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Generalized continuum media confronted with long and short wavelength instabilities in architected materials
Abstract
In the context of architected materials, it has been observed that both long-wavelength instabilities leading to eventual localisation and short-wavelength instabilities commensurate with cell size leading to the appearance of a deformation pattern can occur.
This work compares the ability of two families of higher-order equivalent media, namely strain-gradient media and micromorphic media, to capture both cell-size commensurate mesoscale instabilities and long-wavelength macroscopic instabilities in these materials.
The architectural material studied consists of a very simple one-dimensional arrangement of non-linear springs, thus allowing an analytical or quasi-analytical treatment of the problem, ruling out any uncertainty or inaccuracy from a numerical method.
A numerical solution of the problem is then used to compare the post-buckling prediction of the two models.
The study concludes that, even on a very simple case, it is impossible for a Taylor series expansion type deformation gradient homogenisation method to capture the commensurate instabilities at the cells while the micromorphic medium can capture both instabilities but does not converge correctly in the post-buckling regime when localisation appears.
Micromorphic media are therefore the preferred family of equivalent continuum models when dealing with the possibility of patterning within a structured medium, but if localisation is to be considered, it would be interesting to combine the two strategies in a gradient-enhanced micromorph equivalent medium.