Irreducible decomposition of strain gradient tensor in isotropic strain gradient elasticity

Abstract

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