Fig. 10: Computational evaluation of a simple shear stress state for a uniform diameter near cubic bowtie 80∘ specimen and a typical near cubic conventional specimen.
From: Mechanics of reinforced concrete column confinement with architected auxetic steel lattices

ρt/ρl = 1.1 compared to the uniform diameter auxetic with ρt/ρl = 3.35. Both designs have a similar relative density of ρtot = 0.057 ± 0.01, Ec = 26 GPa, and ψ = 38∘. The relationship between the shear and normal reactions generated represents the dilatancy of the concrete matrix \(\psi =\arctan \left(d{\varepsilon }_{v}^{p}/d{\varepsilon }_{s}^{p}\right)\) that connects the plastic volumetric strain with the plastic shear strain of the concrete matrix.