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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.

Irreducible decomposition of strain gradient tensor in isotropic strain gradient elasticity