A review of the works devoted to stability of Bingham flows with respect to perturbations of various kinds is presented. Both hydrodynamic aspects and bifurcation approaches to stability are ...affected. Much attention is given to Il’yushin’ articles in the late 1930s and the early 1940s of the twentieth century which had been pioneer in these subjects.
To investigate attrition processes in pneumatic conveying, it is distinguished between process parameters, determining the stress conditions (SC) the particles are subjected to during conveying ...(process function), and material properties, being responsible for the individual reaction of different materials to these stress conditions (material function). For dilute phase conveying, the process function was determined for a pipe bend preceded by a straight pipe by employing computational fluid dynamics (CFD). The influence of the main parameters as obtained by dimensional analysis, namely, Stokes parameter, Froude number, Reynolds number and the ratio of bend radius to pipe diameter, was investigated and discussed. The results showed that the impact conditions were different from what is commonly expected. The impact angles in a pipe bend (
r
B/
D=5;
D=80 mm) were determined to lie between 5° and 35°. Consequently, the tangential impact velocity components are considerably higher than the normal ones. The experiments carried out to determine the material function revealed that the dominating attrition mechanisms differ between polypropylene (PP) particles on one hand and polymethylmethacrylates (PMMA) and polystyrenes (PS) on the other. By applying dynamic mechanical analysis (DMA), the glass transition temperature of the polymers was identified to be a key factor in the determination of the prevailing attrition mechanism. Based on these findings, a qualitative three-level model of the attrition process, involving stress mode, material-specific attrition mechanisms and basic (microscopic) attrition mechanisms, was developed.
The averaging method is used to determine the material functions of the linear Cosserat theory of elasticity. The proposed method is used to find the material constant in the equilibrium problem for ...an infinite plane weakened by a circular hole.
In the approach presented, attrition of bulk solids in pneumatic conveying is regarded as a result of a process function (stress conditions) and a material function (influence of material ...properties). For dilute phase conveying the process function was determined by employing computational fluid dynamics (CFD). Opposed to what was expected initially, the numerical simulations indicate that sliding friction apparently is of importance in dilute phase conveying. This conclusion can be drawn from the low calculated impact angles in a pipe bend (
r
B/
D
n=5;
D
n=80
mm) which lie between 5 and 35°. Consequently, the tangential impact velocity components ranging from 33 to 44
m/s are considerably higher than the normal ones (5–25
m/s). These results were at first endorsed by observations made in experiments to determine the material function. The relative attrition behavior of four different polypropylenes (PP) under pure sliding friction conditions closely resembles that observed in attrition experiments carried out in a pipe bend of the above geometry, while differences are observed for normal impact conditions. But further experiments with polymethylmethacrylates (PMMA) and polystyrenes (PS) showed that here the attrition behavior encountered under normal impact conditions is similar to that observed in the pipe bend. With dynamic mechanical analysis (DMA) it was possible to show that PP on one hand and PMMA and PS on the other are attrited by different mechanisms and that the glass transition temperature of the polymers is a key factor in the determination of the prevailing attrition mechanism.
An efficient method is proposed to determine the deformation function of a viscoelastic material from experimental data. The deformation function is assumed to be an integral operator with Rabotnov's ...fractional-exponential kernel or a sum of such kernels. This representation enables effective use of the method of operator continued fractions. To illustrate the method, deformation data for polymethylmethacrylate are used. The viscoelastic characteristics of a composite based on this material are obtained using the method of operator continued fractions
A material function of endochronic theory is proposed for investigating the plastic behaviors of material. Depending on the material parameters properly chosen, the present model can be classified ...into four categories, and is appropriate for describing various materials behaving cyclic strain hardening inherently with respect to the deformation history. Experimental verification of the theory was demonstrated using the experimental results of Shiao 1 and Lamba and Sidebottom 2. The theory is in good agreement with experimental results obtained by Shiao 1 through comparing the stress-strain hysteresis loops of SAE 4340 steel under axisymmetrically cyclic loading condition with various amplitudes. In addition, the present model is shown to be capable of describing the behavior of erasure of memory of materials, as experimentally observed by Lamba and Sidebottom 2.
Isotropic both vector and tensor functions in the most general case of scalar and tensor nonlinearity are investigated from a position of stability with respect to perturbations of material ...functions. These vector and tensor functions mean constitutive relations connecting stress tensor and strain rate tensor in continuum with complex rheology (advanced materials). The constitutive relations involve scalar material functions of invariants. Perturbations proportional to some low physical parameter α may be imposed on these material functions. They provoke as a consequence, a perturbation of tensor function itself. Both linear and quadratic in α components of such perturbations are obtained. In each approximation the closed system consisting of the motion equations and incompressibility condition is recorded.
Five Parameter Endochronic Solid Jain, S. K.
Mechanics of advanced materials and structures,
8/21/2007, Letnik:
14, Številka:
6
Journal Article
Recenzirano
Since its inception in 1971 by Valanis, the endochronic theory has undergone periods of both scrutiny and acceptance. Researchers at Virginia Tech showed that computational schemes and the methods of ...determination of material parameters were capable of invalidating this outstanding theory. Since the publication of their work in 1991, no refutation of the endochronic theory has been seen in the literature. This presentation is an extension of their 1991 paper.
A five parameter endochronic solid is constructed by incorporating two exponential terms in the kernel function of the endochronic theory. Methods are presented for efficiently integrating the endochronic equations and a procedure is established for determing the material function. Local constitutive properties of the endochronic solid are investigated. It is shown that the model constructed is promising.
Based on the molecular theory of non-linear viscoelasticity with constrained entanglements in polymer melts, the material functions in simple shear flow were formulated. The theoretical relations of
...η(
γ
̇
) and Ψ
10(
γ
̇
) to shear rate (
γ
̇
) and topologically constrained dimension number n’ and
a were derived. Then, dependence of linear viscoelastic parameters (
η
0 and G
0
N) and topologically constrained dimension numbers (n’,
a and
υ) on the primary molecular weight (Mn), molecular weight between entanglements (Mc) and the entanglement sites sequence distribution on polymer chain are obtained. A new method for determination of viscoelastic parameters (
η
0,Ψ
10,G
0
N and J
0
e), topologically constrained dimension number (n’,
a and
υ) and molecular weight (Mn, Mc and Me) from the simple shear flow measurements was proposed. It was used to determine those parameters and structure of HDPE, and good agreement between these values with those obtained by other methods was found. The agreement provides a quantitative verification for the molecular theory of non-linear viscoelasticity with constrained entanglement in polymer melts.
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