Abstract
Two homogenisation schemes (first-order or local, and second-order or non-local) are employed in this paper. In case second-order homogenisation is applied, it turns out that elastic behaviour at the micro-scale implies the appearance of second-order space and time derivatives of macroscopic strain in an otherwise elastic constitutive equation for the macroscopic stress. The coefficients of the second-order terms scale with the size of the Representative Volume Element (RVE) employed in the homogenisation scheme.
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Gitman, I.M., Askes, H. & Aifantis, E.C. The Representative Volume Size in Static and Dynamic Micro-Macro Transitions. Int J Fract 135, L3–L9 (2005). https://doi.org/10.1007/s10704-005-4389-6
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DOI: https://doi.org/10.1007/s10704-005-4389-6