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arXiv · 1301.1890

Matrix representations for 3D strain-gradient elasticity

N. Auffray·H. Le Quang·Q. -C. He
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Abstract

The theory of first strain gradient elasticity (SGE) is widely used to model size and non-local effects observed in materials and structures. For a material whose microstructure is centrosymmetric, SGE is characterized by a sixth-order elastic tensor in addition to the classical fourth-order elastic tensor. Even though the matrix form of the sixth-order elastic tensor is well-known in the isotropic case, its complete matrix representations seem to remain unavailable in the anisotropic cases. In the present paper, the explicit matrix representations of the sixth-order elastic tensor are derived and given for all the 3D anisotropic cases in a compact and well-structured way. These matrix representations are necessary to the development and application of SGE for anisotropic materials

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N. Auffray, H. Le Quang, Q. -C. He. 2013-01-09. Matrix representations for 3D strain-gradient elasticity. https://doi.org/10.1016/j.jmps.2013.01.003

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