Asymptotic, second-order homogenization of linear elastic beam networks - Archive ouverte HAL
Article Dans Une Revue Journal of the Mechanics and Physics of Solids Année : 2024

Asymptotic, second-order homogenization of linear elastic beam networks

Yang Ye
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Basile Audoly
Claire Lestringant

Résumé

We propose a general approach to the higher-order homogenization of discrete elastic networks made up of linear elastic beams or springs in dimension 2 or 3. The network may be nearly (rather than exactly) periodic: its elastic and geometric properties are allowed to vary slowly in space, in addition to being periodic at the scale of the unit cell. The reference configuration may be prestressed. A homogenized strain energy depending on both the macroscopic strain ɛ and its gradient ∇ɛ is obtained by means of a two-scale expansion. The homogenized energy is asymptotically exact two orders beyond that obtained by classical homogenization. The homogenization method is implemented in a symbolic calculation language and applied to various types of networks, such as a 2D honeycomb, a 2D Kagome lattice, a 3D truss and a 1D pantograph. It is validated by comparing the predictions of the microscopic displacement to that obtained by full, discrete simulations. This second-order method remains highly accurate even when the strain gradient effects are significant, such as near the lips of a crack tip or in regions where a gradient of pre-strain is imposed.
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Dates et versions

hal-04549113 , version 1 (17-04-2024)
hal-04549113 , version 2 (17-04-2024)

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Yang Ye, Basile Audoly, Claire Lestringant. Asymptotic, second-order homogenization of linear elastic beam networks. Journal of the Mechanics and Physics of Solids, 2024, 188, pp.105637. ⟨10.1016/j.jmps.2024.105637⟩. ⟨hal-04549113v2⟩
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