Fig. 4: Stress distribution within the lattice structure.

a The selection of a certain range of the elastic properties achieved for the unit cells with a cell angle of \(60^\circ\). In total, the elastic properties of 207 designs with various \({\rho }_{{\rm {h}}}\) values (i.e., 50%, 60%, 70% and 80%) fall within these selected ranges. b The maximum values of the von Mises stress in the structural elements of the corresponding lattice structures when these structures were subjected to two boundary conditions (i.e., \({\varepsilon }_{11}=3 \%\) or \({\varepsilon }_{22}=3 \%\)). Two designs were selected, including one with the minimum (node 1) and one (node 2) with the maximum Euclidean distance from the origin (b, c). The distribution of the von Mises stresses in the selected designs and their deformations under two boundary conditions (i.e., \(\,{\varepsilon }_{11}=3 \%\) or \({\varepsilon }_{22}=3 \%\)) are presented in (d). The axial stresses (S₁₁) in the struts of each design under two boundary conditions (i.e., \(\,{\varepsilon }_{11}=3 \%\) or \({\varepsilon }_{22}=3 \%\)) are calculated and are compared with the axial stresses of the corresponding struts when the lattice structure is composed of an equivalent homogenous material (e).