Fig. 1: Non-uniformly assembled lattices.

a Initial squared framework with one node per edge (i.e., boundary nodes), identified by N0, N1, N2, N3 for building block generation. b Unique beam-based building blocks generated by combinatorially connecting the boundary nodes. c Typical stress–strain curves of non-uniform unit cells under uniaxial compression at five different loading directions (θ ∈ [0°, 23°, 45°, 67°, 90°]). Note that PBCs are imposed with a maximum applied effective strain of 6%. d Examples of n × n non-uniform unit cells with n = 3 composed of two different combinations of building blocks i.e., design G and H, and design G and its 90°-rotated version (identified by a darker green). e Upper panel: normalized effective buckling strength of the basic building blocks (in b) as a function of the loading angle θ. The superior quasi-isotropic buckling performance of design G are clear. Central panel: probability that a 4 × 4 non-uniform unit cell exhibits a normalized effective buckling strength within discretized levels (amplitude 0.1 × 10⁻²). The data with Ω ⩾ 2% are filtered out. Buckling values for sponge-inspired design are added as well as corresponding unit cells. Lower panel: effect of global buckling of uniform (in f) vs. non-uniform (in g) design on the buckling strength (colors refer to f and g). Lines are plotted only to facilitate the interpretation. f Post-buckled shape of a basic uniform design obtained tessellating a single building block (G in this case). Long-wave buckling instability is clearly exhibited. g Post-buckled shape of a non-uniform design obtained by combining two building blocks (G and its 90°-rotated version). Sponge-inspired designs (a: constant mass ratio of 0.5 between diagonal and non-diagonal beams; b: constant slenderness ratio). All values are obtained by FE simulations (see “Methods” section for details).