Fig. 3: Simultaneous mechanical stress modulation in multiple complex regions with distinct target values.

a Design domain, boundary conditions, stress control regions (divided according to colors), and target stress values (\({\overline{\sigma }}^{h}\), in MPa). The variables σ^h and t = 1 MPa are the hydrostatic stress (in MPa) and the applied traction, respectively. b Comparison between the actual and target hydrostatic stresses after optimization. The inset shows the computation of the hydrostatic stress, σ^h, expressed in principal stresses, σ₁ and σ₂, under the plane stress assumption. c Hydrostatic stress field, σ^h, of the initial and optimized designs. d 2-norm errors of hydrostatic stress fields, \(| | {\sigma }^{h}-{\overline{\sigma }}^{h}| {| }_{2}\), of the initial and optimized designs. e,f Two insets illustrating disordered microstructures of the optimized architected materials at two different locations of the sample. Each inset exhibits one frequency combination of a disordered microstructure and corresponding numerical and physical microstructural samples. g Optimized distribution of frequency combinations, \({\overline{\xi }}_{1}\)–\({\overline{\xi }}_{4}\), for each type of basic building block.