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We establish a non-local integral difference quotient representation forsymmetric gradient semi-norms in $BD(\Omega)$ and $LD(\Omega)$, which does notrequire the manipulation of distributional derivatives. Our representationextends the formulas for the symmetric gradient established by Mengesha forvector-fields in $W^{1,p}(\Omega;\mathbb R^d)$, which are inspired by thegradient semi-norm formulas introduced by Bourgain, Brezis and Mironescu in$W^{1,p}(\Omega)$ and by D\'avila in $BV(\Omega)$.

A Bourgain-Brezis-Mironescu representation for functions with bounded deformation