Stress-strain relationships - general description

The classical form of describing relaxations, as mention above, was founded by Maxwell (1868). Following Moelwyn-Hughes (1971) the relaxation time x is connected with the displacement of a particle by a simple equation. It is interesting, that surface rheological properties can be studied by the displacement of hydrophobic particles at viscoelastic interfaces (Maru Wasan 1979), using an equation like 

In the case of a solid, x is large enough to make the last term approximately zero. If the body is viscous, does not remain constant, it means the body relaxes. In a simple compressions experiment is proportional to the outer pressure Ap and the strain is dlnV. The relaxation equation becomes 

Demonstration of the relaxation process of a liquid with real and hypothetical establishment of the stationary state, according to Moelwyn-Hughes (1971) 

The relaxation time is the reciprocal first-order constant which governs the process of equilibrium establishment. On the other hand there are experiments in which the strain is set constant at a time t = t. Such processes can be characterised by pressure-time relationships with B = 0. Thus, the solution of 

From a phenomenological point of view, relaxations are simple fluxes of energy (de Groot 1960). The fluxes of energy between two parts of a system are stimulated by the different temperatures T and T that exist as long as the system as a whole is not in a thermodynamic equilibrium. Therefore, for the change of entropy as driving force for the establishment of the thermodynamic equilibrium one can write 

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A general description of the fundamental relationships governing the dynamic response of linear viscoelastic materials may be found in several sources (28, 37, 93). In general, sinusoidally applied strains (stresses) result in sinusoidal stresses (strains) that are out of phase. Measurements may be made under uniaxial, shear, or dilational loading conditions, and the resultant complex moduli or compliance and loss-phase angle are computed. Rotating radius vectors are usually taken to represent the... 

The theory of linear elasticity (see, for example, Landau and Lifshitz, 1%5) gives the basis for the description of elastic wave propagation. Linear elasticity is given in case of a linear relationship between stress and strain. Rocks are—in general— non-linear but for sufficiently small changes of stress as during a wave propagation, linearity can be assumed. 

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