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