Bulk Compression or Dilatation

If the dimensions of an isotropic cubical element are increased or decreased uniformly by application of normal forces on all faces (Fig. 1-13), ffn = 0-22 = (T33 = —P, the hydrostatic pressure, and all other stress components are zero and the three jkk are equal. Equation 42 then becomes 

A calculation corresponding to that of equations 10 and 12 will provide the time dependence of pressure following a sudden voluminal deformation. For this purpose, the voluminal strain may be defined as the relative change in volume, 

For very small strains, this is i 2 7, the so-called dilation A for compression, A is negative. After an initial change accomplished within a very small time interval at t = 0, we have by an operation analogous to the derivation of equation 12  

Bulk compression would not be expected to involve changes in long-range molecular configuration or contour shape, and in fact the differences between polymers and ordinary liquids and solids are not so striking in compression as in shear. 

The subscript T in the above partial derivative implies an isothermal measurement, and indeed all of the experimental examples given here are supposed to be carried out isothermally. The relation between isothermal and adiabatic moduli is considered in Chapter 5. 

---