PHASE-TRANSITIONS AND ANISOTROPIC RESPONSES OF PLANAR TRIANGULAR NETSUNDER LARGE-DEFORMATION

Responses of triangular networks in large reversible deformation are s tudied analytically at zero temperature and by Monte Carlo simulation at nonzero temperature. Exact expressions for the elastic strain energ y at zero temperature are derived for several models in which the netw ork potential energy depends on either the length of the network eleme nt (i.e., central force interactions) and/or the area of each network triangle. Far nets of Hookean spring elements having a nonzero force-f ree length, cubic terms arise in the strain energy through the sixfold symmetry of the network, and thereby break the symmetric response at small strain. Because of the symmetry of the two-body potential and th e anisotropy of the network, pure compression of the Hookean spring ne t leads to a martensiticlike phase transition at an finite temperature s studied. Networks of elemental tethers or springs that have a zero f orce-free length balanced against a three-vertex potential energy that rises with decreasing triangle area (to emulate volume exclusion in p olymer networks) do not undergo a phase transition, although inclusion of a maximum tether length (to model the polymer chains' contour limi ts) reveals a simple but distinct type of triangular net anisotropy.