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In this paper, we introduce a geometry-based structural design method as an alternative approach for designing low-density structures applicable to material science and mechanical engineering. This method will provide control over internal force-flow, boundary condition, and applied loads. The methodology starts with an introduction to the principles of geometric equilibrium and continues by introducing multiple design techniques to generate truss cellular, polyhedron cellular, and shell cellular (or Shellular) materials by manipulating the geometry of the equilibrium of force. The research concludes by evaluating the mechanical performance of a range of cellular structures designed by this approach. 

Abstract 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.