Anelastic

N. G. McCmm, B. E. Read, and G. WiUiams, Anelastic and Dielectric Effects in Polymer Solids,]ohxs Wiley Sons, Inc., New York, 1967. 

G.E. Duvall, Propagation of Plane Shock Waves in a Stress-Relaxing Medium, in Stress Waves in Anelastic Solids (edited by H. Kolsky and W. Prager), Springer-Verlag, Berlin, 1964, pp. 20-32. 

Finally, Fig. 8.3 shows a third form of elastic behaviour found in certain materials. This is called anelasfic behaviour. All solids are anelastic to a small extent even in the regime where they are nominally elastic, the loading curve does not exactly follow the unloading curve, and energy is dissipated (equal to the shaded area) when the solid is cycled. Sometimes this is useful - if you wish to damp out vibrations or noise, for example you... 

Fig. 8.3. Stress-strain behaviour for an anelastic solid. The axes are calibrated for fibreglass.

Nowick, A.S. and Berry, B.S. (1972) Anelastic Relaxations in Crystalline Solids (Academic Press, New York). 

Zener, C. (1948) Elasticity and Anelasticity of Metals (The University of Chicago Press, Chicago). 

McCrum, N.G., Read, B.E. and Williams, G. (1967) Anelastic and Dielectric Effects in Polymeric Solids (Wiley, London and New York) (Reprinted in 1991 by Dover). 

For a Hookian material, the concept of minimum strain energy states that a material fails, for example cell wall disruption occurs, when the total strain energy per unit volume attains a critical value. Such an approach has been used in the past to describe a number of experimental observations on the breakage of filamentous micro-organisms [78,79]. Unfortunately, little direct experimental data are available on the Young s modulus of elasticity, E, or shear modulus of elasticity G representing the wall properties of biomaterial. Few (natural) materials behave in an ideal Hookian manner and in the absence of any other information, it is not unreasonable to assume that the mechanical properties of the external walls of biomaterials will be anisotropic and anelastic. 

This apparent time dependent cell disruption is caused because of the statistically random distribution of the orientation of the cells within a flow field and the random changes in that distribution as a function of time, the latter is caused as the cells spin in the flow field in response to the forces that act on them. In the present discussion this is referred to as apparent time dependency in order to distinguish it from true time-dependent disruption arising from anelastic behaviour of the cell walls. Anelastic behaviour, or time-dependent elasticity, is thought to arise from a restructuring of the fabric of the cell wall material at a molecular level. Anelasticity is stress induced and requires energy which is dissipated as heat, and if it is excessive it can weaken the structure and cause its breakage. 

The effects of anelasticity are seen clearly in the strain-time schematic plot of Fig. 7. The time independent strain, 0, occurs immediately as the stress is apphed. The additional strain, o, is associated with stress-induced anelasticity. The total strain, -i- o, is approached exponentially. When the stress is removed the time independent strain is recovered immediately, while the anelastic component relaxes exponentially with a relaxation time constant, k. 

If the material is anelastic, the stress and the strain will not coincide. The strain will lag behind by an amount which is determined by the phase angle, ( ). Thus ... 

McCrum NG, Read BE, Willianis G (1967) Anelastic, dielectric effects in polymeric... 

When y radiation hits an electron, it is deviated from its original trajectory and, losing energy, changes its frequency. The increase in frequency consequent upon anelastic scattering is only a function of the angle between incident and deflected rays and does not depend on the energy of the incident radiation. The importance of this fact, known as the Compton effect, increases as the atomic number of the element decreases. 

We also compared two sets of specimens that had been drawn to the same extent. Both were allowed to relax for 48 h after stretching, one set clamped at its specified elongation, the other allowed to relax freely, undamped. The dichroism results show a large difference between the recoverable (elastic+anelastic) deformation and the total deformation for both XL and NXL phases (see Ligures 3 and 4 of Davidson and Gounder ). 

Figure 14-5. Anelastic strain as a function of time 1) for a given load and 2) after removal of the load.

Figure 14-5 defines the creep below the critical shear stress. It is called anelastic creep and is to a large extent recoverable. The anelastic strain for a given stress below °crk approaches its equilibrium value u0 as... 

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