Showing papers by "Kumbakonam R. Rajagopal published in 2006"

A Theoretical Model of Enlarging Intracranial Fusiform Aneurysms

Abstract: The mechanisms by which intracranial aneurysms develop, enlarge, and rupture are unknown, and it remains difficult to collect the longitudinal patient-based information needed to improve our understanding. We submit, therefore, that mathematical models hold promise by allowing us to propose and test competing hypotheses on potential mechanisms of aneurysmal enlargement and to compare predicted outcomes with limited clinical information—in this way, we may begin to narrow the possible mechanisms and thereby focus experimental studies. In this paper, we present a constrained mixture model of evolving thin-walled, fusiform aneurysms and compare multiple competing hypotheses with regard to the production, removal, and alignment of the collagen that provides the structural integrity of the wall. The results show that this type of approach has the capability to infer potential means by which lesions enlarge and whether such changes are likely to produce a stable or unstable process. Such information can better direct the requisite histopathological examinations, particularly on the need to quantify collagen orientations as a function of lesion geometry.

On implicit constitutive theories for fluids

Abstract: We consider generalizations of fluid models wherein the fluid is assumed to be incompressible, but with the viscosity depending on the pressure. We show that a natural setting for the development of such models is a class of implicit constitutive relations, which, in addition to the fluid model described here, provides a means for developing other complex models for viscoelastic fluids which cannot be set within the ambit of classical explicit constitutive relations for the stress in terms of the histories of appropriate kinematical variables.

Information flow and its relation to stability of the motion of vehicles in a rigid formation

Abstract: In this note, we consider the effect of information flow on the propagation of errors in spacing in a collection of vehicles trying to maintain a rigid formation during translational maneuvers. The motion of each vehicle is described using a linear time-invariant (LTI) system. We consider undirected and connected information flow graphs, and assume that each vehicle can communicate with a maximum of q vehicles, where q may vary with the size n of the collection. We consider translational maneuver of a reference vehicle, where its steady state velocity is different from its initial velocity. In the absence of any disturbing forces acting on the vehicles during the maneuver, it is desired that the collection be controlled in such a way that its motion asymptotically resembles that of a rigid body. In the presence of bounded disturbing forces acting on the vehicles, it is desired that the maximum deviation of the motion of the collection from that of a rigid body be bounded and be independent of the size of the collection. We consider a decentralized feedback control scheme, where the controller of each vehicle takes into account the aggregate errors in position and velocity from the vehicles with which it is in direct communication. We assume that all vehicles start at their respective desired positions and velocities. Since the displacement of every vehicle at the end of the maneuver of the reference vehicle must be the same, we show that the loop transfer function must have at least two poles at the origin. We then show that if the loop transfer function has three or more poles at the origin, then the motion of the collection is unstable, that is, its deviation from the rigid body motion is arbitrarily large, if the size of the formation is sufficiently large. If l is the number of poles of the transfer function relating the position of a vehicle with its control input, we show that if (q(n)/n)rarr0 as nrarrinfin, then there is a low frequency sinusoidal disturbance of at most unit amplitude acting on each vehicle such that the maximum errors in spacing response increase at least as Omega(((radicn/q(n))l+1)).A function p(n) is Omega(q(n)) if there exists a nonzero constant c>0 and a N* such that |p(n)|gesc|q(n)| for all n>N* . A consequence of the results presented in this note is that the maximum errors in spacing and velocity of any vehicle can be made insensitive to the size of the collection only if there is at least one vehicle in the collection that communicates with at least Omega(n) other vehicles in the collection

A Diagnostic System for Air Brakes in Commercial Vehicles

Abstract: The safe operation of vehicles on roads depends, among other things, on a properly functioning brake system. Air brake systems are widely used in commercial vehicles such as trucks, tractor-trailers, and buses. In these brake systems, compressed air is used as the energy transmitting medium to actuate the foundation brakes mounted on the axles. In this paper, a model-based diagnostic system for air brakes is presented. This diagnostic system is based on a nonlinear model for predicting the pressure transients in the brake chamber that correlates the brake chamber pressure to the treadle valve (brake application valve) plunger displacement and the pressure of the air supplied to the brake system. Leaks and "out-of-adjustment" of push rods are two prominent defects that affect the performance of the air brake system. Diagnostic schemes that will monitor the brake system for these defects will be presented and corroborated with experimental data obtained from the brake testing facility

A heuristic based on multi-stage programming approach for machine-loading problem in a flexible manufacturing system

Abstract: Manufacturing industries are rapidly changing from economies of scale to economies of scope, characterized by short product life cycles and increased product varieties. This implies a need to improve the efficiency of job shops while still maintaining their flexibility. These objectives are achieved by Flexible manufacturing systems (FMS). The basic aim of FMS is to bring together the productivity of flow lines and the flexibility of job shops. This duality of objectives makes the management of an FMS complex. In this article, the loading problem in random type FMS, which is viewed as selecting a subset of jobs from the job pool and allocating them among available machines, is considered. A heuristic based on multi-stage programming approach is proposed to solve this problem. The objective considered is to minimize the system unbalance while satisfying the technological constraints such as availability of machining time and tool slots. The performance of the proposed heuristic is tested on 10 sample problems available in FMS literature and compared with existing solution methods. It has been found that the proposed heuristic gives good results.

On internal constraints in continuum mechanics

Abstract: In classical particle mechanics, it is well understood that while working with nonholonomic and nonideal constraints, one cannot expect that the constraint be workless. It is curious that in continuum mechanics, however, the implications of the result in classical mechanics have not been clearly understood. In this paper, we show that in dealing with the response of dissipative systems, one cannot require that constraints do no work or ignore the fact that the material response functions depend on the constraint reaction. An example of this is the viscosity of a fluid depending on the pressure.

Technical Notes and Correspondence Information Flow and Its Relation to Stability of the Motion of Vehicles in a Rigid Formation

Abstract: In this note, we consider the effect of information flow on the propagation of errors in spacing in a collection of vehicles trying to main- tain a rigid formation during translational maneuvers. The motion of each vehicle is described using a linear time-invariant (LTI) system. We consider undirected and connected information flow graphs, and assume that each vehicle can communicate with a maximum of vehicles, where may vary with the size of the collection. We consider translational maneuver of a reference vehicle, where its steady state velocity is different from its ini- tial velocity. In the absence of any disturbing forces acting on the vehicles during the maneuver, it is desired that the collection be controlled in such a way that its motion asymptotically resembles that of a rigid body. In the presence of bounded disturbing forces acting on the vehicles, it is desired that the maximum deviation of the motion of the collection from that of a rigid body be bounded and be independent of the size of the collection. We consider a decentralized feedback control scheme, where the controller of each vehicle takes into account the aggregate errors in position and velocity from the vehicles with which it is in direct communication. We assume that all vehicles start at their respective desired positions and velocities. Since the displacement of every vehicle at the end of the maneuver of the reference vehicle must be the same, we show that the loop transfer function must have at least two poles at the origin. We then show that if the loop transfer func- tion has three or more poles at the origin, then the motion of the collection is unstable, that is, its deviation from the rigid body motion is arbitrarily large, if the size of the formation is sufficiently large. If is the number of poles of the transfer function relating the position of a vehicle with its con- trol input, we show that if

Pulsatile Flow of a Chemically-Reacting Nonlinear Fluid

Abstract: Many complex biological systems such as blood and polymeric materials can at times be approximated as single constituent homogeneous fluids whose properties can change due to the chemical reactions that take place. For instance, the viscosity of such fluids could change both due to the chemical reactions and the flow. Here, we investigate the pulsatile flow of a chemically-reacting fluid whose viscosity depends on the concentration of a species (constituent) that is governed by a convection-reaction-diffusion equation and the velocity gradient, which can thicken or thin the fluid. We study the competition between the chemical reaction and the kinematics in determining the response of the fluid.

A viscoelastic fluid model for describing the mechanics of a coarse ligated plasma clot

Abstract: Thrombi are formed at the end of a series of complex biochemical processes. There are various types of thrombi, and their rheological properties change depending on the conditions during clot formation. In this paper, a model for a particular type of clot, formed from human plasma, is proposed within a thermodynamic framework that recognizes that viscoelastic fluids possess multiple natural configurations.

Pressure control scheme for air brakes in commercial vehicles

Abstract: Air brake systems are widely used in commercial vehicles such as trucks, tractor-trailers and buses. In these brake systems, compressed air is used as the energy transmitting medium to actuate the foundation brakes mounted on the axles. Here, we present a control scheme for regulating the pressure of air in a brake chamber of these brake systems. This scheme is based on a non-linear model for predicting the pressure transients in the brake chamber that correlates the brake chamber pressure to the treadle valve (brake application valve) plunger displacement and the pressure of the air supplied to the brake system. The control scheme regulates the pressure in the brake chamber by modulating the displacement of the treadle valve plunger. We have implemented this control scheme on the brake testing facility at Texas A&M University and present results for a variety of test runs in which the controller tracks realistic desired pressure trajectories. (A)

On Constitutive Equations For Anisotropic Nonlinearly Viscoelastic Solids

Abstract: Many biological, geological and synthetic bodies are anisotropic. In particular, some of these bodies reflect the anisotropy due to fiber reinforcement along a direction or more than one direction. In a recent paper Merodio developed constitutive equations for fiber-reinforced transversely isotropic nonlinearly viscoelastic bodies where the transverse isotropy was a consequence of the presence of a single family of unidirectional reinforcements. It was shown that constitutive equations for such materials can be expressed in terms of functions of 18 independent invariants, eight of them associated with the deformation and the orientation of the fiber. Here we provide a corresponding analysis for more general constitutive equations: anisotropic models with two preferred fiber directions, i.e., two families of fiber reinforcements. In this case, we show that the constitutive equations can be expressed in terms of functions of 37 independent invariants. These invariants are analyzed with regard to their prope...

Oscillatory motion of an electrically conducting viscoelastic fluid over a stretching sheet in a saturated porous medium with suction/blowing

Abstract: The effect of an oscillatory motion of a viscoelastic fluid over an infinite stretching sheet through porous media in the presence of magnetic field with applied suction has been studied. The surface absorbs the fluid in a porous medium in the presence of magnetic field and the velocity oscillates depending on the stretching rate (b). Analytical expressions for the velocity and the coefficient of skin friction have been studied, first by the perturbation method and then by power series method. The effect of viscoelastic parameter k1, porous parameter k2, magnetic parameter Mn, and the vertical distance x in the presence of suction/blowing on the velocity and the flow characteristics are discussed. The velocity of the viscoelastic fluid is found to decrease in the presence of magnetic field and porous media, as compared to the study of viscous fluid. It is also found that the effect of unsteadiness in the wall velocity and skin friction are found to be appreciable in the presence of suction/blowing parameter.

Heat transfer in a visco-elastic fluid past a stretching sheet with viscous dissipation and internal heat generation

Abstract: This paper deals with the study of heat transfer characteristics in the laminar boundary layer flow of a visco-elastic fluid over a linearly stretching continuous surface with variable wall temperature subjected to suction or blowing. The study considers the effects of frictional heating (viscous dissipation) and internal heat generation or absorption. An analysis has been carried out for two different cases of heating processes namely: (i) Prescribed surface temperature (PST) and (ii) Prescribed wall heat flux (PHF) to get the effect of visco-elastic parameter for various situations. Further increase of visco-elastic parameter is to decrease the skin friction on the sheet. The solutions for the temperature and the heat transfer characteristics are obtained in terms of Kummers function.

Unsteady Exact Solution for Flows of Fluids with Pressure-Dependent Viscosities

Abstract: There are many applications, elasto-hydrodynamics being one, where the fluid can be modelled as an incompressible fluid with a viscosity that depends on the pressure (see [15]). The justification for such an assumption stems from the fact that while the density changes by merely a few percent, the pressure can change significantly and the viscosity can change by several orders of magnitude. Of course, there is the possibility that the dependence of viscosity on density is such that even a small change in density causes this change. Experiments clearly suggest that viscosity varies exponentially with pressure and that it is the relationship between the viscosity and the pressure that causes the tremendous change that occurs in the viscosity. That the viscosity of liquids could depend upon the pressure was known to the pioneers of the field. Stokes [14] is in fact very careful to delineate the special class of flows, those in channels and pipes at moderate pressures, when viscosity could be assumed a constant. There is also a considerable amount of literature even prior to 1930 concerning the variation of viscosity with pressure (see Bridgman [4] on the physics of high pressures for a detailed discussion of the same). Bridgman [4] makes it abundantly clear that he devoted a great deal of attention to determining the variation

Thermomechanical Framework for the Constitutive Modeling of Asphalt Concrete

Abstract: This study is concerned with the constitutive modeling of asphalt concrete. Unlike most constitutive models for asphalt concrete that do not take into account the evolution of the microstructure of the material, this study incorporates the evolution of the microstructure by using a framework that recognizes that a body's natural configurations can evolve as the microstructure changes. The general framework, on which this study is based, is cast within a full thermomechanical setting. In this paper, we develop models within the context of a mechanical framework that stems from the general framework for models based on the full thermodynamic framework and the resulting equations represent a nonlinear rate type viscoelastic model. The creep and stress relaxation experiments of Monismith and Secor are used for validating the efficacy of the model, and it is found that the predictions of the theory agree very well with the available experimental results. The advantages of using such a framework are many, especially when one wants to model the diverse mechanical and thermodynamic response characteristics of asphalt and asphalt concrete.

On Burgers fluids

Abstract: We investigate several qualitative aspects concerning the solutions to the flow of a Burgers fluid, a model that has been used to describe a variety of materials: polymeric liquids, asphalt and asphalt mixtures, and the earth's mantle. Continuous dependence of the solutions with respect to initial data and supply terms, uniqueness of solutions and the impossibility of localization of the solutions are proved. Exponential stability and structural stability are analysed. We also consider uniaxial shear flows. We prove instability of solutions whenever the constitutive parameters do not satisfy certain relations. Also we study the spatial behaviour of the solutions. Copyright © 2006 John Wiley & Sons, Ltd.

On the Deformation of the Circumflex Coronary Artery During Inflation Tests at Constant Length

Abstract: Here we investigate whether the deformation observed in an experiment in which the porcine circumflex coronary artery is subjected to inflation at constant length included in the class, $$r$$ $$=$$ $$r(R)$$ , $$\theta$$ $$=$$ $$\Theta$$ , $$z$$ $$=$$ $$\Lambda Z$$ . We find that this is not the case and discuss its implications in the study of the mechanics of this artery. Moreover, we identify and quantify the uncertainty in the value of the invariants of the left Cauchy–Green tensor inferred from the 2D motion of markers affixed to the surface of the test specimen, and suggest that 3D tracking of markers is needed due to inherent bending and twisting induced by pressurization in vitro.

A Thermodynamic Framework for Describing Solidification of Polymer Melts

Abstract: A thermodynamic framework is presented that can be used to describe the solidification of polymer melts, both the solidification of atactic polymers into an amorphous elastic solid and the crystallization of other types of polymer melts to semi-crystalline elastic solids. This framework fits into a general structure that has been developed to describe the response of a large class of dissipative bodies. The framework takes into account the fact that the natural configuration of the viscoelastic melt and the solid evolve during the process and that the symmetries of these natural configurations also evolve. Different choices are made as to how the material stores energy, produces entropy, and for its latent heat, latent energy, etc., that lead to models for different classes of materials. The evolution of the natural configuration is dictated by the manner in which entropy is produced, how the energy is stored etc., and it is assumed that the constitutive choices are such that the rate entropy production is maximized, from an allowable class of constitutive models. Such an assumption also determines the crystallization kinetics, i.e., provides equations such as the Avrami equation. Using the framework, a model is developed within which the problem of fiber spinning is studied and we find that the model is able to predict observed experimental results quite well.

Homogenization and Global Responses of Inhomogeneous Spherical Nonlinear Elastic Shells

Abstract: Homogenization of radially inhomogeneous spherical nonlinear elastic shells subject to internal pressure is studied. The equivalent homogeneous material is defined in such a way that it gives rise to exactly the same global response to the pressure load as that of the inhomogeneous shell. For a shell with general strain–energy function and inhomogeniety, the strain–energy function of the equivalent homogeneous material is determined explicitly. The resulting formula is used to study layered composite shells. The equivalent homogeneous material for an infinitely fine layered composite shell is examined, and is found to give not only the same global response, but also the same average stress field as the composite shell does.

Developing a Diagnostic System for Air Brakes Used in Commercial Vehicles

Abstract: The safe operation of vehicles on roads depends amongst other things, on a properly functioning brake system. Air brake systems are widely used in commercial vehicles such as trucks, tractor-trailers and buses. In these brake systems, compressed air is used as the energy transmitting medium to actuate the foundation brakes mounted on the axles. In this report, a model-based diagnostic system for air brakes is presented. This diagnostic system is based on a nonlinear model for predicting the pressure transients in the brake chamber that correlates the brake chamber pressure to the treadle valve (brake application valve) plunger displacement and the pressure of the air supplied to the brake system. Leaks and “out-of-adjustment” of push rods are two prominent defects that affect the performance of the air brake system. Diagnostic schemes that will monitor the brake system for these two defects are presented. These schemes are corroborated with experimental data obtained from the brake testing facility constructed at Texas A&M University.

Rate-Type Model for Bituminous Mixtures and Its Application to Sand Asphalt

Abstract: A variety of hot mix asphalt mixtures are used in highway and runway pavement construction. Each mixture caters to specific needs. Mixtures differ from one another in the type and percentage of aggregates and asphalt used, and their response can be markedly different, and thus there is a need to develop constitutive models that can differentiate between the different kinds of mixtures. In this paper, we outline a general procedure for the constitutive modeling of bituminous mixtures. We illustrate the efficacy of this approach by means of an application to sand asphalt. The governing equations for this special problem reduce to a stiff nonlinear ordinary differential equation and this is solved numerically using Gear’s method. We compare the results of the predictions of the model that we have developed with the compressive creep experiments carried out by Wood and Goetz on a typical sand asphalt mixture and find them to be in good agreement.

Diagnosing the air brake system of commercial vehicles

Abstract: Air brake systems are widely used in commercial vehicles like trucks, tractor-trailers and buses. In this article, we present, model-based diagnostic schemes for detecting faults in air brake systems. Leaks and push rod out-of-adjustment are two prominent defects that affect the performance of the brake system. We will present schemes that will monitor the brake system for these defects and corroborate these schemes with experimental data.