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arXiv · 1604.07254

Irreducible decomposition of strain gradient tensor in isotropic strain gradient elasticity

Markus Lazar
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Abstract

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.

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Markus Lazar. 2016-04-25. Irreducible decomposition of strain gradient tensor in isotropic strain gradient elasticity. https://doi.org/10.1002/zamm.201500278

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