Non-affinity: The emergence of networks from amorphous planar graphs

The primary research of physics is to reveal the underlying law of the physical world. However, for a complex system consisting of multiple components, even if we know every details of each component, we still cannot predict the collective behavior due to the emergence phenomenon. The amorphous networks of mass points hinged by springs belong to such a complex system. Owing to the non-affinity, one of the emergence phenomena of the network, the displacements field of the internal mass points under the external load tends to be chaotic, and there is no well-established theoretical framework to describe these points’ collective behavior analytically. The non-affine mechanical responses of the amorphous networks are very common, whereas the affine response is rare and it occurs only in those lattices with one site per unit cell. The network’s non-affinity prevents us from further investigating the relationship between its intrinsic properties (such as the contact number, local structure, and topological characteristics) and the mechanical behaviors. As a result, it is very complicated and difficult to predict the responses of an amorphous network to an imposed strain. Interestingly, a sort of amorphous network derived from the jammed particles is reported to have almost perfect affine mechanical behavior, in a stark contrast with the general perception. These findings may shed light on uncovering the structural factors that affect the network’s affinity. This article will give a short review of the latest advances in this area.