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

New Nonconforming Elements for Linear Strain Gradient Elastic Model