Stiffness and Elasticity

Relaxation of the Chemical Bond, Springer Series in Chemical Physics 108, DOI 10.1007/978-981-4585-21-7 26, Springer Science+Business Media Singapore 2014 

In practice, one can only measure the product of the Young s modulus and the wall thickness, or called stiffness, (Tf)i, of the SWCNT, rather than the individual component, Yi or fj. Although the measured values of t and Y are widely scattered, the product of (7t)i surprisingly approaches a constant value of 0.368 0.005 TPa nm [21]. Therefore, discriminating the Ti value Irom the product of (K)i is essential. 

In contrast, the multi-walled (MW) CNTs demonstrate two typical trends of the change in Y values  

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The second major assumption is that the material is elastic, meaning that the strains are directly proportional to the stresses applied and when the load is removed the deformation will disappear. In engineering terms the material is assumed to obey Hooke s Law. This assumption is probably a close approximation of the material s actual behavior in direct stress below its proportional limit, particularly in tension, if the fibers are stiff and elastic in the Hookean sense and carry essentially all the stress. This assumption is probably less valid in shear, where the plastic carries a substantial portion of the stress. The plastic may then undergo plastic flow, leading to creep or relaxation of the stresses, especially when the stresses are high. 

FIGURE 21.10 (a) The schematic drawing of the sample deformation for an elastic sample, (b) The comparison between force-distance curves for stiff and elastic samples. 

Wang, K., McCarter, R., and Wright, J. (1991a). Regulation of skeletal muscle stiffness and elasticity by titin isoforms A test of the segmental extension model of resting tension. Proc. Natl. Acad. Sci. USA 88, 7101-7105. 

Other explicit equations for the relationship between the elastic-stiffness and elastic-compliance coefficients in the various crystal classes can be found in Nye s book (Nye, 1957). 

Mixtures of isocyanates are commonly used for convenience in commercial production of the diisocyanate, since the pure toluene 2,4-diisocyanate is more expensive to produce. The resulting prepolymer is then mixed with either a glycol, such as 1,6-hexanediol, or a deactivated (sterically hindered) diamine plus pigment if required, and then promptly poured into a preheated mold of the desired shape. In about half an hour the mixture sets to a pliable shape with stiffness and elasticity controlled by the components and processing details used [29]. Similar procedures produce high-strength polyurethane fiber (e.g., Perlon U) or elastomeric fibers (e.g., Spandex and Lycra). 

The simplest dependency exists between composition and glass transition temperature Independent from the ratio A/B one finds two values for Tg, one for the block from monomer A and one for the block of B. More complex are the dependencies with the mechanical properties. Here, parameters like the ratio A/B, number of blocks, block length, and alternation of the blocks play a decisive role. This is shown in Examples 3.47 and 3.48 with triblock copolymers of butadiene or isoprene with styrene. If the content of the diene blocks is around 20%, a stiff and elastic, transparent thermoplastic material is obtained. Instead, if the diene content is raised to about 70%, a highly elastic but still rather stiff thermoplastic elastomer is obtained. It has to be stressed that these properties can only be reached, when the polystyrene blocks are the terminal ones. 

Clark RE, Apostolou S and Kardos JL, Mismatch of mechanical properties as a cause of arterial prosthesis thrombosis . Surgical Forum, 1976 27 208-210. HowTV, Mechanical properties of arteries and arterial grafts , in Cardiovascular Biomaterials, G. W. Hastings (ed.). Springer Verlag, New York, 1992 1-35. Hayashi K, Handa H, Nagasawa S, Okumura A and Moritake K, Stiffness and elastic behavior of human intracranial and extracranial arteries , J. Biomech., 1980 19 351-358. 

Interval variables in this example are the damping coefficient cq and elastic shear stiffness 0 of NRB, the plastic shear stiffness and elastic shear stiffness of LRB, and the damping coefficient vector Cf and the horizontal stiffness vector kf of the superstructure. The set of interval variables is denoted by... 

As the peel speed increases, the peel force generally also increases until it drops precipitously when the adhesive becomes very stiff and elastic at the pull speed (see Fig. 15.1). Since the failure is normally interfacial at all test speeds, yet the peel varies dramatically with speed and substrate (see Table 15.1), peel is clearly not a measure of the strength of the adhesive, but rather of the work done on it under a particular set of conditions. 

The peel test measures the work done on the entire tape. If the backing is stiff and elastic, such as polyethylene terephthalate (PET), no work will be done on the backing and the peel force is unaffected. However, if the backing can also yield, such as aluminum, then the peel value will be increased in proportion to the work done. If the tape is curled or otherwise distorted after the test then some work has been consumed in the backing. Even if the backing does not deform, its thickness can have an effect on the peel force since it changes the precise angle at the peel front which influences the way the adhesive deforms and thus the work done on it. Peel increases with adhesive thickness, but not proportionately, provided that the... 

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