Ultralight cellular composite materials with architected geometrical structure

A novel computational approach is presented to predict the overall hyperelastic 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. The repetitive unit cell (RUC) approach is employed to model the fabricated cellular micro-lattices. Each member of the cellular structure is modeled using only one finite beam element with 12 degrees of freedom, and the nonlinear coupling of axial, bidirectional-bending, and torsional deformations is studied for each 3D spatial beam element. Since the cellular composite material is fabricated via the assemblage of building blocks by mechanical interlocking connections, we utilize the standardized Ramberg-Osgood function for the moment-rotation relation at the ends of adjacent members to enable tuning the appropriate flexibility for connections between two extreme limits of pin-jointed or rigid-jointed connections. The mixed variational functional in the updated Lagrangian co-rotational reference frame is obtained to derive explicitly the stiffness matrix. Then, we use newly proposed homotopy methods to solve the algebraic equations.