Energy storage and dissipation

In particular it can be shown that the dynamic flocculation model of stress softening and hysteresis fulfils a plausibility criterion, important, e.g., for finite element (FE) apphcations. Accordingly, any deformation mode can be predicted based solely on uniaxial stress-strain measurements, which can be carried out relatively easily. From the simulations of stress-strain cycles at medium and large strain it can be concluded that the model of cluster breakdown and reaggregation for prestrained samples represents a fundamental micromechanical basis for the description of nonlinear viscoelasticity of filler-reinforced rubbers. Thereby, the mechanisms of energy storage and dissipation are traced back to the elastic response of tender but fragile filler clusters [24]. 

Figure 9.6 Depiction of interaction of electric and magnetic fields of incident signals with EMI shield leading to energy storage and dissipation.

The major types of adipose tissue are (1) white adipose tissue, which manufactures, stores, and releases lipid and (2) brown adipose tissue, which dissipates energy via uncoupled mitochondrial respiration. Obesity research includes evaluation of the activity of adrenergic receptors and their effect on adipose tissue with respect to energy storage and expenditure or thermogenesis. 

Slip is not always a purely dissipative process, and some energy can be stored at the solid-liquid interface. In the case that storage and dissipation at the interface are independent processes, a two-parameter slip model can be used. This can occur for a surface oscillating in the shear direction. Such a situation involves bulk-mode acoustic wave devices operating in liquid, which is where our interest in hydrodynamic couphng effects stems from. This type of sensor, an example of which is the transverse-shear mode acoustic wave device, the oft-quoted quartz crystal microbalance (QCM), measures changes in acoustic properties, such as resonant frequency and dissipation, in response to perturbations at the surface-liquid interface of the device. 

Polyurethanes have a combination of elastic and viscous properties that can be explained in standard engineering terms using DMA methods. Information can be obtained on the properties of polyurethanes that relates to the storage and dissipation of energy applied during use. 

It will be seen in Chapter 3 that many perturbations affect wave propagation. In general, perturbations change both energy storage and power dissipation and thus result in a combination of velocity and attenuation changes. The manner in which the propagation of the wave is described is therefore important and will be discussed here briefly. 

In Section 3.2.4 we considered the effects of an ideal mass layer on SAW response. In the model used to derive the mass-loading response, the layer was assumed to be (1) infinitesimally thick, and (2) subject only to translational motion by the SAW. Translational motion was found to induce a change in SAW velocity proportional to the areal mass density (pfc) contributed by the film — the mass loading response. Since no power dissipation arises in film translation, no attenuation response was predicted. With an actual film having finite thickness and elastic properties, it is important to also consider the effects of SAW-induced film deformation. Energy storage and power dissipation due to film deformation cause additional contributions to SAW velocity and attenuation that were neglected in the earlier treatment. 

Structured gel and emulsion formulations, designed to suspend particles or oils, are generally viscoelastic. They have both viscous and elastic properties. Such formulations are characterized by their elastic modulus (( ) and loss modulus (G"). The elastic modulus (elastic component) is a measure of energy storage and the loss modulus (viscous component) is a measure of energy dissipation. For viscoelastic fluids G > G" and for viscous fluids G < G". For a suspension or emulsion to be stable G should be greater than G" over the range of temperature required for stability. 

The dynamic modulus E (or G ), which is the real component of E (or G ), is associated with energy storage and release in the periodic deformation and is therefore called the storage modulus. The imaginary part of the modulus, E" (or G"), is associated with viscous energy dissipation and is a measure of the energy lost per cycle per unit volume ( g), since... 

Considerable information about elastic and viscoelastic parameters may be derived by measuring the response of a polymer to a small-amplitude cyclic deformation. Molecules perturbed in this way store a portion of the imparted energy elastically, and dissipate a portion in the form of heat (Ferry, 1970 Meares, 1965 Miller, M. L., 1966, pp. 243-253 Nielsen, 1962, Chapter 7 Rosen, 1971 Schultz, 1974, pp. 67-71 Williams, D. J., 1971), the ratio of dissipation to storage depending on the temperature and frequency. In dynamic mechanical spectroscopy experiments, a cyclic stress is applied to a specimen, and two fundamental parameters are measured the storage modulus E a measure of the energy stored elastically, and the loss modulus a measure of the energy dissipated. The loss modulus E" may be calculated as follows ... 

Molecules perturbed in this way store a portion of the imparted energy elastically and dissipate a portion in the form of heat (1-4). The quantity E, Young s storage modulus, is a measure of the energy stored elastically, whereas E", Young s loss modulus, is a measure of the energy lost as heat (see Rgure 8.6) (22). 

The storage and dissipation of energy is also discussed in exercise 26. 

The real part is defined as the storage modulus, E (o>), and the imaginary part is defined as the loss modulus , E (oi). It will be shown later that these respective quantities can be related to the energy stored and dissipated in a loading cycle. 

It is useful to note that the dynamic behavior of any system that incorporates both energy storage and energy dissipation must have at least one characteristic time. Another example is an electrical circuit that includes both resistance and capacitance. Furthermore, we note that Eq. 4.15 is the same as Eq. 4.12, with Fq replaced by Gq and % by T. The Maxwell element is thus said to be a mechanical analog of the viscoelastic behavior described by Eq. 4.12. It will often prove useful in our discussion of the linear viscoelastic behavior of polymers to refer to the viscoelastic analog of the Maxwell element. 

---