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151.
Model networks of poly(dimethylsiloxane) (PDMS) were prepared by tetrafunctionally endlinking hydroxyl-terminated chains of various molecular weights. Some networks were prepared from mixtures of chains so as to yield a bimodal distribution of network chain lengths and, in some cases, these networks were prepared in solution. The stress–strain behavior of these unimodal and bimodal networks was studied in pure shear, which was imposed by stretching a sheet of the network having a large ratio of width to length in the direction perpendicular to the width. The pure-shear moduli of both types of networks generally were found to depend markedly on strain. Stress–strain isotherms for unimodal networks prepared from chains of one or the other of two molecular weights were well interpreted using the constrained-junction model of Flory and Erman. The bimodal networks showed large increases in the pure-shear modulus at high strains which were similar to those reported for uniaxial extension and compression. Endlinking in solution decreases the modulus in general and its upturn in particular, presumably because of diminished chain-junction entangling. 相似文献
152.
The problem of approximation by algebraic polynomials is considered on function classes characterized by the value of thekth generalized modulus of smoothness defined by the Jacobi generalized shift operator.
Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 425–436, March, 1998. 相似文献
153.
At relatively high temperatures and low frequencies the electrical properties of many polymers are dominated by ionic conductivity. In cases where the glass transition is obscured by conductivity, it can be revealed by treating the data in terms of the electric modulus. The magnitude of the activation energy for conductivity (24–67 kcal/mol) for Nylons 6, 66, and 6I, polybutylene terephthalate, and polycarbonate indicates that the transport of charged particles requires the motion of polymer segments. 相似文献
154.
155.
借助于光滑模ωψ^rλ(f,t)(0≤λ≤1)给出了Bernstein算子线性组合同时逼近的点态结果。 相似文献
156.
Surface Acoustic Wave Characterization of Equivalent Young's Moduli for Patterned Films北大核心CSCD
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Based on the equivalent elasticity theory for layered materials, the micro-mechanics equivalent models for single and dual damascene structures were established. The equivalent elastic constant of the patterned structure was introduced, to establish the propagation model for the surface acoustic waves propagating in the layered structure of the patterned film/ substrate, and the theoretical dispersion curves of the surface acoustic waves were calculated with Green’s function and the matrix method. The finite element method was used to calculate 24 numerical examples of damascene structures with different volume ratios, and the results were compared with those of the strain energy method. The results show that, the average relative errors of the equivalent Young’s moduli of the 300 nm-thick dual damascene film and the 100 nm-thick single damascene film are 2.06% and 2.27%, respectively. The research verifies the correctness of the equivalent patterned structure model and the feasibility of the surface acoustic wave method to characterize the mechanical properties of patterned films, and provides a reference for the development of suitable chemico-mechanical polishing technologies for patterned films under low pressure. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved. 相似文献
157.
Research into cavitation phenomena in various fields shows that the elastic modulus of a boundary has a potential impact on cavitation erosion. To obtain the direct relationship between the elastic modulus of the boundary and cavitiation erosion, single-layer samples with different chemical composition and moduli, and double-layer samples with different elastic moduli and the same surface layer material, were prepared with silicone rubber. The results of cavitation experiments on single-layer samples, show that the coating chemical composition and mechanical properties together affect the cavitation morphology of the coating, and dominant factors vary with erosion stage. Through the cavitation test of double-layer samples, it was found that there is a positive correlation between the elastic modulus of the coating and the degree of cavitation. This study helps us to understand the relationship between coating elastic modulus and cavitation more directly, and provides theoretical and technical guidance for the application of anti-cavitation for elastic coating in engineering. 相似文献
158.
Based on the complex viscosity model various steady-state and transient material functions have been completed. The model is investigated in terms of a corotational frame reference. Also, BKZ-type integral constitutive equations have been studied. Some relations between material functions have been derived.
C
–1
Finger tensor
-
F[], (F
–1[])
Fourier (inverse) transform
-
rate of deformation tensor in corotating frame
-
h(I, II)
Wagner's damping function
-
J
(x)
Bessel function
-
m
parameter inh (I, II)
-
m(s)
memory function
-
m
k, nk
integers (powers in complex viscosity model)
-
P
principal value of the integral
-
parameter in the complex viscosity model
-
rate of deformation tensor
-
shear rates
-
[], []
incomplete gamma function
-
(a)
gamma function
-
steady-shear viscosity
-
*
complex viscosity
-
,
real and imaginary parts of
*
-
0
zero shear viscosity
-
+,
1
+
stress growth functions
-
–,
1
-
stress relaxation functions
-
(s)
relaxation modulus
-
1(s)
primary normal-stress coefficient
-
ø(a, b; z)
degenerate hypergeometric function
-
1, 2
time constants (parameters of
*)
-
frequency
-
extra stress tensor 相似文献
159.
Professor K. Osaki 《Rheologica Acta》1993,32(5):429-437
Published data of the damping function of the shear relaxation modulus, h(), are reviewed. This is the ratio of the relaxation modulus measured at a finite magnitude of shear, , to that at the limit of = 0. Majority of the data are in accord with the universal function of the Doi-Edwards tube model theory, in which the damping or the decrease of h() is attributed to the contraction along the tube of extended polymer chains. The weaker damping seems to be attributed to 1) comb-branching such as in LDPE; 2) lack of entanglement in too short chains; 3) bimodal molecular weight distribution. However, a star-branching does not cause a deviation from the tube model theory and a broadness of molecular weight distribution is not a major origin of a weaker damping. A star-branched polystyrene with 15 arms exhibits no strain dependence: h() = 1. For highly entangled systems with more than 50 entanglement points per molecule, the strain dependence is stronger than that of the Doi-Edwards theory. This could be due to a slip or an instability of deformation in the material. 相似文献
160.