Model elastomers, viscoelastic behavior

The viscoelastic properties of a series of fully cured epoxy resins with different crosslink densities and their trends have been discussed in some details in the previous section. Qualitatively these properties are shared by all crosslinked elastomers, although quantitatively they depend on molecular architecture and the chemical type of the network polymer and the crosslinking agent. Hence it is instructive to show the viscoelastic behavior of other model network systems and compare them. 

The investigations of model compositions, based on linear elastomers and various fillers, have shown that the yield stress also may be characterized by the value of the complex shear modulus measured at various frequencies. The dependence of the dynamic modulus on the filler concentration characterizes critical concentrations of the filler, above which the viscoelastic behavior of composition drastically changes. Dynamic modulus corresponding to the yield stress does not depend on the matrix viscosity or its nature. This fact indicates a predominant role of the structural frame for rheological properties of filled polymers. 

Most adhesives are polymer-based materials and exhibit viscoelastic behavior. Some adhesives are elastomer materials and also exhibit full or partial rubberlike properties. The word elastic refers to the ability of a material to return to its original dimensions when unloaded, and the term mer refers to the polymeric molecular makeup in the word elastomer. In cases where brittle material behavior prevails, and especially, when inherent material flaws such as cracks, voids, and disbonds exist in such materials, the use of the methods of fracture mechanics are called for. For continuum behavior, however, the use of damage models is considered appropriate in order to be able to model the progression of distributed and non-catastrophic failures and/or irreversible changes in material s microstructure, which are sometimes described as elastic Hmit, yield, plastic flow, stress whitening, and strain hardening. Many adhesive materials are composite materials due to the presence of secondary phases such as fillers and carriers. Consequently, accurate analysis and modeling of such composite adhesives require the use of the methods of composite materials. 

The accuracy of Finite Element Analysis is wholly dependent on the precision of the material model employed. In the realm of elastomers, accurate material models are difficult to create due to the nonlinear behavior of the material as well as other viscoelastic effects, such as creep, stress relaxation, compression set, and cyclic softening. 

An area of continued research is in development of elastomeric material models which can incorporate cyclic behavior into one model casting aside the need to switch from non-cyclic to cyclic models. Further, other areas of research involve more accurately predicting viscoelastic behavior such as stress relaxation, creep, and most importantly for cyclic applications, compression set. As these models are developed, the accuracy and abilities of Finite Element Analysis of elastomers will improve dramatically and provide a much better method to predict the complex loading conditions over time that elastomeric parts commonly see. 

The preceding equations provided a reasonable foundation for predicting DE behavior. Indeed the assumption that DEs behave electronically as variable parallel plate capacitors still holds however, the assumptions of small strains and linear elasticity limit the accuracy of this simple model. More advanced non-linear models have since been developed employing hyperelasticity models such as the Ogden model [144—147], Yeoh model [147, 148], Mooney-Rivlin model [145-146, 149, 150] and others (Fig. 1.11) [147, 151, 152]. Models taking into account the time-dependent viscoelastic nature of the elastomer films [148, 150, 151], the leakage current through the film [151], as well as mechanical hysteresis [153] have also been developed. 

Hyperelastic models are often used to represent the behavior of crosslinked elastomers, where the viscoelastic response can sometimes be neglected compared with the nonlinear elastic response. Because UHMWPE behaves differently than do elastomers, there are only a few specific cases when a hyperelastic representation is appropriate for UHMWPE simulations. One such case is when the loading is purely monotonic and at one single loading rate. Under these conditions it is not possible to distinguish between nonlinear elastic and viscoplastic behavior, and a hyperelastic representation might be considered. Note that if a hyperelastic model is used in an attempt to capture the... 

They presented a theoretical approach to predict the behavior of silicone rubber under uniaxial stress. The model is based on the concept of the classical Maxwell treatment of viscoelasticity and stress relaxation behavior, and the Hookean spring component was replaced by an ideal elastomer component. From the test data, the substitution permits the new model estimation of the cross-link density of the silicone elastomer and allows a stress level to be predicted as a complex function of extension, cross-link density, absolute temperature, and relaxation time. Tock and co-workersh" ] found quite good agreementbetweenthe experimental behavior based on the new viscoelastic model. By using dynamic mechanical analysis (DMA), the authors would have been able to obtain similar information on the silicone elastomer. 

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