Fig. 1 Schematic of the two-dimensional contact model between a rigid ( a ) flat and ( b ) cylindrical nanoindenter on a finite-thickness elastic layer attached to a rigid substrate More about this image found in Schematic of the two-dimensional contact model between a rigid ( a ) flat a...

Fig. 2 Predictions of the ( a ) normal pressure, ( b ) normal displacement, ( c ) normal stress, and ( d ) shear stress distributed on the surface of a finite-thickness layer punched by a flat nanoindenter for different dimensionless parameters l / a related to the surface effect. The solid line... More about this image found in Predictions of the ( a ) normal pressure, ( b ) normal displacement, ( c ) ...

Fig. 3 Predictions of the ( a ) normal pressure, ( b ) normal displacement, ( c ) normal stress, and ( d ) shear stress distributed on the surface of a finite-thickness layer punched by a flat nanoindenter for different normalized thicknesses h / a . The solid lines with and without embedded symb... More about this image found in Predictions of the ( a ) normal pressure, ( b ) normal displacement, ( c ) ...

Fig. 4 Variations of the normalized half contact width a / a c with the normalized thickness h / a c for different values of ϕ 0 b / P , in which the classical result without surface effect (the line with black sphere symbols) is also given for a comparison More about this image found in Variations of the normalized half contact width a / a c with the normali...

Fig. 5 Predictions of the ( a ) normal pressure, ( b ) normal displacement, ( c ) normal stress, and ( d ) shear stress distributed on the surface of a finite-thickness layer punched by a cylindrical nanoindenter for different dimensionless parameters ϕ 0 b / P characterizing the surface effec... More about this image found in Predictions of the ( a ) normal pressure, ( b ) normal displacement, ( c ) ...

Fig. 6 Predictions of the ( a ) normal pressure, ( b ) normal displacement, ( c ) normal stress, and ( d ) shear stress distributed on the surface of a finite-thickness layer punched by a cylindrical nanoindenter for different normalized thicknesses h / a c . The solid lines with and without emb... More about this image found in Predictions of the ( a ) normal pressure, ( b ) normal displacement, ( c ) ...

Fig. 7 Variations of the normalized indentation hardness H / H c with the normalized layer thickness h / a c for different surface effect-related parameters ϕ 0 b / P (both the external load P and the indenter size R are given). The classical result without surface effect (the line w... More about this image found in Variations of the normalized indentation hardness H / H c with the norma...

Fig. 1 Schematic illustration of lattice structure design process More about this image found in Schematic illustration of lattice structure design process

Fig. 2 Distribution and pairwise correlations of each elastic constant of the obtained 2000 samples More about this image found in Distribution and pairwise correlations of each elastic constant of the obta...

Fig. 3 Mechanical properties of lattice cell: ( a ) the primary domain D 0 and subdomains D i ( i = 1 , 2 , 3 , 4 ) selected for the detailed analysis, ( b ) distribution of the equivalent relative modulus E ~ and Poisson ratio ν x... More about this image found in Mechanical properties of lattice cell: ( a ) the primary domain ...

Fig. 4 ( a ) Mechanical property distribution by equivalent relative modulus. The distribution is stratified into five regions ( R 1 to R 5 ), with each region representing a sequential increase in equivalent relative modulus, ranging from the lowest in R 1 to th... More about this image found in ( a ) Mechanical property distribution by equivalent relative modulus. ...

Fig. 5 Validation of Eq. (7) across five regions R i ( i = 1 , 2 , 3 , 4 , 5 ): ( a ) regression evaluation indicators R 2 and RMSE obtained from the fitting relationship Eq. (7) across regions R i ( i = 1 , 2 , 3 , 4 , 5 ) and ( ... More about this image found in Validation of Eq. (7) across five regions R i ( i = 1 , ...

Fig. 6 Inverse design of irregular lattice structures framework: ( a ) the distribution of equivalent relative Young’s modulus and Poisson ratio at dimensionless thicknesses of 0.03 , 0.04 , 0.05 , 0.06 , 0.07 , and 0.08 , ( b ) selection process for the elite... More about this image found in Inverse design of irregular lattice structures framework: ( a ) the dis...

Fig. 7 Inverse design of three typical target mechanical properties, including target values, design structures, quantitative comparisons between finite element analysis and experimental results, as well as comparisons of deformation diagrams. Scale bar 20 mm. More about this image found in Inverse design of three typical target mechanical properties, including tar...

Fig. 8 Microstructure design of facial expressions: ( a ) microstructure design of the “smiling face,” ( b ) finite element simulation, ( c ) experimental validation, ( d ) microstructure design of the “surprised face,” ( e ) finite element simulation, and ( f ) experimenta... More about this image found in Microstructure design of facial expressions: ( a ) microstructure desig...