Stored energy density

Like with its linear elastic counterpart, the stored energy density W(F) at a given point depends only upon the deformation gradient F at that point. 

From Figure 7.5, it is estimated that the stored energy density is about 8.32MJ/m for the coated SMPF and 5.50MJ/m for the uncoated SMPF, which are higher than the SMA wire used in Reference [3], that is, 0.5 X (240 MPa) X (2.3%) = 2.76 MJ/m. Therefore, it is expected that the SMPF will have better crack closing ability than the SMA wire. 

From Eq. 9.2, the following relationship can be deduced D = 8qE + P (Eq. 3.5), it is valid also for nonisotropic, nonlinear materials. Other equations derivable from the Maxwell s equations for linear and isotropic materials are, for example, Ohm s law J = aE, the power density law (Joule heat) Wy = ct E [watt/m ], and the stored energy density law Ey = /zE-D [joule/m ]. Maxwell s equations are valid for all kinds of electromagnetic radiation and contain the speed of light in the fourth equation (Eq. 9.4) (in another version than Minkowski s). Heaviside played a special role in the development of the Maxwell equations (see Chapter 11). 

Continuum theory generally employs a unit vector field n(x) to describe the alignment of the anisotropic axis in nematic liquid crystals, this essentially ignoring variations in degrees of alignment which appear to be unimportant in many macroscopic effects. This unit vector field is frequently referred to as a director. In addition, following Oseen [1] and Frank [4], it commonly assumes the existence of a stored energy density W such that at any point... 

Let the stored energy density at a point be given by the quadratic form (see Sect. 1.3) ... 

From (1.8.1, 5) we have for the stored energy density, omitting explicit space dependence ... 

In this deformation, the average value of the stored energy density is... 

For metallic conductors, the capacitance is on the order of a few tens of /iF per cm . In order to achieve significant stored energy density, very high surface-area electrodes must be employed. This raises problems of distributed charging processes, which will be addressed in a later section. 

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