Generalized continuum media confronted to long and short wavelength instabilities in architected materials - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2022

Generalized continuum media confronted to long and short wavelength instabilities in architected materials

Résumé

In the context of architected materials, it has been observed that both long-wavelength instabilities leading possibly to localization and short-wavelength commensurate to cell-size instabilities leading to the apparition of a deformation pattern could occur. This work compares the ability of two families of higher order equivalent media, namely strain-gradient and micromorphic media, to capture both mesoscale cell-commensurate and long-wavelength macroscopic instabilities in those materials. The studied architected material consists in a very simple one-dimensional arrangement of non-linear springs, thus allowing for analytical or nearly analytical treatment of the problem, dismissing any uncertainties or imprecisions coming from a numerical method. A numerical solving of the problem is then used to compare the post-buckling predictiion of both models. The study concludes that, even on a very simple case, it is impossible for a strain-gradient Taylor-series expansion type of homogenization method to capture the cell-commensurate instabilities while the micromorphic medium can capture both instabilities but fails to converge properly in the post-buckling regime when localization appears. Micromorphic media are thus the family of equivalent continuum model that are to prefer when dealing with the possibility of patterning inside a structured medium, but if localization is to consider, it would be interesting to combine both strategies into a micromorphic, gradient enhanced equivalent medium.
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Dates et versions

hal-03521030 , version 1 (11-01-2022)
hal-03521030 , version 2 (27-01-2022)

Identifiants

  • HAL Id : hal-03521030 , version 1

Citer

Christelle Combescure. Generalized continuum media confronted to long and short wavelength instabilities in architected materials. 2022. ⟨hal-03521030v1⟩
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