Random lattice networks generally exhibit spurious heterogeneity that can overshadow important aspects of material behavior, particularly when modeling fracture in homogeneous materials. This issue is resolved through the innovative use of a crack band model for fracture within the Rigid-Body-Spring Network approach. Analyses of concrete compact tension specimens are conducted to demonstrate model objectivity with respect to size and geometry of the network components. During mode I cracking, fracture energy consumption is uniform along the crack path, independent of the meshing strategy.