MESH COLLAPSE IN 2-DIMENSIONAL ELASTIC NETWORKS UNDER COMPRESSION

We consider two-dimensional triangular networks of beads connected by Hookean tethers under isotropic compression. We determine both the com pression and the shear modulus as a function of temperature and compre ssion within simple approximations and by a Monte Carlo simulation. At low temperature, this network undergoes a collapse transition with in creasing compression. In the two phase region, collapsed and non-colla psed triangles coexist. While the compression modulus vanishes in the two phase region, the shear modulus shows only a small anomaly at the transition. With increasing temperature, this transition disappears in our simulation. Anharmonic shear fluctuations invalidate a harmonic a nalysis in large regions of the phase space. In application to the red blood cell membrane, we obtain good agreement with more microscopic m odels for the shear modulus. Our results also indicate that strong com pression will lead to non-trivial elastic behavior of the cell membran e.