Ultralight Cellular Composite Materials with Architected Geometrical Structure

In this paper we present a novel computational approach to predict the overall hyperelastic mechanical properties of ultralight cuboct cellular lattices made of brittle carbon fiber-reinforced polymer composites, such as the ones recently fabricated at the MIT Media Lab-Center for Bits and Atoms. These architected cellular composites, by combining both the specific features of composite materials used for each member, and by architecting the geometries of cellular structures, have introduced materials with mechanical properties filling gaps between the existing materials and the unattainable materials in the low-density region. For such new materials, we present a novel computational procedure whereby each member of the cellular composite material with an arbitrary cross section is sought to be modeled by a single nonlinear three-dimensional (3D) spatial beam element with 12 degrees of freedom (DOF). This will not only enable a very efficient homogenization of a repetitive representative volume element (RVE) of the cellular material; but also the direct numerical simulation (DNS) of a cellular macrostructure with an arbitrarily large number of members. The anisotropic property of each of the carbon-fiber-reinforced composite members is considered by postulating a transversely isotropic material property relation between the components of the second Piola-Kirchhoff stress tensor and the Green-Lagrange strain tensor. By assuming the truss or frame-like behavior for the cuboct cellular composite, we study the nonlinear coupling of the axial, bidirectional-bending, and torsional deformations in an updated Lagrangian co-rotational reference frame for the large deformation analysis of the composite strut members. Then, we examine how the truss-like or frame-like behaviors of the cellular composite change as the thickness-to-length ratios of the strut members change. Since the cellular composite material is fabricated via the assemblage of