Kumbakonam R. Rajagopal

Bio: Kumbakonam R. Rajagopal is an academic researcher from Texas A&M University. The author has contributed to research in topics: Constitutive equation & Viscoelasticity. The author has an hindex of 77, co-authored 659 publications receiving 23443 citations. Previous affiliations of Kumbakonam R. Rajagopal include Kent State University & University of Wisconsin-Madison.

A review of interaction mechanisms in fluid-solid flows

Abstract: Multiphase flows have become the subject of considerable attention because of their importance in many industrial applications, such as fluidized beds, pneumatic transport of solids, coal combustion, etc. Fundamental research into the nature of pneumatic transport has made significant progress in identifying key parameters controlling the characteristics of these processes. The emphasis of this study is on a mixture composed of spherical particles of uniform size and a linearly viscous fluid. Section 1 introduces our approach and the importance of this study. In Section 2, the dynamics of a single particle as studied in classical hydrodynamics and fluid dynamics is presented. This has been a subject of study for more than 200 years. In Section 3, we review the literature for the constitutive relations as given in multiphase studies, i.e., generalization of single particle and as given in literature concerning the continuum theories of mixtures or multicomponent systems. In Section 4, a comparison between these representations and the earlier approach, i.e., forces acting on a single particle will be made. The importance of flow regimes, particle concentration, particle size and shape, rotation of the particle, effect of solid walls, etc. are discussed. 141 refs.

Some simple flows of a Johnson-Segalman fluid

Abstract: Unlike most other fluid models, the Johnson-Segalman fluid allows for a non-monotonic relationship between the shear stress and rate of shear in a simple shear flow for certain values of the material parameter. This has been used for explaining a phenomenon such as “spurt”. Here, we study three simple flows of a Johnson-Segalman fluid with a view towards understanding its response characteristics. We find that boundary conditions can have a very interesting effect on the regularity of the solution; changing them continuously leads to solutions that change their regularity. First, we consider the flow through a circular pipe and find solutions that have discontinuous velocity profiles which have been used to explain the phenomenon of “spurt” (cf. [10], [11]). Second, we consider the flow past an infinite porous plate and show that it will not admit solutions which have discontinuous velocity gradients, the solutions being necessarity smooth. Lastly, we study Poiseuille flow in a concentric annulus with porous boundaries. While “spurt” could be explained alternatively by allowing for “stick-slip” at the wall, the Johnson-Segalman model seems particularly suited in describing the appearance of “shear-layers” (cf. [13]).

Analysis of Squeeze Film Dampers Operating With Bubbly Lubricants

Abstract: Rotor-bearing systems supported on squeeze film dampers (SFDs) show large amplitude vibratory motions when traversing critical speeds. At these operating conditions air is drawn into the damper thin film clearance generating a bubbly mixture with the lubricant and producing SFD forces not readily predictable with currently available analysis. A continuum model is proposed for describing the motion of a bubbly fluid in an open ended SFD operating with circular centered journal orbits. Computed predictions for peak-peak dynamic pressures and fluid film forces agree reasonably well with experimental measurements conducted on a SFD test rig operating with a controlled air in oil mixture. The bubbly flow model provides an initial procedure towards the reliable design of SFDs in actual operating conditions.

Modeling of Deformation-Accelerated Breakdown of Polylactic Acid Biodegradable Stents

Abstract: The use of biodegradable polymers in biomedical applications has been successful in nonload bearing applications, such as biodegradable implants for local drug delivery, and in simple load bearing situations such as surgical sutures and orthopedic fixation screws. The desire to incorporate these materials in more complex load bearing situations, such as tissue engineering scaffolds and endovascular or urethral stents, is strong, but the lack of constitutive models describing the evolution of biodegradable polymers over the course of degradation has severely hampered the rational design process for these more complex biodegradable medical applications. With the objective of predicting biodegradable stent behavior, we incorporated constitutive models of biodegradable polymeric materials in a computational setting and the mechanical response of three different stent designs were analyzed as degradation progressed. A thermodynamically consistent constitutive model for materials undergoing deformation-induced degradation was applied to a commonly employed biodegradable polymer system, poly(L-lactic acid), and its specific form was determined by corroboration against experimental data. Depreciation of mechanical properties due to degradation confers time-dependent characteristics to the response of the biodegradable material: the deformation imparted by a constant load increases over time, i.e. the body creeps, and the stress necessary to keep a fixed deformation decreases, i.e. the body relaxes. Biodegradable stents, when subjected to constant pressure in its exterior, deflect inwards and ultimately fail as the structure loses its mechanical integrity. The complex geometry of endovascular stents and their physiological loading conditions lead to inhomogeneous deformations, and consequently, inhomogeneous degradation ensues. Degradation is mostly confined to the bends of the stent rings and junction points, which are the locations that carry most of the deformation, whereas mostly undeformed connector bars remain less degraded. If failure occurs, it will occur most likely at those sensitive locations and large, nondegraded pieces can provoke severe embolic problems. Highly nonuniform degradation indicates that some stent designs are at higher risk for complications. Deformation patterns of stents made of a material that loses its integrity are different than those of permanent stents. Blind adaptation of permanent stent design concepts is ill-suited for biodegradable stent design. The time-dependent aspect of the implant not only must be taken into account but should also be used to interact with the body’s reaction and to enhance healing.

On Kelvin-Voigt model and its generalizations

Abstract: We consider a generalization of the Kelvin-Voigt model where the elastic part of the Cauchy stress depends non-linearly on the linearized strain and the dissipative part of the Cauchy stress is a nonlinear function of the symmetric part of the velocity gradient. The assumption that the Cauchy stress depends non-linearly on the linearized strain can be justified if one starts with the assumption that the kinematical quantity, the left Cauchy-Green stretch tensor, is a nonlinear function of the Cauchy stress, and linearizes under the assumption that the displacement gradient is small. Long-time and large data existence, uniqueness and regularity properties of weak solution to such a generalized Kelvin-Voigt model are established for the non-homogeneous mixed boundary value problem. The main novelty with regard to the mathematical analysis consists in including nonlinear (non-quadratic) dissipation in the problem.

A new constitutive framework for arterial wall mechanics and a comparative study of material models

Abstract: In this paper we develop a new constitutive law for the description of the (passive) mechanical response of arterial tissue. The artery is modeled as a thick-walled nonlinearly elastic circular cylindrical tube consisting of two layers corresponding to the media and adventitia (the solid mechanically relevant layers in healthy tissue). Each layer is treated as a fiber-reinforced material with the fibers corresponding to the collagenous component of the material and symmetrically disposed with respect to the cylinder axis. The resulting constitutive law is orthotropic in each layer. Fiber orientations obtained from a statistical analysis of histological sections from each arterial layer are used. A specific form of the law, which requires only three material parameters for each layer, is used to study the response of an artery under combined axial extension, inflation and torsion. The characteristic and very important residual stress in an artery in vitro is accounted for by assuming that the natural (unstressed and unstrained) configuration of the material corresponds to an open sector of a tube, which is then closed by an initial bending to form a load-free, but stressed, circular cylindrical configuration prior to application of the extension, inflation and torsion. The effect of residual stress on the stress distribution through the deformed arterial wall in the physiological state is examined. The model is fitted to available data on arteries and its predictions are assessed for the considered combined loadings. It is explained how the new model is designed to avoid certain mechanical, mathematical and computational deficiencies evident in currently available phenomenological models. A critical review of these models is provided by way of background to the development of the new model.

The physics of debris flows

Abstract: Recent advances in theory and experimen- tation motivate a thorough reassessment of the physics of debris flows. Analyses of flows of dry, granular solids and solid-fluid mixtures provide a foundation for a com- prehensive debris flow theory, and experiments provide data that reveal the strengths and limitations of theoret- ical models. Both debris flow materials and dry granular materials can sustain shear stresses while remaining stat- ic; both can deform in a slow, tranquil mode character- ized by enduring, frictional grain contacts; and both can flow in a more rapid, agitated mode characterized by brief, inelastic grain collisions. In debris flows, however, pore fluid that is highly viscous and nearly incompress- ible, composed of water with suspended silt and clay, can strongly mediate intergranular friction and collisions. Grain friction, grain collisions, and viscous fluid flow may transfer significant momentum simultaneously. Both the vibrational kinetic energy of solid grains (mea- sured by a quantity termed the granular temperature) and the pressure of the intervening pore fluid facilitate motion of grains past one another, thereby enhancing debris flow mobility. Granular temperature arises from conversion of flow translational energy to grain vibra- tional energy, a process that depends on shear rates, grain properties, boundary conditions, and the ambient fluid viscosity and pressure. Pore fluid pressures that exceed static equilibrium pressures result from local or global debris contraction. Like larger, natural debris flows, experimental debris flows of ;10 m 3 of poorly sorted, water-saturated sediment invariably move as an unsteady surge or series of surges. Measurements at the base of experimental flows show that coarse-grained surge fronts have little or no pore fluid pressure. In contrast, finer-grained, thoroughly saturated debris be- hind surge fronts is nearly liquefied by high pore pres- sure, which persists owing to the great compressibility and moderate permeability of the debris. Realistic mod- els of debris flows therefore require equations that sim- ulate inertial motion of surges in which high-resistance fronts dominated by solid forces impede the motion of low-resistance tails more strongly influenced by fluid forces. Furthermore, because debris flows characteristi- cally originate as nearly rigid sediment masses, trans- form at least partly to liquefied flows, and then trans- form again to nearly rigid deposits, acceptable models must simulate an evolution of material behavior without invoking preternatural changes in material properties. A simple model that satisfies most of these criteria uses depth-averaged equations of motion patterned after those of the Savage-Hutter theory for gravity-driven flow of dry granular masses but generalized to include the effects of viscous pore fluid with varying pressure. These equations can describe a spectrum of debris flow behav- iors intermediate between those of wet rock avalanches and sediment-laden water floods. With appropriate pore pressure distributions the equations yield numerical so- lutions that successfully predict unsteady, nonuniform motion of experimental debris flows.

Solving Ordinary Differential Equations

Abstract: Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Hyperelastic modelling of arterial layers with distributed collagen fibre orientations

Abstract: Constitutive relations are fundamental to the solution of problems in continuum mechanics, and are required in the study of, for example, mechanically dominated clinical interventions involving soft biological tissues. Structural continuum constitutive models of arterial layers integrate information about the tissue morphology and therefore allow investigation of the interrelation between structure and function in response to mechanical loading. Collagen fibres are key ingredients in the structure of arteries. In the media (the middle layer of the artery wall) they are arranged in two helically distributed families with a small pitch and very little dispersion in their orientation (i.e. they are aligned quite close to the circumferential direction). By contrast, in the adventitial and intimal layers, the orientation of the collagen fibres is dispersed, as shown by polarized light microscopy of stained arterial tissue. As a result, continuum models that do not account for the dispersion are not able to capture accurately the stress–strain response of these layers. The purpose of this paper, therefore, is to develop a structural continuum framework that is able to represent the dispersion of the collagen fibre orientation. This then allows the development of a new hyperelastic free-energy function that is particularly suited for representing the anisotropic elastic properties of adventitial and intimal layers of arterial walls, and is a generalization of the fibre-reinforced structural model introduced by Holzapfel & Gasser (Holzapfel & Gasser 2001 Comput. Meth. Appl. Mech. Eng. 190, 4379–4403) and Holzapfel et al. (Holzapfel et al. 2000 J. Elast. 61, 1–48). The model incorporates an additional scalar structure parameter that characterizes the dispersed collagen orientation. An efficient finite element implementation of the model is then presented and numerical examples show that the dispersion of the orientation of collagen fibres in the adventitia of human iliac arteries has a significant effect on their mechanical response.