Viscoelasticity theory of nonlinear

P. E. Rouse. The theory of nonlinear viscoelastic properties of dilute solutions of scaling polymers. J Chem Phys 27 1273-1280, 1953. 

Numerical methods for non-Newtonian fluid dynamics, Vradis G.Q ASME, 1994, 35 (The) phenomenological theory of nonlinear viscoelastic behavior An introduction,... 

Schapery, R.A. (1966) A engineering theory of nonlinear viscoelasticity with applications. Int. J. Solids. Structures, 2,407. 

At small stresses and strains, glassy PC exhibits linear viscoelastic behavior. The limit of applicability of the theory of linear viscoelasticity has been investigated by Yannas et al. over the temperature range 23 °C-130 °C. The critical strain at which, within the precision of their measurement, deviations from the linear theory occur has been found to diminish from about 1.2% at 23 °C to about 0.7 % at 130 °C. According to Jansson and Yannas the transition from linear to nonlinear viscoelastic behavior is marked by the onset of significant rotation around backbone bonds. 

Molecular Theory of Polymer Viscoelasticity — Nonlinear Relaxation Modulus of Entangled Polymers... 

A thermodynamically consistent theory for nonlinear viscoelasticity was first proposed by Schapery.(26) Jhe law can be derived from fundamental principles using the concepts of irreversible thermodynamics. A comprehensive review of the thermodynamics basis of Schap-ery s theory has been presented by Hiel et... 

Origin of Nonlinear Viscoelasticity in Filled Rubbers Theory and Practice... 

Popelar, C. F. and Liechti, K. M., A Distortion-Modified Free Volume Theory for Nonlinear Viscoelastic Behavior , Mechanics of Time-Dependent Materials, 7 89-141, 2003. 

Because homogeneous extensional flows are more difficult to generate than shear flows, one rarely, if ever, opts to use an extensional flow to determine the linear properties of a melt. However, it is useful to compare extensional flow data with the behavior predicted by the theory of linear viscoelasticity. This provides a criterion for evaluating the reliability of the data and also serves as a basis for describing the type of nonlinearity exhibited by a particular polymer. 

Osaki and Doi have discussed the predictions of the Doi-Edwards theory in nonlinear viscoelasticity and compared these with available experimental data [33]. Although this model has a remarkable degree of internal consistency, agreement with data is not always quantitative. As a consequence, the model has been modified on a number of occasions and is still a subject of research [34,58,59]. 

The theories of elastic and viscoelastic materials can be obtained as particular cases of the theory of materials with memory. This theory enables the description of many important mechanical phenomena, such as elastic instability and phenomena accompanying wave propagation. The applicability of the methods of the third approach is, on the other hand, limited to linear problems. It does not seem likely that further generalization to nonlinear problems is possible within the framework of the assumptions of this approach. The results obtained concern problems of linear viscoelasticity. 

Molecular theories, utilizing physically reasonable but approximate molecular models, can be used to specify the stress tensor expressions in nonlinear viscoelastic constitutive equations for polymer melts. These theories, called kinetic theories of polymers, are, of course, much more complex than, say, the kinetic theory of gases. Nevertheless, like the latter, they simplify the complicated physical realities of the substances involved, and we use approximate cartoon representations of macromolecular dynamics to describe the real response of these substances. Because of the relative simplicity of the models, a number of response parameters have to be chosen by trial and error to represent the real response. Unfortunately, such parameters are material specific, and we are unable to predict or specify from them the specific values of the corresponding parameters of other... 

Although attempts to measure and interpret nonlinear behavior are potentially useful, there are few reports in the literature on the measurement of the nonlinear viscoelastic properties of foods. This has been due to a lack of both suitable instrumentation and suitably developed theory nonlinear behavior, the predominant form of which is the exhibition of normal stresses, and a dependence of viscosity on shear rate, is much more complex than linear behavior (Gunasekaran and Ak, 2002). 

As remarked earlier, the nonlinear viscoelastic behavior of entangled wormy micellar solutions is similar to that of entangled flexible polymer molecules. Cates and coworkers (Cates 1990 Spenley et al. 1993, 1996) derived a full constitutive equation for entangled wormy micellar solutions, based on suitably modified reptation ideas. The stress tensor obtained from this theory is (Spenley et al. 1993)... 

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