Relationships Between Elastic Constants

(from Fung, A First Course in Continuum Mechanics)

Although only 2 independent elastic constants are required to completely the properties of an isotropic, elastic medium, there are many different constants from which to choose. Most of these constants arise as constants of proportionality between stress and strain for various loading conditions. For example, the ratio of hydrostatic stress (pressure) to volumetric strain (dilatation) is lam_mu.gif (1018 bytes), which is given the name bulk modulus and the symbol k.gif (897 bytes). The constants referred to below are:

elast1.gif (2700 bytes)

elast2.gif (2380 bytes)

elast3.gif (2267 bytes)

elast4.gif (2855 bytes)

elast5.gif (2414 bytes)

To these we may add the following combinations that appear frequently.

 elast6.gif (1553 bytes)