Irreducible decomposition of strain gradient tensor in isotropic strain gradient elasticity
Classical Physics
2016-11-14 v1 Materials Science
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.
Keywords
Cite
@article{arxiv.1604.07254,
title = {Irreducible decomposition of strain gradient tensor in isotropic strain gradient elasticity},
author = {Markus Lazar},
journal= {arXiv preprint arXiv:1604.07254},
year = {2016}
}