  In isotropic strain gradient elasticity, we decompose the strain gradient
tensor into its irreducible pieces under the n-dimensional orthogonal group
O(n). Using the Young tableau method for traceless tensors, four irreducible
pieces (n>2), which are canonical, are obtained. In three dimensions, the
strain gradient tensor can be decomposed into four irreducible pieces with
7+5+3+3 independent components whereas in two dimensions, the strain gradient
tensor can be decomposed into three irreducible pieces with 2+2+2 independent
components. The knowledge of these irreducible pieces is extremely useful when
setting up constitutive relations and strain energy.
