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.

https://hal.archives-ouvertes.fr/hal-01297725/document

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

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.

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The physics of debris flows

羟氨苄青霉素引起大疱性类天疱疮样疹

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.

Solving Ordinary Differential Equations

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.

https://royalsocietypublishing.org/doi/pdf/10.1098/rsif.2005.0073

Hyperelastic modelling of arterial layers with distributed collagen fibre orientations

A torsional rheometer apparatus for determining rheological properties of a specimen is provided. A stationary plate and a rotatable plate are in generally coaxial position and structured to receive a specimen therebetween. In one embodiment, at least one of the plates and preferably both have roughened specimen engaging surfaces to serve to reduce undesired slippage between the plate and the specimen. A motor is provided to rotate the rotatable plate and a transducer for monitoring forces applied to the stationary plate and generating output signals to a computer which determines the desired rheological properties are provided. In one embodiment, the roughened surfaces consist of projections extending toward the specimen. Where granular material is being evaluated, it is preferred that the roughness of the plate is generally equal to the average size of the granular material being processed. In another embodiment, an air-solid mixture is processed and the roughened portions are pore openings in the plates. Air flows through the region between the two pore containing plates to maintain the solid materials in suspension. In yet another embodiment, the base of the stationary plate is provided with a deformable capacitance sensor and associated electronic means.

Torsional rheometer for granular materials slurries and gas-solid mixtures and related methods

On the modeling of inhomogeneous incompressible fluid-like bodies

A meaningful discussion of the mathematical properties of the equations governing the flow of fluids requires a proper understanding of what is meant by a fluid as well as a clear understanding of the nature of the specific fluid. It is impossible to provide a definition of fluid, without the definition's inadequacy being laid bare with an easy counterexample. Many of the definitions, including those in renowned dictionaries are circular; a fluid being defined as a material that flows and flow being defined as an innate property of the fluid. For the purposes of this chapter a body as a fluid is regarded, if in the time scale of observation of interest, it undergoes a flow that is discernible to the naked eye because of the application of a shear stress (that can be measured with the aid of reasonably unsophisticated instruments; i.e., the forces in question are robust, not mere picoNewtons). Based on how they are constituted, different fluids respond differently to the application of external stimuli. Many mathematical models have been developed to describe the diverse response exhibited by fluids, but Navier–Stokes fluid model enjoys a central place amongst them.

Chapter 7 - Mathematical Properties of the Solutions to the Equations Governing the Flow of Fluids with Pressure and Shear Rate Dependent Viscosities*

Mixtures do not exhibit Newtonian behavior even when their individual components themselves are Newtonian, and thus classical lubrication theory is not applicable to bearings lubricated with mixtures. Our objective is to extend hydrodynamic lubrication theory to lubrication with mixtures of a Newtonian liquid and an ideal gas. To this end, we make use of the theory of interacting continua and derive two coupled non-linear equations in component densities. The extended theory is tested on finite journal bearings: our results of pressure distribution show good qualitative agreement with the experimental data of Braun et al

Kumbakonam R. Rajagopal

Papers

Torsional rheometer for granular materials slurries and gas-solid mixtures and related methods

On the modeling of inhomogeneous incompressible fluid-like bodies

Chapter 7 - Mathematical Properties of the Solutions to the Equations Governing the Flow of Fluids with Pressure and Shear Rate Dependent Viscosities*

Lubrication With Binary Mixtures: Bubbly Oil

Mechanics and Mathematics of Fluids of the Differential Type