Irreducible decomposition of strain gradient tensor in isotropic strain gradient elasticity

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. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim