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- W4300479109 abstract "We present a piecewise Korn inequality for generalized special functions of bounded deformation ($GSBD^2$) 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 $GSBD^2$ functions have bounded variation after subtraction of a piecewise infinitesimal rigid motion. As an application we prove a density result in $GSBD^2$. Moreover, for all $d ge 2$ we show $GSBD^2(Omega) subset (GBV(Omega;{Bbb R}))^d$ and the embedding $SBD^2(Omega) cap L^infty(Omega;{Bbb R}^d) hookrightarrow SBV(Omega;{Bbb R}^d)$ into the space of special functions of bounded variation ($SBV$). Finally, we present a Korn-Poincar'e inequality for functions with small jump sets in arbitrary space dimension." @default.
- W4300479109 created "2022-10-03" @default.
- W4300479109 creator A5035698976 @default.
- W4300479109 date "2016-04-28" @default.
- W4300479109 modified "2023-09-29" @default.
- W4300479109 title "A piecewise Korn inequality in SBD and applications to embedding and density results" @default.
- W4300479109 doi "https://doi.org/10.48550/arxiv.1604.08416" @default.
- W4300479109 hasPublicationYear "2016" @default.
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