Rigidity and functional properties of BDdev()
Abstract
We provide a structural analysis of the space of functions of bounded deviatoric deformation, BDdev, which arises in models of plasticity and fluid mechanics. The main result is the identification of the annihilator and a rigidity theorem for BDdev-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 and homogenization problems, allowing for integrands with explicit dependence on u as well as Ed u. Our approach overcomes several difficulties as compared to the BD case, in particular due to the lack of invariance of Ed under orthogonalization of the polar directions. Applications to integral representation and Material science are discussed.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.