Journal
INTERNATIONAL JOURNAL OF FRACTURE
Volume 135, Issue 1-4, Pages L3-L9Publisher
SPRINGER
DOI: 10.1007/s10704-005-4389-6
Keywords
multi-scale; homogenisation; Representative Volume Element; gradient elasticity; length scale; time scale
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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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