Network with six-fold symmetry under stress (contd...)

The elastic modulii of the stressed equilateral triangle can be obtained by applying an incremental stress  on the isotropically stressed network and then measuring the incremental strain . In essence we can differentiate the area per vertex of the stressed triangle  with respect to , which yields,

(38.9)

Hence, the incremental strain in the area is given as,

(38.10)

Rearranging, we obtain a linear relation between the incremental stress and incremental strain with a material constant which depends upon the applied stress  on the network,

(38.11)

Here  is the effective area compression modulus of the network. We can then obtain an expression of strain energy per vertex of this network as each chain of the equilateral triangle is extended by an incremental amount ,

(38.12)

Notice that vanishes at suggesting our earlier result that area per vertex grows without bound as the stress increases. This result, however, does not capture the network collapse for negative , i.e. for compression.