Abstract
We study how the rigidity transition in a triangular lattice changes as a
function of anisotropy by preferentially filling bonds on the lattice in one
direction. We discover that the onset of rigidity in anisotropic spring
networks arises in at least two steps, reminiscent of the two-step melting
transition in two dimensional crystals. In particular, our simulations
demonstrate that the percolation of stress-supporting bonds happens at
different critical volume fractions along different directions. By examining
each independent component of the elasticity tensor, we determine universal
exponents and develop universal scaling functions to analyze isotropic rigidity
percolation as a multicritical point. We expect that these results will be
important for elucidating the underlying mechanical phase transitions governing
the properties of biological materials ranging from the cytoskeletons of cells
to the extracellular networks of tissues such as tendon where the networks are
often preferentially aligned.