Elastic relaxation dissipation process

The question of a mechanically normal behaviour has an analogous bearing upon the range of validity of the linear phenomenological flow equations of irreversible thermodynamics. Somewhere between a normal fluid and a gel there must exist systems which are still fluid but where an elastic relaxation dissipation process invalidates the main assumptions used in both approaches, or makes them incomplete. In such systems, Pick s laws may no longer be vahd. ... 

Because all tissues are viscoelastic this means that their mechanical properties are time dependent and their behavior is characterized both by properties of elastic solids and those of viscous liquids. The classic method to characterize a viscoelastic material is to observe the decay of the stress required to hold a sample at a fixed strain (stress relaxation) or by the increasing strain required to hold a sample at a fixed stress (creep) as diagrammed in Figure 7.1 and explained further in Figure 7.2. Viscoelastic materials undergo processes that both store (elastic) and dissipate (viscous)... 

Many materials, particularly polymers, exhibit both the capacity to store energy (typical of an elastic material) and the capacity to dissipate energy (typical of a viscous material). When a sudden stress is applied, the response of these materials is an instantaneous elastic deformation followed by a delayed deformation. The delayed deformation is due to various molecular relaxation processes (particularly structural relaxation), which take a finite time to come to equilibrium. Very general stress-strain relations for viscoelastic response were proposed by Boltzmann, who assumed that at low strain amplitudes the effects of prior strains can be superposed linearly. Therefore, the stress at time t at a given point in the material depends both on the strain at time t, and on the previous strain history at that point. The stress-strain relations proposed by Boltzmann are [4,39] ... 

Viscoelasticity will clearly have a large effect in some processing operations and little or none in others, and we require a way to discriminate between these cases. One clue follows from the linear viscoelastic experiments shown in Figures 9.2 and 9.3 and the accompanying spectral description in Equations 9.11a-b. The entangled network is able to relax at low frequencies, so the elastic contribution to the stress is negligible and the deformation is mostly dissipative (G 0). The stress at high fre-... 

Notice that an implicit assumption is made that energy is not dissipated in irreversible processes other than fracture. Whatever energy is applied to deform the components is assumed to be fully regained when the deformation is removed. Although this assumption can be relaxed to take into account some plastic or viscous response, the analysis is simpler and more straightforward if the components are ideally elastic. 

The linear elastic analysis of section II predicts infinite stresses at the crack tip (eqn (2.5)). In reality, this divergence is relaxed by the dissipative pull-out process which takes place at the crack tip. The pull-out process is expected to occur in an approximately planar cohesive zone directly ahead of the crack tip. A thorough investigation of cohesive zone models can be found in Eager et al. (1991). See also Xu et al. (1991). 

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