Linking material symmetry and domain of elastic behavior: new numerical insights

In the context of the growing industrial use of architected materials, it is crucial to predict the critical loads at which their mechanical response transitions from linear to nonlinear. The sources of nonlinearity can be multiple, including material nonlinearity and/or multiscale buckling. The set of critical loadings defines a surface in stress or strain space that delineates the region within which the behavior remains elastic, also referred to as the linearity domain . This article presents a numerical investigation of the connections between the symmetries of a periodic architected material and the corresponding symmetries of its linearity domain. This investigation yields novel insights: (i) the rotational symmetry order of the linearity domain is directly related to that of the underlying architected material; (ii) the material’s chirality manifests itself in the geometry of its linearity domain, which in this case appears tilted; and (iii) the angle of this tilt is correlated with the angle of the parent mesostructure.