  We establish a new H2 Korn's inequality and its discrete analog, which
greatly simplify the construction of nonconforming elements for a linear strain
gradient elastic model. The Specht triangle [41] and the NZT tetrahedron [45]
are analyzed as two typical representatives for robust nonconforming elements
in the sense that the rate of convergence is independent of the small material
parameter. We construct new regularized interpolation estimate and the
enriching operator for both elements, and prove the error estimates under
minimal smoothness assumption on the solution. Numerical results are consistent
with the theoretical prediction.
