Engineering models for synthetic microvascular materials with interphase mass,momentum and energy transfer

New materials are being developed that consist of a solid matrix with pores or vessels through which a functional fluid phase may pass. The fluid can provide expanded functionality such as healing and remodeling, damage disclosure, enhanced heat transfer, and controlled deformation, stiffness and damping. This paper presents a class of engineering models for synthetic microvascular materials that have fluid passages much smaller than a characteristic structural length such as panel thickness. The materials are idealized as two-phase continua with a solid phase and a fluid phase occupying every volume. The model permits the solid and fluid phases to exchange mass, momentum and energy. Balance equations and the entropy inequality for general mixtures are taken from existing continuum mixture theory. These are augmented with certain definite types of solid–fluid interactions in order to enable adequately general, but workable, engineering analysis. The thermomechanical characteristics of this restricted class of materials are delineated. By demanding that the law of increase of entropy be satisfied for all processes, much is deduced about the acceptable forms of constitutive equations and internal state variable evolution equations. The paper concludes with a study of the uniaxial tension behavior of an idealized vascular material.     

On non-physical response in models for fiber-reinforced hyperelastic materials

Soft biological tissues are sometimes composed of thin and stiff collagen fibers in a soft matrix leading to a strong anisotropy. Commonly, constitutive models for quasi-incompressible materials, as for soft biological tissues, make use of an additive split of the Helmholz free-energy into a volumetric and a deviatoric part that is applied to the matrix and fiber contribution. This split offers conceptual and numerical advantages. The purpose of this paper is to investigate a non-physical effect that arises thereof. In fact, simulations involving uniaxial stress configurations reveal volume growth at rather small stretches. Numerical methods such as the Augmented Lagrangian method might be used to suppress this behavior. An alternative approach, proposed here, solves this problem on the constitutive level.     

Effect of fiber geometry on stress in fiber-reinforced composite materials

Eleven two-dimensional photoelastic models of fiber-reinforced composite-material configurations were designed for the purpose of investigating the effects of various fiber-end shapes, various fiber arrangements and broken fibers on the shear-stress distribution in an elastic matrix. Maximum shear stresses in the matrix in the vicinity of fiber discontinuities are presented. The peak stress resulting from a gradually tapered fiber was found to be slightly higher than that from a square-ended fiber, and a round-ended fiber produced a peak stress which was slightly lower than that from the square-ended fiber. Peak stresses resulting from two square-ended fibers butted closely together were considerably higher and decreased with increasing gap length between fiber ends. It made little difference whether the gap between the butted fiber ends was open, simulating a void resulting from a broken fiber, or filled with matrix material.Paper was presented at 1966 SESA Spring Meeting held in Detroit, Mich., on May 4–6.     

Failure of unidirectional fiber-reinforced materials—New methodology and results

An experimental procedure has been developed in order to determine a failure envelope for unidirectional fiber-reinforced materials (FRM). This method provides failure data for a wide range, \( - 0.47< \sigma _{22} /\sigma _{12}< 0.47\) . These results provided a way to build a failure envelope for investigated material as well as to verify failure criteria. The proposed method of inducing bidimensional state of stress may be used for a wide range of other materials as well as FRM.     

On the modeling of fiber dispersion in fiber-reinforced elastic materials

When an isotropic material is subject to a uniaxial tension, the principal strain transverse to the direction of applied load is always negative. However, in fiber reinforced materials the transverse principal strain can change its sign as the load increases, passing through the zero-points, known as perversions. We investigate how the number of perversions in a material reinforced by two symmetrically aligned families of distributed fibers depends both on the degree of fiber dispersion and the model used for fiber dispersion. Angular integration and three variants of the generalized structure tensor approach are considered and discussed. The study of perversions clearly demonstrates the qualitative difference between these approaches in the case of high dispersion of fibers. The results suggest that this difference is primarily due to the way compressive fibers are modeled.     

Dynamic universal solutions for fiber-reinforced incompressible isotropic elastic materials

We consider the effect of a fiber-reinforcement on the dynamic universality of the following families of motions: bending and shearing of a rectangular block; straightening and shearing of a sector of a circular tube; inflation, eversion, extension, bending and shearing of a sector of a circular tube; inflation, extension, bending and azimuthal shearing of a sector of a circular tube.

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Résumé Nous avons considéré l'effet d'un renforcement par fibre sur l'universalité dynamique des familles de mouvement suivant: courbage et cisaillement d'un bloc rectangulaire; redressement et cisaillement d'un secteur de tube circulaire; gonflement, retournement, allongement, courbage et cisaillement d'un secteur de tube circulaire; gonflement, allongement, courbage et cisaillement azimuthal d'un secteur de tube circulaire.

     

Growth and remodeling in highly stressed solid tumors

Meccanica - Growing biological media develop residual stresses to make compatible elastic and inelastic growth-induced deformations, which in turn remodel the tissue properties modifying the actual...     

Heat and mass transfer at the surface of glass-graphite materials in a high-temperature flow of gas

The article discusses the mutual effect of vaporization and combustion processes during the breakdown of glass-graphite materials in a hypersonic flow of gas. It demonstrates the possibility of the appearance of a nonunique dependence of the vaporization rate on the temperature of the heated surface. The effect of the composition of a material on the principal characteristics of the process of its breakdown is established.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 6, pp. 71–87, November–December, 1972.     

Experimental determination of the basic characteristics of heat and mass transfer upon thermoerosion fracture of materials

Using an original technique, heat and mass transfer in the interaction between a high-temperature heterogeneous jet with a high concentration of particles and the surface of structural materials was studied for the first time. The characteristics of heat and mass transfer were obtained under conditions of intense destruction of the materials under the action of a heterogeneous jet whose axis is perpendicular to the heating surface. Based on the results of experimental studies, some signs of high-temperature fracture of steel and cement grout under the action of a heterogeneous jet were revealed. Deceased. Tomsk State University, Tomsk 634050. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 138–143, March–April, 2000.     

Growth and remodeling of load-bearing biological soft tissues

The past two decades reveal a growing role of continuum biomechanics in understanding homeostasis, adaptation, and disease progression in soft tissues. In this paper, we briefly review the two primary theoretical approaches for describing mechano-regulated soft tissue growth and remodeling on the continuum level as well as hybrid approaches that attempt to combine the advantages of these two approaches while avoiding their disadvantages. We also discuss emerging concepts, including that of mechanobiological stability. Moreover, to motivate and put into context the different theoretical approaches, we briefly review findings from mechanobiology that show the importance of mass turnover and the prestressing of both extant and new extracellular matrix in most cases of growth and remodeling. For illustrative purposes, these concepts and findings are discussed, in large part, within the context of two load-bearing, collagen dominated soft tissues—tendons/ligaments and blood vessels. We conclude by emphasizing further examples, needs, and opportunities in this exciting field of modeling soft tissues.     

Quasi-linear heat and mass transfer

Flow, Turbulence and Combustion - From the assumption that the heat flux (mass flux with respect to the mass-average velocity) vector is an isotropic function of the temperature (mass-fraction)...     

The application of interferometric techniques to the nondestructive inspection of fiber-reinforced materials

A method for increasing the sensitivity of dynamic materials evaluation (DME) to localized damage in fiber-reinforced composites was examined. To obtain this improved sensitivity, different aspects of DME were examined. These included an increase in the frequency used to evaluate the dynamic properties, utilization of mode-shape information and different procedures for evaluating the experimental data.The extent of the internal damage was determined using measured changes in the dynamic properties of the system (loss factor, dynamic stiffness and mode shape). To obtain the response information at higher frequencies a modalanalysis system was built around the performance characteristics of a laser doppler vibrometer (LDV) and an electronic speckle pattern interferometer (ESPI). These two devices provided complementary information for the determination of the dynamic characteristics of each vibration mode. With this system, damage-induced changes in the dynamic characteristics of composite materials were measured at frequencies up to 10 kHz.The results of this study showed the following. (1) Torsion modes provide the most sensitivity to localized internal damage. (2) The evaluation of higher frequency NDI data requires the ability to correlate the measured loss factor and resonant frequencies with the actual mode shape. (3) The data obtained over the frequency range of the test could be reduced to a series of slopes that provide a sensitive indication of the material condition. (4) The sensitivity of the dynamic method to localized damage is limited by the measurement of the loss factor.     

A method to produce uniform plane-stress states with applications to fiber-reinforced materials

This work is concerned with a new method for testing material properties under uniform plane-stress conditions by means of a specially designed plane specimen. Photoelastic analysis showed that in the significant section of the specimen it is possible to produce uniform plane stress, with high accuracy, subject to the limitation that the principal stresses are of different signs. An important special case of loading produces pure shear on the significant section. The specimen is of particular importance for fiber-composite testing. The experimental results presented are encouraging.     

Particle-liquid mass transfer in viscoelastic media

The problem of mass transfer from a solid sphere to a viscoelastic fluid has been examined theoretically. It is shown that fluid elasticity increases marginally the mass transfer rate in the creeping flow regime. This will have serious implications on the mass transfer from bubbles if impurities are present. Some conclusions on mass transfer at high Reynolds numbers are also offered.     

Heat and mass transfer in a dispersive medium

Macroscopic equations for the conservation of heat (or the mass of a diffusing impurity) in a continuous medium containing distributed particles of a dispersed phase are formulated neglecting the effect of random fluctuations of the medium and particles by the transfer process. The problem of convective heat conduction or diffusion near an isolated particle is also formulated, the solution of which permits calculation of all the parameters entering into the indicated equations. This problem has been solved in the particular case of small Peclet numbers, which characterize heat and mass exchange in the vicinity of a single particle.