ABSTRACT
Spring network (or lattice) models are based, in principle, on the atomic lattice models of materials. These models work best when the material may naturally be represented by a system of discrete units interacting via springs, or, more generally, rheological elements. It is not surprising that spatial trusses and frameworks have been the primary material systems thus modeled. Spring networks can also be used to model continuum systems by a lattice much coarser than the true atomic one. In engineering mechanics that idea dates back, at least, to Hrennikoff (1941), if not to Maxwell (1869), in a special setting of optimal trusses. This obviates the need to work with an enormously large number of degrees of freedom that would be required in a true lattice model, and allows a very modest number of nodes per single heterogeneity (e.g., inclusion in a composite, or grain in a polycrystal). As a result, spring networks are a relative of the much more widespread finite element method. In this chapter we focus on basic concepts and applications of spring networks, in particular to antiplane elasticity, planar classical elasticity, and planar nonclassical elasticity. The chapter ends with an additional section on the mechanics of a helix, a 1D nonclassical continuum.
