Modeling hyperelastic behavior of rubber: A novel invariant‐based and a review of constitutive models

A constitutive phenomenological model completing the Gent‐Thomas concept is carried out to formulate laws governing the hyperelastic behavior of incompressible rubber materials. It is shown that the phenomenological Gent‐Thomas model (1958) and the constrained chain model (1992) give similar precise results at small to moderate deformation. On the other hand, comparisons of the outcome of the proposed model with that of the molecular model from the combined concepts of Flory‐Erman and Boyce‐Arruda (2000), and with those of the phenomenological models of Ogden (1982), Yeoh‐Fleming (1997), Pucci‐Saccomandi (2002) and Beda (2005) are made. Residual inconveniences raised by attractive continuum models in rubber elasticity literature have been successfully overcome. Results from both the statistical and phenomenological mechanics concepts are compared with the data of some useful classical materials (rubbers of Treloar, Rivlin‐Saunders, Pak‐Flory and Yeoh‐Fleming). The results permit one to see salient equivalence of the two theories for a more reliable prediction of stress‐stretch response for all states of any mode of deformation. A complete and exhaustive analysis of the Mooney plot that combines small and very large extension‐compression has been quite essential in assessing the validity of models. A method of identification of material parameters is presented and data of the simple tension suffice for the determination of the parameter values. It is shown that the ordinary identification procedures, such as the usual least squares, a very much used numerical method in materials investigation, can be unsuitable in some cases of hyperelastic modeling. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1713–1732, 2007     

A note on dephasing and pair-breaking

It is shown that the dephasing which suppresses the weak localization correction to the conductivity has the same physical origin than pair-breaking in superconductors and thus-following de Gennes-may be expressed in terms of the correlation function of the operator for time reversal.     

Unoccupied electronic states of epitaxial iron layers on Cu(100)

Inverse photoemission spectra were taken for thin epitaxial iron films on Cu(100). For a film thickness of eight monolayers the observed electronic states are characteristic for a fcc(100) surface. Thed-bands of iron show a ferromagnetic exchange splitting of 1.1 eV, considerably smaller than the bulk value of 1.8 eV, which we observe for film thicknesses above 18 monolayers.     

Adaptation of an echelle spectrograph to a large CCD detector

A broad range echelle spectrograph with a CCD matrix detector is developed for different applications in atomic spectroscopy. The compact optical design in combination with a dispersive entrance slit illumination offers a low stray light level and high throughput in the UV spectral region comparable only with spectrographs of higher focal length. Ray tracing calculations for typical wavelengths and the multi-line spectrum of an iron arc show the excellent overall spectrum quality. The subtraction of two partial spectra of different steel alloys demonstrates the spectra evaluation possibilities of the CCD spectrograph.     

Liquid crystal properties of some substituted pyrazines

A number of biphenyl, terphenyl analogues and ethynes which contain a pyrazine ring have been made and their liquid crystal transition temperatures, together with examples of birefringence measurements, are reported. All the 2,5-disubstituted pyrazine systems are liquid crystalline showing high birefringence values for the biphenyl and terphenyl analogues, whereas the 1,5-disubstituted systems are not liquid crystalline. The pyrazine ethyne systems exhibit very high birefringence values. X-ray diffraction has been used to identify the liquid crystal phases of 2-n-nonyloxy-5-(4'-propylbiphenyl-4-yl)pyrazine.     

Plant polysaccharides I. Polysaccharides ofLagochilus and their biological activity

Institute of the Chemistry of Plant Substances, Academy of Sciences of the Republic of Uzbekistan, Tashkent, fax (3712) 89 14 75. Translated from Khimiya Prirodnykh Soedinenii, No. 2, pp. 313–314, March–April, 1995. Original article submitted November 7, 1994.     

A high performance liquid chromatographic assay for AMP-deaminase activity in the erythrocytes of healthy subjects and patients with inherited purine disorders

A novel method for measuring AMP-deaminase activity in human erythrocytes is presented, based on the determination of the reaction product, IMP, using high performance liquid chromatography. IMP formation was found to be proportional both to the incubation time and the amount of haemolysate over a wide range. The minimal detectable AMP-deaminase activity was more than 1000 times lower than the mean activity found in healthy controls (1083 nmol/h/mg Hb). No marked difference of activity was found in the patients with the following inherited purine disorders: familial juvenile gouty nephropathy and deficiencies of adenosine deaminase, hypoxanthine-guanine phosphoribosyltransferase or adenine phosphoribosyltransferase. The activity in the erythrocytes of patients with chronic renal failure was also similar to controls. The existence of subjects with low erythrocyte AMP-deaminase activity in the population has been confirmed.     

On the diameter and radius of randon subgraphs of the cube

The n-dimensional cube Qⁿ is the graph whose vertices are the subsets of {1,…n}, with two vertices adjacent if and only if their symmetric difference is a singleton. Clearly Qⁿ has diameter and radious n. Write M = n2^n-1 = e(Qⁿ) for the size of Qⁿ. Let Q = (Q_t)_o^M be a random Qⁿ-process. Thus Q^t is a spanning subgraph of Qⁿ of size t, and Q_t is obtained from Q_t–1 by the random addition of an edge of Qⁿ not in Q_t–1, Let t^(k) = τ(Q;δ?k) be the hitting time of the property of having minimal degree at least k. We show that the diameter d_t = diam (Q_t) of Q_t in almost every Q? behaves as follows: d_t starts infinite and is first finite at time t⁽¹⁾, it equals n + 1 for t⁽¹⁾ ? t⁽²⁾ and d_t, = n for t ? t⁽²⁾. We also show that the radius of Q_t, is first finite for t = t⁽¹⁾, when it assumes the value n. These results are deduced from detailed theorems concerning the diameter and radius of the almost surely unique largest component of Q_t, for t = Ω(M). © 1994 John Wiley & Sons, Inc.