Mechanical Properties of Hair 236 the consumer. Bending results in a combination of extensional and compressional strains, while twisting results in shearing strains in a fiber. The relevant modulus of elasticity for twisting is the shear modulus, G. These properties are much more complex to measure than extensional properties, but the effort may be justified because of their contribution to consumer relevant hair behavior. Bogaty46 first pointed out how important the behavior of hair under torsional and bending strains is to both water setting and permanent waving of hair, and introduced the idea of a torsional spring model for a hair curl. The stiffness of a spring depends on the torsional and bending moduli of the material which the spring is formed from, so the appearance, feel, and response of a hair curl to deformation will depend on these properties as well. (Refer to Chapter 5, Figure 3 and Eq. 2 for more details.) Bending properties of hair have long been recognized to contribute to consumers’ perception of hair “body.”47-49 Response to torsion or bending stress is highly dependent on hair diameters as both the bending and torsional moments of inertia depend on the fourth power of cross-sectional dimensions as we will see. Because of this extreme dependence on cross- sectional dimensions, the cuticle is expected to contribute more to torsion or bending stiffness than to tensile strength, especially with very fine hairs. Bogaty46 reported that permanent waving decreased the torsional rigidity of hair in the wet state but increased it slightly at 65% RH. Harper and Kamath50 reported that at low RH the shear modulus of bleached hair was higher than untreated hair, but above 70% RH the shear modulus of bleached hair was lower than that of untreated hair. The most convenient way to measure the reaction of a fiber to shearing stresses is with a torsion pendulum. In this type of apparatus a small cylindrical weight is hung from the fiber and a small torque is applied to the weight to start it rotating back and forth. The weight is then allowed to rotate freely with no further applied torque. Within a certain range the period of rotation depends only on the shear modulus of the hair and not on the amplitude