Fig. 1 Illustration of the L-shaped beam: ( a ) design domain and boundary conditions and ( b ) FE mesh. Reproduced from Ref. [ 23 ] with permission. More about this image found in Illustration of the L-shaped beam: ( a ) design domain and boundary...

Fig. 2 Illustration of the topology: ( a ) the homogeneous strongest M1, ( b ) the optimal structure from SoSO, and ( c ) the optimal structure from mixed SOpology optimization (mixed SO) More about this image found in Illustration of the topology: ( a ) the homogeneous strongest M1, ...

Fig. 3 Stress distribution of ( a ) the homogeneous strongest M1, ( b ) the optimal structure from SoSO, and ( c ) the optimal structure from mixed SO More about this image found in Stress distribution of ( a ) the homogeneous strongest M1, ( b ...

Fig. 4 Final crack pattern of ( a ) the homogeneous strongest M1, ( b ) the optimal structure from SoSO, and ( c ) the optimal structure from mixed SO More about this image found in Final crack pattern of ( a ) the homogeneous strongest M1, ( b ...

Fig. 5 Comparison of stiffness, toughness, and strength response: ( a ) load–displacement curves of homogeneous stiff M1 and homogeneous soft M2; ( b ) load–displacement curves of the homogeneous stiff M1, homogeneous soft M2, SoSO, and mixed SO designs; ( c ) stiffness amp... More about this image found in Comparison of stiffness, toughness, and strength response: ( a ) lo...

Fig. 6 Energy evolution curves of the two homogeneous and two optimized L-shaped structures under the incremental displacement load: ( a ) fracture energy and ( b ) elastic energy More about this image found in Energy evolution curves of the two homogeneous and two optimized L-shaped s...

Fig. 7 Illustration of the mode-I example: ( a ) design domain, boundary conditions, and the initial pre-crack and ( b ) finite element mesh More about this image found in Illustration of the mode-I example: ( a ) design domain, boundary c...

Fig. 8 Fracture response of the homogeneous M1, M2, and M3: ( a ) load–displacement curves of the three homogeneous materials, ( b ) initial crack representation of the mode-I test by PFM, and ( c ) final crack pattern for the three homogeneous materials More about this image found in Fracture response of the homogeneous M1, M2, and M3: ( a ) load–dis...

Fig. 9 Optimized structures and their stress distribution from mixed SO: ( a ) the final topology of M-A (left) and the stress distribution of M-A (right) and ( b ) the final topology of M-B (left) and the stress distribution of M-B (right) More about this image found in Optimized structures and their stress distribution from mixed SO: ( a ...

Fig. 10 Crack patterns of the mixed SO design M-A: ( a ) u = 0.46 mm , ( b ) u = 0.47 mm , and ( c ) final crack More about this image found in Crack patterns of the mixed SO design M-A: ( a ) u = 0.46 mm...

Fig. 11 Crack patterns of the mixed SO design M-B: ( a ) u = 0.45 mm , ( b ) u = 0.51 mm , and ( c ) final crack More about this image found in Crack patterns of the mixed SO design M-B: ( a ) u = 0.45 mm...

Fig. 12 Comparison of the fracture response of the homogenous M1 and M3, mixed SO designs M-A and M-B: ( a ) four load–displacement curves; ( b ) amplification of stiffness ( E / E M 1 ), toughness ( T / T M 1 ), strength ( S / S M 1 ), and failu... More about this image found in Comparison of the fracture response of the homogenous M1 and M3, mixed SO d...

Fig. 13 Energy evolution curves of the three homogeneous and two optimized structures under mode-I test: ( a ) fracture energy and ( b ) elastic energy More about this image found in Energy evolution curves of the three homogeneous and two optimized structur...

Fig. 14 ( a ) A sketch of the dog-bone sample used for tensile testing, ( b ) fabricated samples showing homogeneous stiff (left) and soft (right) materials, ( c ) the stress–strain curve of material VPW, and ( d ) the stress–strain curves of Agilus30 and FLXA9885 a... More about this image found in ( a ) A sketch of the dog-bone sample used for tensile testing, ( ...

Fig. 15 A sample of the homogeneous soft material with the initial crack and indication of dimensions (unit: mm) More about this image found in A sample of the homogeneous soft material with the initial crack and indica...

Fig. 16 Printed samples of the ( a ) pure stiff homogeneous material, ( b ) pure soft homogeneous material, ( c ) optimized dual-material structure 1, and ( d ) structure 2 More about this image found in Printed samples of the ( a ) pure stiff homogeneous material, ( b )...

Fig. 17 The MTS. It is integrated with the environmental chamber, where the liquid nitrogen circulation and heating modules are used for cooling and heating control, respectively. More about this image found in The MTS. It is integrated with the environmental chamber, where the liquid ...

Fig. 18 Force versus extension curves and final crack patterns: ( a ) VPW (pure homogeneous stiff material) and structure 2 (optimally designed) and ( b ) DM85A (pure homogeneous soft material). Experimental investigations at low temperatures ( 2 − 3 ∘ C ). More about this image found in Force versus extension curves and final crack patterns: ( a ) VPW (...

Fig. 19 Sequential images of the test loading process (left) and the stress simulation analysis (right) More about this image found in Sequential images of the test loading process (left) and the stress simulat...