00030___d9d069d5b97d241bde0841cc8e3b8142 - Sec. 1.2 LINEAR...

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Sec. 1.2 LINEAR SOLIDS WITH MEMORY: MODELS OF . . . 9 1.2. LINEAR SOLIDS WITH MEMORY: MODELS OF VISCOELASTICITY Most structural metals are nearly linear elastic under small strain, as measurements of load-displacement relationship reveal. The existence of normal modes of free vibrations which are simple harmonic in time, is of- ten quoted as an indication (although not as a proof) of the linear elastic character of the material. However, when one realizes that the vibration of metal instruments does not last forever, even in a vacuum, it becomes clear that metals deviate somewhat from Hooke’s law. Thus, other consti- tutive laws must be considered. The need for such an extension becomes particularly evident when organic polymers are considered. In this section we shall consider a simple class of materials which retains linearity between load and deflection, but the linear relationship depends on a third parameter, time. For this class of material, the present state of deformation cannot be determined completely unless the entire history of
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