  Problems of flexible mechanical metamaterials, and highly deformable porous
solids in general, are rich and complex due to nonlinear mechanics and
nontrivial geometrical effects. While numeric approaches are successful,
analytic tools and conceptual frameworks are largely lacking. Using an analogy
with electrostatics, and building on recent developments in a nonlinear
geometric formulation of elasticity, we develop a formalism that maps the
elastic problem into that of nonlinear interaction of elastic charges. This
approach offers an intuitive conceptual framework, qualitatively explaining the
linear response, the onset of mechanical instability and aspects of the
post-instability state. Apart from intuition, the formalism also quantitatively
reproduces full numeric simulations of several prototypical structures.
Possible applications of the tools developed in this work for the study of
ordered and disordered porous mechanical metamaterials are discussed.
