Extensional Definition

Knowledge of the variation of stress and strain through the laminate thickness is essential to the definition of the extensional and bending stiffnesses of a laminate. The laminate is presumed to consist of per-... 

Figure 1.17 Definition of the deformation tensor E for a general extensional deformation of a unit cube. (From Larson 1988, with permission.)...

Turning now to the extensionally described generic ring systems, there are additional complexities. First, the ring description should not require the exhaustive generation of all of the specific forms of the class. Secondly, it should not depend on the orientation or form of definition of the structure. The example of Figure 13 underlines these points. 

If we now wish to obtain the extensional compliance at an angle 9 to the symmetry axis (3-axis) we recall from the definition of a fourth rank tensor that this will depend on terms which involve the product of four direction cosines... 

There are three types of melt behavior in a simple shear flow dilatant (D) (shear thickening) Newtonian (N), and pseudoplastic (P) (shear thinning). Similarly, in an extensional flow, the liquids may be stress hardening (SH), Troutonian (T), or stress softening (SS). By definition, the response considered here is taken at sufficiently... 

Eiastic Materiai Functions. The material functions that are used here for an isotropic, elastic material are the shear modulus G, the extensional modulus E, the bulk modulus K, and the Poisson s ratio v. However, any two of these provides the full set of information needed to describe such a material, as they are not all independent. For simple deformations, the definitions of these moduli are... 

In addition, Schaffner mentions that part-whole relation might hold between the objects of the reduced and the reducing sciences domains. We shall come back to this later on (Chap. 8). Note that the way Schaffner s model is presented here, all cases of la/b and 2a/b combinations in Schaffner s definition are met. Depending on how we interpret derivability of domain in Schaffner s model, this condition will be the one that does maybe not require cross-theoretic identities (if, say, an extensional relation is sufficient). 

Extensional flow (steady and unsteady) is treated under one heading for convenience. The definitions of important rheological parameters imder each of the three headings are given below. 

Figure 4 Definition diagram for uniaxial extensional flow.

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