A Korn-type inequality in SBD for functions with small jump sets - Friedrich, Manuel (Mathematical Models & Methods in Applied Sciences, 2017)
We present a Korn-type inequality in a planar setting for special functions of bounded deformation. We prove that for each function in SBD2 with a sufficiently small jump set the distance of the function and its derivative from an infinitesimal rigid motion can be controlled in terms of the linearized elastic strain outside of a small exceptional set of finite perimeter. Particularly, the result shows that each function in SBD2 has bounded variation away from an arbitrarily small part of the domain.
CRIS-Team Scopus Importer:2021-10-21
Keywords: brittle materials; Functions of bounded deformation; Korn's inequality; Korn-Poincaré inequality; variational fracture