The elastic constants of isotropic media at small strains

1 The elastic constants of isotropic media at small strains 

As stated above. Young s modulus E is defined by the equation 

By assuming the linearity of response of the material and considering the effect of applying a tensile stress cr in all three directions simultaneously, which is equivalent to applying a pressure —cr, it can be shown (see example 6.1) that 

The shear (or rigidity) modulus G is defined in terms of the shear strain 6 produced by the shear stresses a, shown in fig. 6.4 (where 9 is assumed to be very small), so that 

Like the bulk modulus, G can also be related to Young s modulus and Poisson s ratio (see problem 6.1). The relationship is 

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