The kinematics of infinitesimal deformations is traditionally described in terms of displacement fields. In the presence of dislocations, however, the elastic strain need not be compatible, and a globally defined displacement may no longer exist.
In this talk, we develop an intrinsic description of boundary kinematics based on the Frank tensor
\[
\mathfrak F(E):=(\operatorname{Curl}E)^T,
\]
and the two canonical boundary traces associated with the Saint-Venant incompatibility operator.
For compatible strains, the Frank tensor coincides with the gradient of the infinitesimal rotation. Together with the two boundary traces, it provides a geometric description of three fundamental aspects of boundary deformation: the variation of the first fundamental form, the tangential transport of infinitesimal rotations, and the variation of the second fundamental form.
We then extend this interpretation to incompatible strains by introducing the dislocation contortion tensor (\kappa) through Kröner's relation
\[
\operatorname{inc}E=\operatorname{Curl}\kappa.
\]
The resulting local decomposition
\[
\mathfrak F(E)=\nabla\theta+\kappa
\]
reveals a natural gauge invariance and clarifies the contribution of dislocations to rotational kinematics.
The approach provides a strain-based description of boundary metric, curvature and rotation that remains meaningful beyond compatibility. We conclude by discussing its implications for intrinsic boundary conditions in elastic bodies containing defects.