Design of the P-surfaced shellular, an ultra-low density material with micro- architecture

The P-surface is an intersection-free smooth surface that has constant mean curvature everywhere on the surface, and periodicity in three directions in 3D space. A cellular material composed of thin shells in this configuration, named Shellular, reveals stretching-dominated deformation under external loading. The thin continuous shell of a Shellular could play the role of a transfer interface between the two subvolumes, as well as a mechanical load support. This paper presents a preliminary study to design an optimal shape of the P-surfaced Shellular. Analysis of the geometry and finite element analyses are performed to investigate the effects of the geometric parameters and boundary conditions on their mechanical properties. It is shown that the geometry and mechanical properties of a P-surfaced Shellular can be expressed in empirical equations with only two independent dimensionless parameters, i. e., the volume fraction and the ratio of the wall thickness to cell size; and that the effect of the volume fraction is substantial. A low volume fraction is very beneficial to achieve high strength, and suppresses elastic buckling to delay the transition of the failure mode from plastic yielding to elastic buckling as the wall thickness is decreased. (C) 2017 Published by Elsevier B. V.