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The discrete modeling of a large class of mechanical structures can be basedon a stick-and-spring concept. We here present a stick-and-spring theory withpotential application to the statics and the dynamics of such nanostructures asgraphene, carbon nanotubes, viral capsids, and others. A key feature of ourtheory is its geometrical nonlinearity: we combine exactly defined strainmeasures with a general linear stress response; another, rarely found featureis a careful account of prestress states. A linear version is firstly proposed,where attention is restricted to study small displacements from an unstressedreference placement. Next, a theory linearized about a prestressed (preloadedor not) placement is displayed, which is based on a careful analysis of thetangent stiffness operator and its two parts, the elastic and prestressstiffness operators. Finally, two examples are proposed and solved; when ananalytical solution is of prohibitive complication, numerical solutions aregiven, by the use of a specifically implemented `stick-and-spring' code.

A Nonlinear Theory of Prestressed Elastic Stick-and-Spring Structures