  Based on a new H$^2-$Korn's inequality, we propose new nonconforming elements
for the linear strain gradient elastic model. The first group of elements are
H$^1-$conforming but H$^2-$nonconforming. The tensor product NTW element
[Tai:2001] and the tensor product Specht triangle are two typical
representatives. The second element is based on Morley's triangle with a
modified elastic strain energy. We proved new interpolation error estimates for
all these elements, which are key to prove uniform rates of convergence for the
proposed elements. Numerical results are reported and they are consistent with
the theoretical prediction.
