Design and mechanical properties of elastically isotropic trusses

The present article addresses design of stiff, elastically isotropic trusses and their mechanical properties. Isotropic trusses are created by combining two or more elementary cubic trusses in appropriate proportions and with their respective nodes lying on a common space lattice. Two isotropic binary compound trusses and many isotropic ternary trusses are identified, all with Young's moduli equal to the maximal possible value for isotropic strut-based structures. In finite-sized trusses, strain elevations are obtained in struts near the external free boundaries: a consequence of reduced nodal connectivity and thus reduced constraint on strut deformation and rotation. Although the boundary effects persist over distances of only about two unit cell lengths and have minimal effect on elastic properties, their manifestations in failure are more nuanced, especially when failure occurs by modes other than buckling (yielding or fracture). Exhaustive analyses are performed to glean insights into the mechanics of failure of such trusses.