Selecting Generalized Continuum Theories for Nonlinear Periodic Solids Based on the Instabilities of the Underlying Microstructure
Abstract
In the context of architected materials, it has been observed that both long-wavelength instabilities leading possibly to localization and short-wavelength instabilities leading to the apparition of a deformation pattern could occur. This work proposes for the first time a comparison of the ability of two families of higher order equivalent media, namely straingradient and micromorphic media, to capture both patterning and long-wavelength macroscopic instabilities in those materials. The studied architected material consists in a simple one-dimensional arrangement of non-linear springs, thus allowing for analytical or nearly analytical treatment of the problem, avoiding any uncertainties or imprecisions coming from a numerical method. A numerical solution of the problem is then used to compare the postbuckling prediction of both models. The study concludes that, micromorphic media are the appropriate choice of equivalent continuum models to emply when dealing with the possibility of patterning inside a structured medium, but if long-wavelength global instability is of interest, a strain-gradient type equivalent medium is well suited.
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