Viscoelastic functions summary

A summary of analytic expressions obtained in this manner for all the viscoelastic functions is presented in Table 4 and 5 for the linear and cubic arrays. The well-known phenomenological analogy (8) between dynamic compliance and dielectric permittivity allows the formal use of Eqs. (T 5), (T 6), and (T 11), (T 12) for the dielectric constant, e (co), and loss, e"(co), of the linear and cubic arrays, respectively (see Table 6). The derivations of these equations are elaborated in the next section and certain molecular weight trends are discussed. 

An alternative procedure for calculating the spectra involves fitting the experimental results for the viscoelastic functions by means of spline functions. The derivatives of Eqs. (9.81) and (9.82) are determined by means of these functions, and thus the spectra can be obtained. A summary of these and other approximations used to calculate retardation and relaxation spectra from the measured compliance and relaxation functions, respectively, can be found in Refs. 1 and 5. 

This chapter deals with fundamental definitions, constitutive equations of a viscoelastic medium subject to infinitesimal strain, and the nature and properties of the associated viscoelastic functions. General dynamical equations are written down. Also, the boundary value problems that will be discussed in later chapters are stated in general terms. Familiar concepts from the Theory of Linear Elasticity are introduced in a summary manner. For a fuller discussion of these, we refer to standard references (Love (1934), Sokolnikoff (1956), Green and Zerna (1968), Gurtin (1972)). Coleman and Noll (1961) have shown that the theory described here may be considered to be a limit, for infinitesimal deformations, of the general (non-linear) theory of materials with memory. 

Summary In this chapter, a discussion of the viscoelastic properties of selected polymeric materials is performed. The basic concepts of viscoelasticity, dealing with the fact that polymers above glass-transition temperature exhibit high entropic elasticity, are described at beginner level. The analysis of stress-strain for some polymeric materials is shortly described. Dielectric and dynamic mechanical behavior of aliphatic, cyclic saturated and aromatic substituted poly(methacrylate)s is well explained. An interesting approach of the relaxational processes is presented under the experience of the authors in these polymeric systems. The viscoelastic behavior of poly(itaconate)s with mono- and disubstitutions and the effect of the substituents and the functional groups is extensively discussed. The behavior of viscoelastic behavior of different poly(thiocarbonate)s is also analyzed. 

The present article focuses on 5ueld and crazing in polymers and does not deal directly with the viscoelastic response, though it is recognized that jdeld and viscoelasticity share many of the same features—strain rate and temperature dependence (1) and even concepts such as time-temperature superposition (2) (see Viscoelasticity Aging, Physical). We first present a summary of conventional yield criteria, these being methods to quantify the yield stress as a function of... 

Summary Non-stationary random vibrations of polvcfonally shaped slightly damped Kirchhoff-plates are presented. The frequency response function of the undamped structure is calculated by an advanced bound-ary-integral equation method with Green s functions of finite domains. Subsequently, light hysteretic damping is built in by applying the quadrature type of elastic-viscoelastic correspondence. ... 

In linear viscoelasticity, the creep function and the relaxation function are interrelated and each would permit the derivation of the viscoelastic constitutive relation under the condition that the principle of time invariance can be applied, meaning that the material is influenced only by a t) and s(f) and no other influencing variables are being effective. In summary, in the idealized case of the isothermal linear viscoelasticity under the conditions of static stress or strain, the linear viscoelastic behavior of a material may adequately be described by the creep function F t), the relaxation function R t), the retardation spectrum or the relaxation spectrum. 

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