A piecewise korn inequality in SBD and applications to embedding and density results

Friedrich M (2018)

Publication Type: Journal article

Publication year: 2018

Journal

SIAM Journal on Mathematical Analysis Society for Industrial and Applied Mathematics

Book Volume: 50

Pages Range: 3842-3918

Journal Issue: 4

DOI: 10.1137/17M1129982

Abstract

We present a piecewise Korn inequality for generalized special functions of bounded deformation (GSBD2) in a planar setting generalizing the classical result in elasticity theory to the setting of functions with jump discontinuities. We show that for every configuration there is a partition of the domain such that on each component of the cracked body the distance of the function from an infinitesimal rigid motion can be controlled solely in terms of the linear elastic strain. In particular, the result implies that GSBD2 functions have bounded variation after subtraction of a piecewise infinitesimal rigid motion. As an application we prove a density result in GSBD2 in dimension two. Moreover, for all d = 2 we show GSBD2(ω) C (GBV (ω; R))d and the embedding SBD2(ω) L1(ω; Rd) → SBV (ω; Rd) into the space of special functions of bounded variation (SBV). Finally, we present a Korn{Poincaŕe inequality for functions with small jump sets in arbitrary space dimension.

Authors with CRIS profile

Manuel Friedrich

Involved external institutions

Westfälische Wilhelms-Universität (WWU) Münster DE Germany (DE)

How to cite

APA:

Friedrich, M. (2018). A piecewise korn inequality in SBD and applications to embedding and density results. SIAM Journal on Mathematical Analysis, 50(4), 3842-3918. https://doi.org/10.1137/17M1129982

MLA:

Friedrich, Manuel. "A piecewise korn inequality in SBD and applications to embedding and density results." SIAM Journal on Mathematical Analysis 50.4 (2018): 3842-3918.

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