Elasticity nonideal

Fig. 2.6. Observed wave forms in the elastic-plastic regime are quite diverse representing nonideal elastic and viscoplastic behaviors (after Davison and Graham [79D01]).

The piezoelectric response investigation also provides direct evidence that significant inelastic deformation and defect generation can occur well within the elastic range as determined by the Hugoniot elastic limit. In quartz, the Hugoniot elastic limit is 6 GPa, but there is clear evidence for strong nonideal mechanical and electrical effects between 2.5 and 6 GPa. The unusual dielectric breakdown phenomenon that occurs at 800 MPa under certain... 

The concept of a welt defined elastic range to large strain is not realistic. The concept of well defined stress at which mechanical yielding occurs leading to well defined elastic-inelastic conditions is not realistic. Actually, such conclusions could well be anticipated from strength studies at atmospheric pressure, but there has been little explicit reason to consider the nonideal effects from the mechanical-response shock studies. 

Note that the preceding equation is for ideal cases, in which the particles are monodis-persed, spherical, and totally elastic, and the contact surface is clean. In practice, the particles are usually nonspherical and polydispersed the collision could have involved some heat loss, plastic deformation, or even breakup and the contact surface may have impurities or contaminants. In these cases, a correction factor tj is introduced to account for the effects of these nonideal factors. The applicable form of the electric current through the ball probe is, thus, given by... 

Relevance of Nonideal Elasticity (Hysteresis) to Efficient Performance of Mechanical Work... 

To account for the nonideal nature of real soUds and liquids, the theory of Unear viscoelasticity provides a generaUzation of the two classical approaches to the mechanics of the continuum-that is, the theory of elasticity and the theory of hydromechanics of viscous Uquids. Simulation of the ideal boundary properties elastic and viscous requires mechanical models that contain a combination of the ideal element spring to describe the elastic behavior as expressed by Hooke s law, and the ideal element dash pot (damper) to simulate the viscosity of an ideal Newton Uquid, as expressed by the law of internal friction of a liquid. The former foUows the equation F = D -x (where F = force, x = extension, and D = directional force or spring constant). As D is time-invariant, the spring element stores mechanical energy without losses. The force F then corresponds to the stress a, while the extension x corresponds to the strain e to yield a = E - e. 

Plots of cr/(a- 1/a ) versus Ha are found to be linear, especially at low elongation (see Figure 9.15) (57). The intercept on the a = 0 axis yields 2Ci, and the slope yields 2C2. The value of 2Q varies from 2 to 6 kg/cm but the value of 2C2, interestingly, remains constant near 2 kg/cml Appendix 9.2 describes a demonstration experiment that illustrates both rubber elasticity [see equation (9.34)] and the nonideality expressed by equation (9.50). 

Knunyants, N. N., Lyapunova, M. A., Manevich, L. I., Oshmyan, V. G., Shaulov, A. Yu. (1986). The Simulation of Nonideal Adhesional Coupling Influence on Elastic Properties of Particulate-Filled Composite. Mekhanika Kompozitnykh Materialov, 21(2), 231-234. 

In this regard, it is roughly equivalent to an augmentation of the elastic modulus. But another mode of action must be present in nonideal (i.e., real) systems which, because it relates to local stress amplification, should be much more important than the contribution to the (never-observed) ideal strength. Also, this mode of action... 

The idealized laws cannot describe the behavior of matter if the ratios of stress to strain or of stress to rate of strain are not constant (stress anomalies). Plastic deformation is a common example of such nonideal behavior. It occurs for solids if the elastic limit is exceeded and irreversible deformation takes place. Another deviation from ideal behavior occurs if stress depends simultaneously on strain and rate of strain (time anomalies) — i.e., the substance shows both solid and liquid behavior at the same time. If only time anomalies are present, the behavior is called linear viscoelasticity. In this case the ratio of stress to strain is a function of time alone, and not of the stress magnitude. 

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