Influence of randomness in topology, geometry and material properties on the mechanical response of elastic central-force networks

• There is a strong correlation between the lattice network's mechanical response and the two model parameters of the Ising model with fixed “magnetization”.
• The results suggests that topology should be one of the primary subjects of investigations regarding general networks.
• Similar results were observed by reinterpreting the results in terms of mean relative direction γ   and variance of the node degree σf2.

We show that topological features have strong influence on the mechanical response of random elastic networks. In the simple case of a planar central force network under uni-axial compression, we vary first randomly topological characteristics under the condition that the numbers of nodes and edges in the network are fixed. Subsequently, we vary simultaneously topology and geometry and topology and local stiffness, respectively. It turns out that the characteristics related to topology determine the major trend in the mechanical behavior while randomness in geometry and local stiffness plays a minor role.