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We present a quantitative geometric rigidity estimate for special functionsof bounded deformation in a planar setting generalizing the result byFriesecke, James, M\"uller obtained in nonlinear elasticity theory and thepiecewise rigidity result by Chambolle, Giacomini, Ponsiglione for brittlematerials which do not store elastic energy. We show that for each deformationthere is an associated triple consisting of a partition of the domain, acorresponding piecewise rigid motion being constant on each connected componentof the cracked body and a displacement field measuring the distance of thedeformation from the piecewise rigid motion. We also present a related estimatein the geometrically linear setting which can be interpreted as a `piecewiseKorn-Poincar\'e inequality'.

A quantitative geometric rigidity result in SBD