The representative volume size in static and dynamic micro-macro transitions

Inna M. Gitman; Harm Askes; Elias C. Aifantis

doi:10.1007/s10704-005-4389-6

The representative volume size in static and dynamic micro-macro transitions

Inna M. Gitman^*, Harm Askes, Elias C. Aifantis

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

62 Citations (Scopus)

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.

Original language	English
Pages (from-to)	L3-L9
Journal	International journal of fracture
Volume	135
Issue number	1-4
DOIs	https://doi.org/10.1007/s10704-005-4389-6
Publication status	Published - Sept 2005
Externally published	Yes

Keywords

Gradient elasticity
Homogenisation
Length scale
Multi-scale
Representative Volume Element
Time scale

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10.1007/s10704-005-4389-6

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AU - Askes, Harm

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AB - 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.

KW - Gradient elasticity

KW - Homogenisation

KW - Length scale

KW - Multi-scale

KW - Representative Volume Element

KW - Time scale

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IS - 1-4

ER -

The representative volume size in static and dynamic micro-macro transitions

Abstract

Keywords

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