Computing the effective bulk and normal to shear properties of common two-dimensional architectured materials

In the current work we analyze the bulk and normal to shear properties of a wide range of two-dimensional artificial materials under small deformations. To that scope, we employ reentrant, chiral, triangular and rectangular-shaped based unit-cell arrangements. We characterize their mechanical response, using a homogenization analysis method. We identify inner material architectures of high and low relative resistance to pressure and to shear loads. We classify the metastructures' mechanical behavior with respect to the one expected for common isotropic engineering materials. We observe considerable differences for most of the analyzed structures for which we provide insights making use of symmetry analysis notions. What is more, we identify lightweight inner material designs for certain bulk and normal to shear behaviors to be obtained, while we unravel the role of the Poisson's ratio value on the retrieved effective attributes. We quantify the impact of alterations in the metamaterials' inner design parameters, such as in the slenderness ratio of its inner elements, reporting unit-cell designs that yield macroscopic relative mechanical properties (bulk and normal to shear attributes) that are insensitive to inner element slenderness changes.