This chapter takes lattice models to more general settings. There are four themes: rigidity, randomness, dynamics, and optimality. The first two of these involve the introduction of spatial randomness into a lattice as a departure from an originally periodic geometry of, say, the central-force triangular network of Chapter 3. One path is through a random depletion of bonds, which leads to a total loss of stiffness, or rigidity, of the lattice. Another way of creating a random lattice is through a random (instead of a regular) network of, say, a Poisson-Delaunay variety. The third theme considered here is a generalization from statics to dynamics, with nodes acting as quasi-particles-here we have a coarse scale cousin to molecular dynamics, and, at the same time, an alternative to finite element methods. Finally, the fourth topic is that of optimal use of material for given loading and support conditions, where a special case of central-force lattices arises, Michell trusses being the basic paradigm.

4.1.1 Structural Topology and Rigidity Percolation