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.

Thermodynamic framework for the constitutive modeling of asphalt concrete: theory and applications

Abstract: The response of an asphalt concrete pavement to external loading depends on its internal structure. Using a recent framework that associates different natural (stress-free) configurations with distinct internal structures of the body, asphalt concrete is modeled. The authors assumed asphalt concrete to be a mixture of aggregate matrix and asphalt mortar matrix with evolving natural configurations. The evolution of the natural configuration is determined using a thermodynamic criterion, namely, the maximization of the rate of dissipation. Appropriate choices for the Helmholtz potential, the rate of dissipation and the other thermodynamic criteria are assumed to describe how energy is stored and the manner of the rate of dissipation. As an example, a specific form for the Helmholtz potential and the rate of dissipation function that leads to a generalized "upper convected Burgers's model" were chosen, its linearized version being the viscoelastic model that is usually used for modeling asphalt concrete. This model is just one example of how a class of thermodynamically consistent models can be generated to describe the nonlinear behavior of materials such as asphalt concrete. The uniaxial compressive and tensile creep of asphalt concrete for 2 different types of specimens and test methods are modeled. Details are provided of the numerical scheme used to solve the initial value problem, and the experimental data of Monismith and Secor (1962) is compared with predictions of the model.

On a constitutive theory for materials undergoing microstructural changes

Abstract: Of particular interest is a two-network theory of polymer response. The mechanical response depends on the deformation of both the remaining portion of the original material and newly formed one. A particular constitutive equation is introduced. The original and newly formed material are both treated as incompressible isotropic nonlinear neo-Hookean elastic materials, but with different reference configurations

Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

Abstract: To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships.

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 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.