Owing to the fact that effective properties of low‐density cellular solids heavily rely on their underlying architecture, a variety of explicit and implicit techniques exists for designing cellular geometries. However, most of these techniques fail to present a correlation among architecture, internal forces, and effective properties. This paper introduces an alternative design strategy based on the static equilibrium of forces, equilibrium of polyhedral frames, and reciprocity of form and force. This novel approach reveals a geometric relationship among the truss system architecture, topological dual, and equilibrium of forces on the basis of 3D graphic statics. This technique is adapted to devise periodic strut‐based cellular architectures under certain boundary conditions and they are manipulated to construct shell‐based (shellular) cells with a variety of mechanical properties. By treating the materialized unit cells as representative volume elements (RVE), multiscale homogenization is used to investigate their effective linear elastic properties. Validated by experimental tests on 3D printed funicular materials, it is shown that by manipulating the RVE topology using the proposed methodology, alternative strut materialization schemes, and rational addition of bracing struts, cellular mechanical metamaterials can be systematically architected to demonstrate properties ranging from bending‐ to stretching‐dominated, realize metafluidic behavior, or create novel hybrid shellulars.

This article investigates how reciprocal form and force polyhedrons can be used to develop procedures for the design of three-dimensional trusses and funicular structures, analogous to the well-known techniques of graphic statics for two-dimensional structural systems. It demonstrates how global equilibrium of a system of forces can be established by constructing a closed force polyhedron, if the forces can be replaced by a resultant force alone, without a resultant couple. It also describes the three-dimensional equivalent of the “closing string,” which is the basis in graphic statics for the construction of funicular solutions for given loads and support locations. Furthermore, it provides a procedure for constructing a constrained funicular form for a simple, determinate boundary condition. Finally, it discusses some of the difficulties involved with similar constructions and procedures for non-concurrent forces and in particular with those systems of forces that can only be replaced by a resultant force and couple.