ABSTRACT
Deformation and stress in certain materials are known to vary with time even though the external excitations, regardless of displacement or loads, are constant with time. In terms of dynamic problems, vibrations in solids are known to damp with time. In a sense, there appears a viscous effect in the solid. A solid can exhibit such a time effect but remains elastic. In reality, there may be some permanent deformation remains in the body, depending on the magnitude of the excitations. The theory of viscoplasticity was introduced in Section 5.17. However, if such permanent deformation is relatively small, we can model it as viscoelastic. That is, when the excitation is removed, the body returns to its original shape and size. Theoretical formulation that deals with such a viscoelastic body is called viscoelasticity. There are two extremes of viscoelasticity: if viscous response is negligible, the solid is purely elastic; if the elastic response is negligible, the material is a viscous fluid. Time-dependent creeping has been reported in both rock and soil slopes, and deformation in excavated tunnels is often found to increase with time. There have been many examples of delayed geomechanical failure after loadings have been applied. Therefore, viscoelasticity finds its application in many applications in geotechnical problems. A special feature of viscoelastic solids is that their present state of deformation cannot be determined if their entire loading history is not known. In other words, a viscoelastic body appears to have memory of its entire past. Because of this the deformation of viscoelastic solid at time t must be summed from its total loading history. In the case of stress relaxation (i.e., imposing strain as a controlling parameter), the current stress is a function of the current strain as well as its entire strain history. In the case of creeping (i.e., imposing stress as a controlling parameter), the current deformation is a function of the current stress as well as its entire stress history. If the loading is applied at a different rate, clearly because of this memory effect, the response of a viscoelastic solid will also change. Therefore, viscoelastic solids should also be considered rate sensitive. The actual micromechanism for such a time-dependent effect is still a mystery in most materials. If a solid is purely elastic, its response should not depend on how its current state is attained through its loading history. In a sense, there must be some irreversible processes involved in the deformation process. Energy must have been dissipated because as viscous effect is involved. Therefore, viscoelasticity has been linked to entropy evolution through irreversible thermodynamics (Fung, 1965). These irreversible processes have been modeled by using hidden state variables and their associated generalized forces. However, such models will not be considered here.
