Rigidity and functional properties of $\mathrm{BD}_{dev}(\Omega)$
Abstract
We provide a structural analysis of the space of functions of bounded deviatoric deformation, , which arises in models of plasticity and fluid mechanics. The main result is the identification of the annihilator and a rigidity theorem for -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 as well as . Our approach overcomes several difficulties as compared to the case, in particular due to the lack of invariance of under orthogonalization of the polar directions. Applications to integral representation and Material science are discussed.
Cite
@article{arxiv.2505.23348,
title = {Rigidity and functional properties of $\mathrm{BD}_{dev}(\Omega)$},
author = {Marco Caroccia and Nicolas Van Goethem},
journal= {arXiv preprint arXiv:2505.23348},
year = {2025}
}