Stress and strain in elastomer materials

Mechanical loads can be applied in a static or a dynamic way. For static loads, the modulus of elasticity is a real quantity like the spring constant in Hooke s law. It is called the storage modulus, because it stores the applied work as potential energy of deformation. For dynamic loads a phase shift between the driving force and the sample deformation is observed. This phase shift is related to the loss modulus, which describes the energy uptake and the associated sample heating [Elil]. Therefore, for dynamic deformations the distribution of strains, the phase shifts between stress and strain, and the resulting distribution of temperatures are quantities of interest for materials characterization. 

Because H linewidths in many elastomers are of the order of 3 kHz or less, spin-echo and gradient-echo imaging techniques can be applied. Contrast is introduced by suitable filters like Ti and double-quantum filters or by use of the spectroscopic dimension. Parameter images of T2, the double-quantum signal intensity, or the quadrupolar coupling strength are evaluated and rescaled according to theory or experimental calibration data (cf. Section 7.1.6). 

Double-quantum imaging of static strain distributions 

A different sensitivity scale is accessed when deulerated spy molecules are incorporated into the elastomer netw ork and investigated hy W In contrast to the 

Here r denotes voxel position, k = In jK where is the length of the mechanical wave in the gel, R is the displacement amplitude of the wave, 0 is the gradient phase offset from the mechanical excitation phase, and n is the number of gradient periods. Clearly, the more oscillation periods enter into the integral, the larger the detectable phase shift or the smaller the detectable sample deformations R. 

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