Curvature coupling

W.W. (2003) Imaging coexisting fluid domains in biomembrane models coupling curvature and line tension. Nature, 425 (6960), 821-824. 

Coupling n The linking of a side effect to a principal effect. For composites an anisotropic laminate couples the shear to the normal components, while an unsymmetric one couples curvature with extension. Poisson coupling links lateral contraction to axial extension. The joining together of two or more polymer molecules, which contain terminal chemically reactive groups, by reaction with a third, usually small, molecule capable of reaction with the polymer functional groups which are normally the same. 

Textile fibers must be flexible to be useful. The flexural rigidity or stiffness of a fiber is defined as the couple required to bend the fiber to unit curvature (3). The stiffness of an ideal cylindrical rod is proportional to the square of the linear density. Because the linear density is proportional to the square of the diameter, stiffness increases in proportion to the fourth power of the filament diameter. In addition, the shape of the filament cross-section must be considered also. For textile purposes and when flexibiUty is requisite, shear and torsional stresses are relatively minor factors compared to tensile stresses. Techniques for measuring flexural rigidity of fibers have been given in the Hterature (67—73). 

Classical solutions to laminated shell buckling and vibration problems in the manner of Chapter 5 were obtained by Jones and Morgan [6-47]. Their results are presented as normalized buckling loads or fundamental natural frequency versus the Batdorf shell curvature parameter. They showed that, for antisymmetrically laminated cross-ply shells as for plates, the effect of coupling between bending and extension on buckling loads and vibration frequencies dies out rapidly as the number of layers... 

The effect of the specific values of the B j can be readily calculated for some simple laminates and can be calculated without significant difficulty for many more complex laminates. The influence of bending-extension coupling can be evaluated by use of the reduced bending stiffness approximation suggested by Ashton [7-20]. If you examine the matrix manipulations for the inversion of the force-strain-curvature and moment-strain-curvature relations (see Section 4.4), you will find a definition that relates to the reduced bending stiffness approximation. You will find that you could use as the bending stiffness of the entire structure,... 

The distinguishing performance characteristic of the torque converter, in contrast to the fluid coupling, is that It IS capable of multiplying torque. Torque multiplication is made possible by vane curvature and the presence of the reactor. When the converter is stalled—that is, the turbine and the reactor are stationary—the torque delivered to the gearbox is typically 2... 

Fig. 2.4 BPM simulation results for polymer microring resonators (a) Round trip attenuation vs. the core cladding index contrast and radius of curvature, (b) Coupling induced attenuation vs. the length and gap of the coupler. The width and height of the waveguide is 2 pm. The wavelength used in the calculations is 1.55 pm. Reprinted from Ref. 15 with permission. 2008 Institute of Electrical and Electronics Engineers...

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