The role of anisotropy on the static and wave propagation characteristics of two-dimensional architectured materials under finite strains

Abstract

In the current work, we analyze the role of anisotropy on the static and wave propagation characteristics of architectured materials. In particular, we study the mechanical behavior of nearly isotropic, moderately and highly anisotropic metamaterials under finite shear and normal strains. Thereupon, we quantify the effect of finite deformations with respect to their magnitude and loading direction, relating the metamaterials' initial degree of anisotropy to its finite strain static attributes. We distinguish between the effect of finite shear and normal strains, noting that highly anisotropic material designs do not uniquely entail shear strain sensitive structural behaviors. Contrariwise, we observe that finite normal loads in certain loading directions can lead to instabilities at rather low strain magnitudes already for moderately anisotropic material designs. Moreover, we show that strain-induced instabilities can be detected as negative phase velocity increments before the stiffness matrix loses its positive definiteness. What is more, we demonstrate that anisotropy and non-reciprocity can be used as mechanisms for wave propagation tuning. We provide evidence that for enhanced tuning capabilities to be observed, inner material density variations need to be exploited. The latter require the application of normal rather than shear strains, as shear deformations are volume preserving.