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T. Beda 《Journal of Polymer Science.Polymer Physics》2007,45(13):1713-1732
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 相似文献
44.
Eiji Yanagida 《Journal of Dynamics and Differential Equations》2007,19(4):895-914
This paper is concerned with the irregular behavior of solutions for Fisher’s equation when initial data do not decay in a
regular way at the spatial infinity. In the one-dimensional case, we show the existence of a solution whose profile and average
speed are not convergent. In the higher-dimensional case, we show the existence of expanding fronts with arbitrarily prescribed
profiles. We also show the existence of irregularly expanding fronts whose profile varies in time. Proofs are based on some
estimate of the difference of two distinct solutions and a comparison technique.
Dedicated to Professor Pavol Brunovsky on his 70th birthday. 相似文献
45.
J. Feuer 《Journal of Mathematical Analysis and Applications》2007,332(1):564-569
In this paper, we will study two classes of difference equations which are piecewise-linear and of similar forms. We will show that all nontrivial solutions of one equation are eventually periodic with prime period three. We will show this result for one case of the second equation. 相似文献
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An initial boundary value problem for the dynamic system of anisotropic elasticity in a half space is studied in the paper. A novel method of finding an exact solution of this problem for a special polynomial form of initial data and inhomogeneous term of the system is described. On the base of this method the simulation of elastic waves in different homogeneous anisotropic half spaces is implemented. 相似文献
48.
Yuan-Ming Wang 《Journal of Mathematical Analysis and Applications》2007,328(1):137-150
The aim of this paper is to investigate the asymptotic behavior of solutions for a class of three-species predator-prey reaction-diffusion systems with time delays under homogeneous Neumann boundary condition. Some simple and easily verifiable conditions are given to the rate constants of the reaction functions to ensure the convergence of the time-dependent solution to a constant steady-state solution. The conditions for the convergence are independent of diffusion coefficients and time delays, and the conclusions are directly applicable to the corresponding parabolic-ordinary differential system and to the corresponding system without time delays. 相似文献
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《Journal of Differential Equations》2003,190(2):663-685
The existence of global smooth solutions to the multi-dimensional hydrodynamic model for plasmas of electrons and positively charged ions is shown under the assumption that the initial densities are close to a constant. The model consists of the conservation laws for the particle densities and the current densities, coupled to the Poisson equation for the electrostatic potential. Furthermore, it is proved that the particle densities converge exponentially fast to the (constant) steady state. The proof uses a higher-order energy method inspired from extended thermodynamics. 相似文献