Anelastic behaviour

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. 

Viscoelastic materials can follow at least three different behaviors, i.e. linear vis-coleasticity, nonlinear viscoelasticity and anelastic behaviour. 

Dynamic mechanical analysis (DMA) is a suitable technique that allows the characterisation of the solid-state rheological behaviour of materials, including biomaterials , in a broad temperature and frequency ranges. Specifically, this technique has been used in the characterisation of bone cements or hydrogels ". Such materials display usually an anelastic behaviour and DMA is able to monitor the complex mechanical modulus (E = E + E where E" is the storage modulus and E is the loss modulus, and the complex compliance (D - D - iD ). The loss factor, tan 6 = EVE = D D , measure the damping capability of the material. 

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.

Fig. 2 Typical stress-strain curves for amorphous polymers, a Elastic, anelastic, strain softening, and plastic flow regions can be seen, b Plastic flow occurs at the same stress level as required for yielding so strain softening does not exist, c Strain hardening occurs very close to yielding, suppressing both strain softening and plastic flow behaviour...

These last numerical results show that the plastic strain is obviously greatly influenced by the presence of the creep/relaxation phenomenon. In fact, the level of the plastic strain was considerably reduced from 0.004 to 0.0018, i.e a reduction ratio of 2.2 based on the reference case (Figure 6), which does not take into accormt creep behaviour of the ramming paste. Also, the anelastic strain level at the end of the simulation (i = 40 hours) is almost negligible compared to the other strains (e.g., plastic, thermal, etc.). This result directly ensues from the assumption that the baked ( = 1) ramming p>aste creep/relaxation behaviour is similar to that of the carbon cathode block (Richard et al., 2006). This case study thus shows the importance of taking all the relevant phenomena including creep behaviour into account in similar problems. A similar analysis could be done for all other deformations (chemical, thermal, plastic, etc.). 

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