiert, nämlich .SumàrioIn questa memoria viene considerato il seguente problema: Sia xt una soluzione dell'equazione differenziale stocastica: dxt = m(xt, t) dt + σ (xt, t)dyt in cui yt è il processo di movimento Browniano. Sia xt(n) la soluzione della equazione differenziale ordinaria ottenuta dall'equazione differenziale stocastica sostituendo yt come n → ∞. Se xt é la soluzione dell'equazione differenziale stocastica (nel senso di Ito), la sequenza delle soluzioni xt(n) convergerà su xt ? E' indicato come la risposta in generale sia negativa; è però dimostrato che xt(n) converge in media sulla soluzione di un'altra equazione differenziale stocastica che è: .РефератB paбoтe paccмaтpивaeтcя cлeдyющaя зaдaчa: Пycь xt. являeтcя peщeниeм cтoчacтичecкoгo диффepeнциaльнoгo ypaвнeния dxt = m(xt, t)dt + σ(xt, t)dyt, гдe yt oбoзнaчaeт пpoцecc движeния Бpayнa. Пycть xt(N) являeтcя peщним oбынoeeннoo диффepeнциaльнoгo ypaвнeния, пoлyчeннoгo из cтoчacтичecкoгo ypaвнeния пyтeм зaмeны yt нa yt(n), гдe yt(n) нeпpepывнaя, кycoчнo линeйнaя, aпpoгcимaцня движeкия Бpayнa и, чтo yt(n) cтpeмитcя к yt для n → ∞. Ecли xt являeтcя peщeниeм cтoчacтичecкoгo диффepeнциaльнoгo ypaвнeния (в cмыcлe Итo) имeeм вoпpoc: cчoдитcя пocдeлoвaтeльнocть peщeний xt(n)kxt? Дoкaзывaeтcя, чтo в oбщeм cлyчae, oтвeт бyдeт oмpццaмe ьным, нo дoкaзывaeтcя тaкжe, чтo xt(n) cчoдитcя в cpeнeм к peщeнию ∂pyoo cтoчacтичecкoгo ypaвнeния, для кoтopoгo имeeм; .

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Article

The paper investigates the issue of existence of solutions to the stationary Navier–Stokes equations in a two-dimensional bounded domain. The system is studied with nonhomogeneous slip boundary conditions admitting flow across the boundary. The main result proves the existence of weak solutions for arbitrary data. An advantage of our approach is that the proof is constructive. Properties of the obtained result allow to study turbulent flows in description of such phenomena as polymers and blood motion.

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Article

This paper presents a new method for solving transient 2D thermo-(poro-) elastic problems involving blocky systems with singular points and lines of discontinuity. The efficiency and accuracy of the method arise from using complex variables (CV) and solving a problem in two separate stages. In the first stage, CV-BEM is combined with the dual reciprocity method (DRM) for transient heat (liquid) flow to obtain, as a solution, the sum of (i) a “quasi-steady” part (which may account for discontinuities and singular points) and (ii) a smooth unsteady part which is a linear combination of smooth radial basis functions (RBF). These parts, found by integrating a system of ordinary differential equations, are stored in array, which contains values for each small integration step. From these arrays, data for selected time instances, which are of interest for thermo-(poro-) elastic analysis, are used in the second stage to find stresses and stress intensity factors (SIFs) at the instances of interest. The second stage solution employs CVH-BEM for blocky systems with discontinuities and singular points: a common code of the CVH-BEM is complemented with evaluation of two pairs of addends on the right hand side of the boundary integral equation solved; one of the addends is the sum of well-known terms for the “quasi-steady” part, while the other is a linear combination of particular solutions corresponding to a standard RBF. The particular solution needed is found for the Gaussian RBF in a simple analytical form by using the CV. The efficiency and accuracy of the method are illustrated by studying stresses and stress intensity factors in a square plate with a crack under thermal shock applied either to the plate sides, or to the crack surfaces. An interesting and not obvious effect is revealed: it appears that under thermal shock on the crack surfaces, the flux intensity factor is actually independent of the crack length for short time instances, which results in moderate stress intensity factors after the thermal shock.

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Article

We proposed a constitutive model for the two-dimensional analysis of concrete structures. The proposed model treats concrete as an orthotropic nonlinear material. The equivalent principal strain based approach allows the model to represent the mechanical behavior of concrete by using two equivalent uniaxial stress–strain relations. The biaxial behavior of concrete is described using the concept of current strength in a principal stress space. The fracture energy method is incorporated to solve the problem of mesh non-objectivity, and the concept of current fracture energy gives an improved description of the post-peak behavior of concrete. Secant-stiffness-based finite-element formulations are implemented in a smeared rotating crack fashion. Correlative studies using available experimental test results are presented to demonstrate the performance of the model at a structural level.

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Article

A theoretical model is developed to simulate transport phenomena in a proton exchange membrane fuel cell (PEMFC). The primary focus of this paper is the modelling and assessment of two-dimensional effects neglected in previous studies. The work is motivated by the need to understand the transport processes in fuel cells in order to improve heat and water management, and to alleviate mass transport limitations. The model takes into account diffusion of the humidified fuel (H2, CO2 and H2O(v)) and oxidant gases (O2, N2 and H2O(v)) through the porous electrodes, and convective and electro-osmotic transport of liquid water in the electrodes and the membrane. The thermodynamic equilibrium potential is calculated using the Nernst equation, and reaction kinetics are determined using the Butler–Volmer equation. A finite volume procedure is developed to solve the system of differential equations.The model is validated against available experimental data, and numerical simulations are presented for various one- and two-dimensional isothermal cases. The results indicate that the cathode potential loss, associated with the slow O2 reaction rate, is dominant at all practical current densities. The simulations also show that two-dimensionality has a significant effect on water management and on some aspects of fuel cell performance. In particular, the anode and cathode water fluxes are found to vary considerably along the oxidant and fuel flow channels, and two new transitional water transport regimes are revealed by the two-dimensional simulations. The influences of flow configuration and electrode porosity on predicted cell performance are also discussed.

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Article

Velocity fluctuations over evolving scales of motion, on the scale of observation, often lead to anomalous dispersion of conservative tracers in heterogeneous porous media. Recent theories of anomalous dispersion lead to space-time non-local constitutive models for the flux of concentration. We review one such model, which has its foundations in non-equilibrium statistical mechanics. The basic premise is that knowledge of the evolution of the self-part of the intermediate scattering function, , is all that is required to model the phenomena of interest. We review the basic integro-partial-differential equation that satisfies and solve the inverse problem to obtain the kernels, and then use these to describe the wave-vector and frequency dependent dispersive process. Subsequently we use this information to study the transition from anomalous to Fickian regime. We also make use of the finite size Lyapunov exponent in the description of the dispersive process. Two-camera, three-dimensional particle tracking velocimetry experiments are undertaken to study dispersion within matched-index porous media. Particle trajectories, mean square displacements, velocity covariance’s, intermediate scattering functions, classical dispersion tensors, wave-vector and frequency dependent generalized dispersion tensors, and the finite-size Lyapunov exponents are obtained. Comparisons are made in the small frequency and small wave vector limits to obtain the transition from pre-asymptotic to asymptotic dispersion.

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Article

We give a new and explicit estimate for the asymptotic behavior of the solutions of the problem , x > 0,t> 0, with conditions u(0, t) = 1, t > 0 and , x > 0, for a class of functions and parameter 0 < p < 1. We use an approximate solution given by the heat balance integral method with the innovation property which fixes appropriately the asymptotic limit of the corresponding approximate free boundary.

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Article

The problem of unsteady, two-dimensional, laminar, boundary-layer flow of a viscous, incompressible, electrically conducting and heat-absorbing fluid along a semi-infinite vertical permeable moving plate in the presence of a uniform transverse magnetic field and thermal and concentration buoyancy effects is considered. The plate is assumed to move with a constant velocity in the direction of fluid flow while the free stream velocity is assumed to follow the exponentially increasing small perturbation law. Time-dependent wall suction is assumed to occur at the permeable surface. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. The obtained analytical results reduce to previously published results on a special case of the problem. Numerical evaluation of the analytical results is performed and some graphical results for the velocity, temperature and concentration profiles within the boundary layer and tabulated results for the skin-friction coefficient, Nusselt number and the Sherwood number are presented and discussed.

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Article

The transient features of the Couette flow of an electrically conducting fluid subject to rotation and magnetic field have been analysed when one of the plates has been set into uniformly accelerated motion. The resulting boundary value problem has been solved exactly and explicit expressions for the velocity and skin friction have been obtained. The variations of these with respect to the Hartmann and Ekman numbers have been shown. It is seen that the primary velocity increases with magnetic field and decreases with rotation, while the magnitude of secondary velocity has the opposite effect with respect to these processes.

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Article

A closed form solution is presented for a dynamically accelerating, semi-infinite, anti-plane shear crack in a Achenbach-Chao linear viscoelastic solid in the limiting case of a vanishing equilibrium shear modulus. Simple expressions for the crack-face displacement and the stress intensity factor are constructed for arbitrary time dependent crack-face traction and crack-tip velocity, (t), subject only to the restriction that , where c is the short time (glassy) shear wave speed. The extent of material memory in the stress intensity factor and crack-face relative displacement during the transition from an initial accelerating crack growth phase to a constant crack speed regime are compared for loads travelling with the crack-tip and for stationary loads. The viscoelastic and elastic stress intensity factors are shown to exhibit the same degree of limited dependence upon the initial acceleration phase whereas the viscoelastic and elastic crack-face displacements behave quite differently with the former exhibiting a persistent and the latter a limited memory of the initial acceleration phase.

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Article

An asymptotic approach is proposed to investigate nonlinear parametric vibration of axially accelerating viscoelastic strings. The string is constituted by the Kelvin model with the material time derivative. Both the Mote model and the Kirchhoff model of transverse motion are analyzed via the asymptotic approach in principal parametric resonance. The modulation equation is derived from the solvability condition. Closed-form expressions of the amplitudes and the existence conditions of steady-state responses are solved from the modulation equation. Numerical results are presented to highlight the effects the initial stress, the parameters in the Kelvin model, and the axial speed fluctuation amplitude on the amplitudes and the existence conditions of steady-state responses.

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Article

Similarity equations governing steady hydromagnetic boundary-layer flow over an accelerating permeable surface in the presence of such effects as thermal radiation, thermal buoyancy, and heat generation or absorption effects are obtained. These equations are solved numerically by an implicit finite-difference method. Favorable comparisons with previously published work are obtained. The effects of the various parameters on the velocity and temperature profiles as well as the skin-friction coefficient and wall heat transfer are presented graphically and in tabulated form.

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Article

Blood flow with body acceleration forces, studied by Sud and Sekhon [1], has been re-examined. It is observed that Sud and Sekhon [1] have obtained exact analytic solutions for flow variables in terms of Bessels functions with complex arguments. The flow variables have not been computed from these exact expressions. Perhaps, it might have been thought that the computation of flow variables through these complicated expressions of Bessels functions with complex argument may be very difficult, if not impossible. In the present analysis, we have been able to get the exact analytic solutions for flow variables as functions of real variables. The evaluation of these exact solutions is not as difficult as expected. The advantage of the exact solution over approximate solutions is two-fold: (a) while calculating flow variables from approximate solutions one has to use two expressions, one for small values of Rep and Reb (pulsatile and body acceleration Reynolds numbers) and other for large values of Rep and Reb; in contrast to this, in exact solutions one does not have to bother about this switching of expressions; (b) for situations where Rep or Reb or both are of the order of 2, these approximate solutions can not provide sufficiently accurate results, error is of the order of 15%; in contrast to this, the exact solutions of the present analysis have no such restriction.

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Article

The paper deals with a theoretical study of the flow-field in a porous stenotic artery when it is subjected to a single cycle of body acceleration using an appropriate mathematical model. The simulated artery is taken as an isotropic elastic tube containing a viscous incompressible fluid representing the flowing blood. The shape of the stenosis in the arterial lumen is chosen to be irregular in order to improve resemblance to the in-vivo situation. Instead of having a constant seepage rate along the axis of the artery, the wall deformability has been accounted for so that the hydraulic membrane permeability is treated to be contained in the wall velocity. The equations governing the motion of the system are solved analytically in both the steady and the unsteady states with the use of the appropriate boundary conditions. Numerical computations have finally been performed in order to have a thorough quantitative measure of the effects of body acceleration and the hydraulic membrane permeability on the flow velocity, the flux, the resistive impedances and the wall shear stress just to validate the applicability of the present mathematical model.

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Article

Pulsatile flow of blood through a rigid tube has been studied under the influence of body acceleration. With the help of finite Hankel and Laplace transforms, analytic expressions for axial velocity, fluid acceleration, wall shear and instantaneous volume flow rate have been obtained. It is of interest to note that these solutions can be used for all the feasible values of pulsatile and body acceleration Reynolds numbers Rep and Reb. This is in contrast with the existing results where different approximate solutions have to be used for different ranges of Rep and Reb. Using physiological data, the following qualitative and quantitative results have been obtained. The amplitude of the instantaneous volume flow rate, for flows with body acceleration, decreases shaprly as the tube radius decreases (from aorta to arteriole). This variation of amplitude is very slow for flows with no body acceleration. Another interesting result is the maximum of the axial velocity and fluid acceleration shifts from the tube axis to the vicinity of the tube wall as the tube diameter increases. The variation of the amplitude of wall shear with tube diameter (aorta to coronary) is less for flows with body acceleration than that of flows with no body acceleration. The phase lag between pressure gradient and flow rate changes sharply with tube diameter in narrow tubes, it varies asymptotically in wide tubes. The obtained results are qualitatively in good agreement with existing theoretical observations. Quantitatively, they differ from the other theoretical results (19 to 3000%). The difference in the results of the analyses decreases as the tube diameter increases (arteriole to aorta).

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Article

In this work the conditions of propagation of acceleration waves are studied in different types of micropolar media: (a) in simple media whose constitutive equations are given in functional form, (b) in linear viscoelastic media of which the constitutive equations are obtained in the limit of small deformations from a simple micropolar medium obeying the axiom of fading memory. In contrast to the first case, two kinds of acceleration waves can propagate independently in the second case.RésuméDans cet article, les conditions de propagation d'ondes d'accélération sont étudiées dans différents milieux micropolaires: (a) dans des milieux dits ‘simples’ dont les lois de comportement sont données sous forme fonctionnelle, (b) dans des milieux viscoélastiques linéaires dont les lois de comportement sont obtenues, à la limite des déformations infinitésimales, à partir d'un milieu micropolaire ‘simple’ obéissant à l'axiome de mémoire évanescente. Par opposition au premier cas, deux sortes d'ondes d'accélération peuvent, dans le second cas, se propager indépendemment l'une de l'autre.ZusammenfassungIn dieser Arbeit werden die Bedingungen der Fortpflanzung von Beschleunigungswellen in verschiedenen Typen mikropolarer Stoffe untersucht: (a) in einfachen Stoffen, deren Materialgleichungen in funktionaler Form gegeben werden, (b) in linearen viskoelastischen Stoffen, deren Materialgleichungen in der Grenze kleiner Deformationen von einem einfachen mikropolaren Stoff erhalten werden, das dem Axiom entschwindeden Gedächtnisses unterliegt. Zum Unterschied vom ersten Falle, können sich im zweiten Falle zwei Arten von Beschleunigungswellen unabhängig fortpflanzen.ResumenIn questo articolo vengono studiate le condizioni di propagazione delle onde di accelerazione in differenti tipi di mezzi micropolari: (a) in mezzi semplici le cui equazioni costitutive vengono date in forma funzionale; (b) in mezzi viscoelastici lineari, le cui equazioni costitutive vengono ottenute al limite di piccole deformazioni da un semplice medio micropolare che obbedisce all'assioma della memoria evanescente. In contrasto col primo caso, due tipi di onde di accelerazione possono propagarsi indipendentemente nel secondo caso.Рефератv; p;a;бo;тe; изc;khcy;e;ны c;y;лo;v;ия p;a;y;пp;o;y;тp;a;нe;ния v;o;лн c;y;кo;p;e;ния v; микp;o;пo;ляp;ныч y;p;e;дa;ч p;a;злиkhcy;ныч v;идo;v;: (a;) v; пp;o;y;тыч y;p;e;дa;ч, кo;нy;титc;тиv;ныe; c;p;a;v;нe;ния кo;тo;p;ыч дa;ютy;я v; фc;нкциo;нa;льнo;й фo;p;мe;, (б) v; линe;йныч v;язкo;элa;y;тиkhcy;ныч y;p;e;дa;ч, кo;нy;титc;тиv;ныe; c;p;a;v;нe;ния кo;тo;p;ьгч цo;лc;khcy;a;ютy;я v; пp;e;дe;лa;ч нe;бo;льшич дe;фo;p;мa;ций из пp;o;y;тo;й микp;o;пo;ляp;нo;й y;p;e;ды v; y;o;o;тv;e;тy;тv;ии y; a;кy;иo;мo;й нe;пo;y;тo;яннo;гo; зa;пo;минa;ния. v; o;тлиkhcy;ии o;т пe;p;v;o;гo; y;лc;khcy;a;я v;o; v;тo;p;o;м v;o;змo;жнo; нe;зa;v;иy;имo;e; p;a;y;пp;o;y;тp;a;нe;ниe; v;o;лн c;y;кo;p;e;ния дv;c;ч типo;v;.

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Article

Conjugate natural convection flow in a thick walled semi-circular cavity containing molten core material has been analysed numerically. The lower plenum debris bed represents decay heating, heat conduction, and heat convection within the debris. The internal heat generation resulting from the radioactive decay of fission products ensures that most of the pool remains molten and also causes natural convection in the pool. Bottom circular wall of the cavity is taken to be thick with finite conductive properties, while top wall is considered to be isothermal. In carrying out the analysis, various constituents of the core material are assumed to be mixed homogenously. Thus a homogeneous fluid, for which Pr number is 0.45, has been considered while Ra number range from 3.2×107 to 3.2×1012 has been investigated. Present results for non-conjugate semi-circular cavity compare very well with previously published experimental studies.

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Article

This paper presents an infrared data processing developed to analyse the calorific manifestations accompanying elastoplastic transformation during tensile tests. The surface temperature images are provided by an experimental set-up essentially made of a testing machine coupled with an infrared camera equipped with a home-made numerizer. The `inverse' passage from temperatures to heat sources is detailed in the case of flat and thin parallelepipedic samples. The infrared image processing, based on Fourier’s techniques, was checked using spectral solutions of the heat equation in the case of realistic examples close to experiments. Numerical simulations are shown which attest coherence and efficiency of the method for several heat source distributions and different sets of noisy data. The method is then applied to experimental data files coming from tensile tests on mild steels at the room temperature. Sudden dissipative effects due to the propagation of the Lüders bands during the plastic plateau can be observed. Then, during the strain hardening, gradual and precocious concentrations of dissipation are shown; they herald the local necking of the sample. Finally, the interest of such experimental results is briefly discussed by referring to the specialised literature dealing with localisation phenomena and behaviour identification.

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Article

A simple refined theory of anisotropic laminated composite shell-type structures is substantiated. The theory is based upon discarding the Love-Kirchhoff hypothesis. It incorporates transverse shear deformation effect, the geometrical nonlinearities and fulfills the geometric and static continuity conditions between the contiguous layers. It is shown that within its linearized counterpart, several theorems, analogous to the ones in the 3-D elasticity theory could be established. These ones concern e.g. Betti's reciprocity theorem, the uniqueness theorem for the solution of boundary-value problem of elastic composite shells, the minimum energy theorems, etc. Comparative remarks on the refined and the standard first order transverse shear deformation theories are made and pertinent conclusions about its usefulness and further developments are outlined.

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Article

The problem of hydraulic fracture propagation is considered by using its
recently suggested modified formulation in terms of the particle velocity, the
opening in the proper degree, appropriate spatial coordinates and
$\varepsilon$-regularization. We show that the formulation may serve for
significant increasing the efficiency of numerical tracing the fracture
propagation. Its advantages are illustrated by re-visiting the Nordgren
problem. It is shown that the modified formulation facilitates (i) possibility
to have various stiffness of differential equations resulting after spatial
discretization, (ii) obtaining highly accurate and stable numerical results
with moderate computational effort, and (iii) sensitivity analysis. The
exposition is extensively illustrated by numerical examples.

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Article

The linear electroelastic equations for small dynamic fields superposed on a static bias obtained from the general rotationally invariant nonlinear electroelastic description are presented. Since these linear equations are obtained from a properly invariant description, they may be and, indeed, are referred to the known reference coordinates, which are convenient to use because they never change with any bias. Intrinsically linear descriptions must be referred to the changed position coordinates when any bias, even a homogeneous temperature bias, is present. These coordinates are inconvenient to use and can lead to and, indeed, have led to unnecessary errors. It is shown that the linear equations referred to the known reference coordinates result in a far more accurate description of the behavior of electroelastic devices subject to different biases, including homogeneous thermal, than the intrinsically linear equations.

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Article

A systematic derivation of the approximate coupled amplitude equations governing the propagation of a quasi-monochromatic Rayleigh surface wave on an isotropic solid is presented, starting from the non-linear governing differential equations and the non-linear free-surface boundary conditions, using the method of mulitple scales. An explicit solution of these equations for a signalling problem is obtained in terms of hyperbolic functions. In the case of monochromatic excitation, it is shown that the second harmonic amplitude grows initially at the expense of the fundamental and that the amplitudes of the fundamental and second harmonic remain bounded for all time.

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Article

The propagation of harmonic acoustic waves in a half-space (i.e., x>0) filled with a viscous, isothermal bubbly liquid is studied. The exact solution to this problem, which corresponds to the compressible Stokes' second problem for the van Wijngaarden–Eringen equation, is obtained and an in-depth analytical and numerical investigation is carried out. Specifically, high- and low-frequency asymptotic results are given for the attenuation coefficient, the wave number, as well as several other propagation parameters, and special/limiting cases are noted. In addition, general features of the solution are illustrated via numerical computations.Most significantly, the analysis shows the following: (i) the attenuation coefficient and wave number are equal at the natural bubble frequency; (ii) the bubbly liquid exhibits anomalous dispersion; (iii) for high-frequencies, there exists a layer adjacent to x=0 that oscillates virtually in phase with the boundary (driving) motion; (iv) for low-frequencies, there exists a layer adjacent to x=0 that is essentially transparent to harmonic waves; (v) the penetration depth exhibits an absolute minimum.

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Article

The nonlinear mode coupling between two co-directional quasi-harmonic Rayleigh surface waves on an isotropic solid is analysed using the method of multiple scales. This procedure yields a system of six semi-linear hyperbolic partial differential equations with the same principal part governing the slow variations in the (complex) amplitudes of the two fundamental, the two second harmonic and the two combination frequency waves at the second stage of the perturbation expansion. A numerical solution of these equations for excitation by monochromatic signals at two arbitrary frequencies, indicates that there is a continuous transfer of energy back and forth among the fundamental, second harmonic and combination frequency waves due to mode coupling. The mode coupling tends to be more pronounced as the frequencies of the interacting waves approach each other.

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Article

The contribution of the thermoelastic effect to the attenuation of surface acoustic waves is calculated for anisotropic piezoelectric media. For LiNbO3, numerical values are given and compared with experimental data by Slobodnik, Carr and Budreau. In layered materials, the effect of the boundary conditions for the heat flux and temperature at the interfaces on the attenuation of surface waves is also discussed.

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Article

A dislocation dependent model for liquids describes the lattice deformation and the fluidity deformation as additive deformations. The lattice deformation represents distortions of an atom's potential energy structure and is a recoverable deformation response. The fluidity deformation represents discontinuous repositioning of atoms by dislocation kinetics in the lattice structure and is a nonrecoverable deformation response. From this model, one concludes that in liquids the acoustic wave approximation is a description of a recoverable oscillation deformation that has dissipation because of dislocation kinetics. Other more complex waves may exist, but such waves would rapidly disappear because of the small thermodynamic potential for dislocation kinetics in liquids.

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Article

Acoustic waves with long wave-lengths are studied in a mixture of compressible fluids when capillarity and viscosity are taken into account. Volume fractions are finite so that the interactions between the fluids are strong. The macroscopic description is obtained from the local description by using the homogenization process for periodic structures. As expected, the equivalent macroscopic medium behaves like a two-phase one, exhibiting a coupling between the two phases as well as added masses and dispersion. Two dilatational waves are displayed. The second one is shown to be mostly unstable.

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Article

A complete investigation of the coupled amplitude theory of nonlinear surface acoustic waves on an isotropic elastic solid, which avoids the limitations encountered in previous theories, is given here. A complete, uniformly valid solution in the interior of the medium is derived. Perspective drawings to study asymptotically the growth-decay cycles the displacement and the velocity profiles, have also been done.

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Article

Acoustic radiation from an infinite cylindrical surface vibrating with an arbitrary, time-harmonic surface velocity distribution while positioned near the rigid/compliant boundary of a semi-infinite ideal compressible fluid medium is determined in an exact fashion using the classical method of separation of variables. The formulation utilizes the appropriate wave-field expansions and the method of images along with the pertinent translational addition theorem to develop a closed-form solution in form of infinite series. The analytical results are illustrated with numerical examples in which the cylindrical source, vibrating in the monopole and dipole-like modes, is positioned near the rigid/compliant boundary of a water-filled acoustic halfspace. Subsequently, the basic acoustic field quantities such as the modal acoustic radiation impedance load, radiated far-field pressure and the radiation intensity distribution are evaluated for representative values of the parameters characterizing the system.

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Article

A technique is presented for the theoretical calculation of the acoustic material signature (AMS) of a multilayered plate with its bottom surface free of traction. The layers are composed of homogeneous isotropic linearly elastic materials and are assumed to be firmly bonded at the interfaces. The plate model can serve to represent either a self supporting membrane, or a multilayered composite with extensive debonding on a plane parallel to the layers. Calculated AMS curves are presented for a uniform plate, a two layered plate and a two layered half-space at 60 MHz exciting frequency. The striking differences in these curves indicate the possibility of using them as quantitative diagnostics for extensive debonding in a layered specimen.

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Article

The dispersion of acoustic or elastodynamic waves in elastic composites are studied using the homogenized model. We consider heterogeneous periodic structures consisting of soft but heavy inclusions embedded in a stiffer matrix. By virtue of the asymptotic homogenization technique in conjunction with an appropriate scaling of the elasticity coefficients in the inclusions, the limit model exhibits the band gaps in wave propagation due to the negative effective mass. This phenomenon can be revealed by studying guided waves in discrete mass–spring structures with scale-dependent parameters. The main purpose of the paper is to justify the applicability of the homogenized model of the heterogeneous elastic continuum for prediction of the band gaps in structures featured by a finite scale of heterogeneities. We show the band gaps numerical identification and discus aspects of anisotropy, microstructure geometry and material contrast between the constituents in the context of the long wave dispersion.

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Article

Small amplitude resonant motions of an inviscid, polytropic gas, contained in a tube of finite length, are investigated. It is postulated that motion of the gas may be represented as the superposition of two small amplitude simple waves which interact only at the boundaries. As a result, the problem reduces to solving a nonlinear difference equation, and this is effected on the basis that the solution is in the neighborhood of a linear standing wave. A consequence is that waves progress as acoustic waves, but the signal carried is determined by a nonlinear equation.

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Article

In this paper, we demonstrate the consequence of using different equivalent models to represent a lattice system consisting of mass-in-mass units and why negative mass is needed in the equivalent model. Dispersive wave propagation in the lattice system is studied and compared to various equivalent models. It is found that, if the classical elastic continuum is used to represent the original mass-in-mass lattice system, the effective mass density becomes frequency dependent and may become negative for frequencies near the resonance frequency of the internal mass. In contrast, if a multi-displacement microstructure continuum model is used to represent the mass-in-mass lattice system, the dispersive behavior of wave propagation and the band gap structure can be adequately described. However, while the acoustic mode is accurately described by the microstructure continuum model, the description of the optical mode is accurate only for a limited frequency range.

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Article

A theoretical study is presented for the propagation of pressure waves in a fluid flowing through a porous medium, with special emphasis on the problems related to the interpretation of the attenuation mechanism of Stoneley's wave in acoustical well logging. Some relevant results regarding the effects of porous medium permeability and fluid viscosity on the pressure wave behaviour in porous formations, generated by Stoneley's wave along the interface separating fluid-saturated porous medium from borehole fluid, are shown. The conditions under which the permeability may be evaluated from Stoneley's wave attenuation, recorded in the acoustical well logging, are also pointed out and discussed.

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Article

The propagation of sound in an infinite rigid cylindrical duct with an inserted expansion chamber whose walls are treated with an acoustically absorbent material is investigated rigorously through the Wiener–Hopf technique. By introducing the Fourier transform for the scattered field and applying the boundary conditions in the transform domain, the problem is reduced into a modified Wiener–Hopf equation. The solution involves four sets of infinitely many constants satisfying four infinite systems of linear algebraic equations. An approximate solution of these systems is obtained by means of numerical procedures.

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Article

The present work gives a mathematical model for an acoustically penetrable or electromagnetically dielectric half plane. An approximate boundary condition is derived which depends on the thickness and material constants which constitute the half plane. A solution is obtained, using the approximate boundary condition, for the problem of diffraction of a line source by a semi-infinite penetrable/dielectric half plane. The mathematical problem which is solved is an approximate model for a noise barrier which is not perfectly rigid and therefore transmits sound. It is shown that for wood or plastic barriers the transmitted sound level is proportional to the quantity (incident sound wave length/barrier thickness). Thus for a given barrier thickness the low frequency sound is transmitted more than the high frequency sound.

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Article

This paper is concerned with the derivation of the partial differential equations that govern the propagation of sonic disturbances in an ideal gas under isentropic conditions. The result is a quasilinear hyperbolic system of first order equations and an inequality constraint. The speed of propagation is pressure dependent. It is shown how to deal with the equations and the constraint and how to calculate characteristics and solutions. It is also shown that shock discontinuities can develop which distinguishes the equations from the traditional linear wave equation.

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Article

The dynamic properties of nonlinear acoustoelectronic interactions over a wide range of surface acoustic wave (SAW) power for the layered Al/ZnO/SiO2/Si were investigated. The existence of a very strong nonlinear dispersion and attenuation of the SAW as well as a possibility of the system's self-transparency and the saturation of the convolution and transverse acoustoelectric voltage (TAV) signal power are pointed out. In the case of inverse-type semiconductor surface conductivity, anomolous change in sign, large amplitude and the threshold character of transverse acoustoelectric voltage are observed. The results of the investigations of the discovered acoustoelectronic (AE) bi- and multistability under conditions of strong nonlinearity including changing external influences are considered. It is noted that there is a close connection between nonlinear AE phenomena and electronic processes on the surface of the semiconductor.

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Article

Propagation of surface waves across a vertical wave barrier inserted between two laterally homogeneous quarter-spaces is considered in this paper. Based on the Green's function technique, an analytical approach is developed to examine the reflection and transmission of Rayleigh surface waves across a composite barrier. The composite barrier consists of a high velocity layer sandwiched between two thin layers of low shear velocity materials. The high velocity layer is represented by differential matrix operators which relate the wave fields on each side of the layer. The low velocity layers are modeled by non-rigid or “unwelded” contact conditions which allow partial sliding at the interfaces. Screening ratios of barriers with various combinations of material, geometric, and non-rigidness parameters are compared and discussed in some detail.

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Article

A continuum theory of surface growth is applied to the mechanical modeling of cell motility. The theory relies on a decomposition of the motion into deformation- and growth-inducing parts. A non-dissipative constitutive relation is adopted and expressed exclusively in terms of the current configuration. The resulting model is used in the simulation of a network of actin filaments, and a simple one-dimensional example is included to showcase its predictive capacity.

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Article

The fundamental problem of the turbulent flow of a biomagnetic fluid (blood) between two parallel plates under the action of a localized magnetic field is studied. The blood is considered to be an electrically conducting, incompressible and Newtonian fluid and its flow is steady, two-dimensional and turbulent. The turbulent flow is described by the Reynolds averaged Navier–Stokes (RANS) equations. For the numerical solution of the problem under consideration, which is described by a coupled and non-linear system of PDEs, with appropriate boundary conditions, the stream function–vorticity formulation is used. For the eddy-kinematic viscosity, the low Reynolds number k–ε turbulence model is adopted. The solution of the problem, for different values of the dimensionless parameter entering into it, is obtained by developing and applying an efficient numerical technique based on finite differences scheme. Results concerning the velocity and temperature field, skin friction and rate of heat transfer, indicate that the presence of the localized magnetic field, appreciable influences the turbulent flow field. A comparison is also made with the corresponding laminar flow, indicating that the influence of the magnetic field decreases in the presence of turbulence.

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Article

Shape memory polymers (SMP’s) are a relatively new kind of smart materials and have significant technological applications ranging from biomedical devices to aerospace technology. First generation SMP’s relied on changes in temperature to fix the temporary shape and have been studied quite extensively in the past. In the last few years a new generation of SMP’s have been synthesized in which the temporary shape is fixed by exposure to light at specific wavelengths (typically in the Ultraviolet, UV, range). Exposure to light at certain wavelengths causes photosensitive molecules, which are grafted on the polymer chains comprising the material, to form covalent bonds. These bonds act as crosslinks and are responsible for the temporary shape. On exposure to light at a different wavelength these bonds cleave and the material returns to its original shape. Our research focuses on modeling the mechanics associated with such light activated shape memory polymers (LASMP’s) undergoing complex deformations. The modeling is done using a framework based on the theory of multiple natural configurations taking into consideration the different aspects of modeling this material, which include developing a model for the original virgin network and for the other networks with different stress-free states, formed due to exposure to light. In addition to this, we also model the initiation and the formation of the light activated networks and the reverse transition resulting in the dissolution of these networks. Anisotropy in the mechanical response is also incorporated into the model. The model is then used to simulate results for specific boundary value problems, such as uni-axial extension and inflation of a cylinder.

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