Long Nonlinear viscoelastic behavior

Measurements of linear and nonlinear viscoelastic behavior of elastomers have a long history. Instead of reviewing the works done in the past by various workers... 

The finite element description of the nonlinear viscoelastic behavior of technical fabric was presented by Klosowski et al. [65]. The technical fabric called Panama used in this model was made of two polyester thread families woven perpendicularly to each other with the 2/2 weave. The long term uniaxial creep laboratory tests in directions were conducted at five different constant stress levels. The dense net model [66] together with the Schapery one-integral viscoelastic constitutive model [67] was assumed for the fabric behavior characterization and the least square method in the Levenberg-Marquardt variant was used for the parameters identification. 

In the solid state deformation, the nonlinear viscoelastic effect is most clearly shown in the yield behavior. The type of stresses applied to a system has little effect on the linear viscoelastic relaxation, but becomes very important as the stress level increases. At high stress levels, the contribution from the external work done on a lattice cell has to be included in the nonlinear viscoelastic analysis. By taking into account the long range cooperative interaction, the external work can,... 

Finally, it is worth mentioning another approach used to describe nonlinear viscoelastic solids nonlinear differential viscoelasticity [49, 178, 179]. This theory has been successfully applied to model finite amplitude waves propagation [180-182]. It is the generalization to the three-dimensional nonlinear case of the rheological element composed by a dashpot in series with a spring. Thus in the simplest case, the stress depends upon the current values of strain and strain rate rally. In this sense, it can account for the nonlinear short-term response and the creep behavior, but it fails to reproduce the long-term material response (e.g., relaxation tests). The so-called Mooney-Rivlin viscoelastic material [183] and the incompressible version of the model proposed by Landau and Lifshitz [184] belraig to this class. 

In Chapter 4 it was explained that the linear elastic behavior of molten polymers has a strong and detailed dependency on molecular structure. In this chapter, we will review what is known about how molecular structure affects linear viscoelastic properties such as the zero-shear viscosity, the steady-state compliance, and the storage and loss moduli. For linear polymers, linear properties are a rich source of information about molecular structure, rivaling more elaborate techniques such as GPC and NMR. Experiments in the linear regime can also provide information about long-chain branching but are insufficient by themselves and must be supplemented by nonlinear properties, particularly those describing the response to an extensional flow. The experimental techniques and material functions of nonlinear viscoelasticity are described in Chapter 10. 

Linear viscoelasticity Linear viscoelastic theory and its application to static stress analysis is now developed. According to this theory, material is linearly viscoelastic if, when it is stressed below some limiting stress (about half the short-time yield stress), small strains are at any time almost linearly proportional to the imposed stresses. Portions of the creep data typify such behavior and furnish the basis for fairly accurate predictions concerning the deformation of plastics when subjected to loads over long periods of time. It should be noted that linear behavior, as defined, does not always persist throughout the time span over which the data are acquired i.e., the theory is not valid in nonlinear regions and other prediction methods must be used in such cases. 

Normally a logarithmic time scale is used to plot the creep curve, as shown in Figure 3.9b, so that the time dependence of strain after long periods can be included. If a material is linearly viscoelastic (Equation 3.17), then at any selected time each line in a family of creep curves (with equally spaced stress levels) should be offset along the strain axis by the same amount. Although this type of behavior maybe observed for plastics at low strains and short times, in most cases the behavior is nonlinear, as indicated in Figure 3.9c. 

Non-Newtonian fluids have both viscous and elastic properties, and they are called viscoelastic fluids. An example is so-called "silly putty," which is made from poly-dimethyl-siloxane (silicone). It flows like a liquid out of the container, but when it forms a ball, it behaves as elastic, i.e., it bounces back. The crucial factor determining the viscous and elastic behavior is the time period of the force applied short force pulse leads to elastic response, whereas long-lasting force causes flow. The viscoelasticity in polymers is due to shear-induced entanglements and nonlinear behavior of tire chains, coils. A well-known natural viscoelastic material is for, example, the egg white, which springs back when a shear force is released. A polymer resembles both liquid and solids. 

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