Preprint

Inserted: 26 jun 2015
Last Updated: 26 jun 2015

Year: 2015

Abstract:

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 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.

Keywords: Functions of Bounded Deformation, Korn's inequality, Brittle materials, variational fracture , Korn-Poincare inequality

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• SBD_korn.pdf