  A unified framework for analyzing the existence of ground states in wide
classes of elastic complex bodies is presented here. The approach makes use of
classical semicontinuity results, Sobolev mappinngs and Cartesian currents.
Weak diffeomorphisms are used to represent macroscopic deformations. Sobolev
maps and Cartesian currents describe the inner substructure of the material
elements. Balance equations for irregular minimizers are derived. A
contribution to the debate about the role of the balance of configurational
actions follows. After describing a list of possible applications of the
general results collected here, a concrete discussion of the existence of
ground states in thermodynamically stable quasicrystals is presented at the
end.
