Rigidity and Functional Properties of BDdev(Ω )

We provide a structural analysis of the space of functions of bounded deviatoric deformation, BDdev BD dev , which arises in models of plasticity and fluid mechanics. The main result is the identification of the annihilator and a rigidity theorem for BDdev BD dev -maps with constant polar vector in the wave cone characterizing the structure of singularities for such maps. This result, together with an explicit kernel projection operator, enables an iterative blow-up procedure for relaxation, homogenization, and integral representation problems, allowing for integrands with explicit dependence on u as well as Ed u E d u . Our approach overcomes several difficulties as compared to the BD BD case, in particular due to the lack of invariance of Ed E d under orthogonalization of the polar directions.