Scaling Theory of Elasticity and Fracture in Disordered Networks

We discuss scaling theories for the elasticity and tensile fracture of random central force spring networks with bond dilution disorder. Effective medium theory works quite well for elasticity but needs very new ingredients to be even qualitatively correct for tensile fracture. A novel “extreme scaling theory” predicts a dilute limit singularity and a size effect in the tensile strength. These predictions are supported by numerical simulations.We extend the above arguments to networks with distributions of bond disorder, and compare the central force network theories to models currently used in the study of rigid cellular materials.