Elasticity energy density

This behavior is similar to the cut growth and fatigue behavior of rubber compounds. The rate of the growth of a cut is a function of the tearing energy [38,39] which itself is proportional to the stored elastic energy density in the test piece. The exact value depends on the shape of the test piece. 

Notice the splitting of the (isotropic) By l in the two parts Bv 2 and Be 2. A similar splitting occurs for the elastic energy density, of course ... 

The craze is modeled by an elastic anisotropic medium with Young s moduli i and 2 corresponding to the stiffness of the cross-tie and the main fibrils ( 1 2). As the strip thickens along the direction 2 (Fig. 4b), the elastic energy density W is stored so that the energy release rate at failure... 

Noticing that the elastic energy density is ( -44/2)1, you may obtain this band-structure contribution to 44, to be compared with the experimental —12.0 x 10" crg/cm. ... 

The scaling law in Eq. (10-33) was predicted by Marrucci (1984) by assuming that the disclination density at steady state is set by a balance between the viscous energy density r]Y and the Frank elastic energy density K ja. Since the areal density pa is proportional to Pvh a h/a, this balance is... 

Figure 3. Elastic energy density in eV/nm for the various islands, displayed in a cross-sectional view. Left column uniform distribution. Right column after MC-FEM. Notice that a different scale is used for islands and substrate. In the figure only, we inserted a void region between island and substrate in order to facilitate the distinction between the island andthe substrate behavior.

Eq. (7.43)]. Explain why the stretching caused by isotropic swelling increases the contribution to the modulus from each combined strand. Why can the elastic modulus be approximated by an elastic energy density ... 

Type (Specific) Maximum strain (%) Maximum pressure (MPa) Specific elastic energy density (j Elastic energy density (J cm ) Coupling efficiency (%) Maximum efficiency (%) Specific density Relative speed (full cycle) Ref. 

This equation considers that both the expansion and contraction in an actuation cycle can exert work. Similarly, the elastic energy density is given by ... 

CNT-polymer composites at very low nanotube loadings exhibit substantial electrostrictive strains when exposed to an electric field that is dramatically lower than that required by neat polymers. Zhang et al. have shown that the crystallinity. Young s modulus, dielectric constant, electrostrictive strain, and elastic energy density of electrostrictive poly(vinylidene fluoride-trifluor-oethylene-chlorofluoroethylene) P(VDF-TrFE-CFE)] can be simultaneously improved by inclusion of only 0.5 wt% of MWNTs. At an applied electric field of 54 MV m the 0.5 wt% nanocomposite generates a strain of 2%, which nearly doubles that of pure P(VDF-TrFE-CFE) polymer. 

In thin film, the relation between film thickness (h) and the size of TFCD, specifically its lateral diameter (2r) is well estabhshed by Fournier et al. [46] and The total energy of FCD results from a balance between the elastic energy density of LC, AFei, and the surface energy at both the air and substrate interfaces... 

The elastic energy density Us of the dielectric elastomer is calculated as follows [Pelrine et al. (2000)] ... 

The elastic energy density averaged over the x,y-plane reads ... 

By introducing the twist, the bend elastic can be reduced, but the trade-off is that the twist elastic energy is increased. The change of the elastic energy density [Eq. (1.146) subtracted by Eq. (1.131)] is... 

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