A unified framework for analyzing the existence of ground states in wideclasses of elastic complex bodies is presented here. The approach makes useof classical semicontinuity results, Sobolev mappings and Cartesiancurrents. Weak diffeomorphisms are used to represent macroscopicdeformations. Sobolev maps and Cartesian currents describe the innersubstructure of the material elements. Balance equations for irregularminimizers are derived. A contribution to the debate about the role of thebalance of configurational actions follows. After describing a list ofpossible applications of the general results collected here, a concretediscussion of the existence of ground states in thermodynamically stablequasicrystals is presented at the end.
