G Shear modulus

F(FG = normal (shear) component of force A = area u(w) = normal (shear) component of displacement o-(e ) = true tensile stress (nominal tensile strain) t(7) = true shear stress (true engineering shear strain) p(A) = external pressure (dilatation) v = Poisson s ratio = Young s modulus G = shear modulus K = bulk modulus. 

In general, CijU is a 9 x 9 tensor with 81 terms, but symmetry reduces this considerably. Thus, for the cubic crystal system, it has only three terms (Cmi, Cm2, and C4444) and for an isotropic material only two terms remain B = bulk modulus and G = shear modulus. A further simplification is that the bulk modulus, B for the cubic system is given by (Cmi + 2Ci2i2)/3, and the two shear moduli are C44 and (Cmi - Ci2i2)/2. 

It is simple to understand the connection between the shear modulus and a. A sphere can be deformed into a prolate ellipsoid either by mechanical stress, or by an electric field. The input work required is measured by G = shear modulus in the first case and by a in the second case. Equating the input work needed in each case and solving for G, yields ... 

G = shear modulus of gel f = friction factor between network and solvent. 

Gg (instantaneous modulus), Hg (residual viscosity) and G (shear modulus) all showed a rapid increase above 30g dm bentonite. This was attributed to the formation of a gel network structure in the continuous medium and the strength of such a gel increased with increase in bentonite concentration. The results could be qualitatively described in terms of the elastic floe model of Hunter and co-workers. Moreover, the settling characteristics of the structured suspensions were found to be consistent with the predictions from the rheological measurements. This demonstrates the value of rheological studies in predicting the longterm physical stability of suspension concentrates. 

Here are 4 - strain, s - stress, t - time, G - shear modulus, f - a form factor for an undefined function A / Lj, g - dimensional constant relating force, m - mass, a - angle. 

In these equations, the subscripts h and s refer to the hard continuous phase and the soft rubbery phase, respectively, E = Young s modulus, G = shear modulus, vh = Poisson s ratio (— 0.35 for polystyrene and most rigid polymers), and cj>8 and h = volume fractions of the components. 

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