Making the connections stiffer and stronger than the strut members means that stress response is governed by the struts. Extending dimensional scaling methods to include the connections shows that the mass density cost of robust connections – which scale with the strut's cross-sectional area – is low for ultralight materials, where strut diameter dominates mass density scaling. The relative density (ρ/ρs) of these materials is the sum of the relative density contribution of the strut members (ρm/ρs) and the relative density contribution of the connections (ρc/ρs). The strut members have a thickness t and length L. The connections transfer forces through load-bearing surface contacts, requiring that the characteristic dimensions of the connections scale with the cross section of the attached strut members, t2, because this dimension determines the maximum stress transferable through the joint.
These definitions give a cubic scaling relation between the relative mass contribution of the joints and the struts thickness-to-length ratio (ρc/ρs ∝ Cc(t/L)3, where Cc is the connection contribution constant determined by the lattice geometry). The struts relative density contribution scales quadratically with the thickness-to-length ratio of the struts (ρm/ρs ∝ Cm (t/L)2), which agrees with the literature on classical cellular materials. Mechanical properties (such as modulus and strength) scale with overall relative density, which in turn scales primarily with the strut and not the connection, considering only open cell lattices with slender struts [t/L < 0.1 (7)], given that the geometric constants Cc and Cm are of the same order of magnitude [ρ/ρs ∝ Cc (t/L)3 + Cm (t/L)2]. The density cost of the mechanical joints decreases with increasing strut member slenderness (decreasing t/L) and decreasing relative density.
Tiling the cross-shaped parts forms the lattice structure. Each part contributes four conjoined strut members to one locally central node and one strut to four peripheral nodes. A shear clip inserted through the four coincident connection holes links the cells.
Each cell includes aligned fiber composite beams and looped fiber load-bearing holes that reversibly chain together to form volume-filling lattices. Mass-produced cells can be assembled to fill arbitrary structural shapes, with a resolution prescribed by the part scale that matches the variability of an application's boundary stress. The periodic nature of assemblies simplifies behavior analysis and prediction.