Fig. 1 A coupled thermo-hydro-chemo-mechanical multiphysics process where each physics affects the other More about this image found in A coupled thermo-hydro-chemo-mechanical multiphysics process where each phy...

Fig. 2 A conceptual schematic showing the ( a ) principle of constitutive modeling where thermodynamical consistency can ensure accurate prediction of material behavior and ( b ) an example where the difference between observed and calculated thermodynamic variables (e.g., stress–strain) is minimi... More about this image found in A conceptual schematic showing the ( a ) principle of constitutive modeling...

Fig. 3 Schematic explaining the mixture theory of biphasic elements ( s = solid ,   f = fluid ) in the reference (undeformed) configuration based on a material body of volume B containing a material point P (adapted from Ref. [ 17 ]) More about this image found in Schematic explaining the mixture theory of biphasic elements ( s = s...

Fig. 4 The characteristic length of the REV is different at micro- and macroscales [ 195 ] (reproduced with permission) More about this image found in The characteristic length of the REV is different at micro- and macroscales...

Fig. 5 A schematic description of various multiphysics dissipative processes in the context of underground hydrogen storage [ 223 ] (reproduced with permission) More about this image found in A schematic description of various multiphysics dissipative processes in th...

Fig. 1 Representative examples of field observations and experiments involving biological fish. Instantaneous structure of fish schools measured using ( a ) ocean acoustic waveguide remote sensing and ( b ) high-resolution sonar imaging. ( c ) Video tracking of fish groupings in a water tunnel at ... More about this image found in Representative examples of field observations and experiments involving bio...

Fig. 2 Representative examples of experiments with mechanical fish abstractions. ( a ) A pair of passively flapping filaments arranged in two different spacings in a soap-film tunnel. ( b ) A couple of actively pitching hydrofoils in a water tunnel [ 97 ]. ( c ) Two heaving hydrofoils traveling in... More about this image found in Representative examples of experiments with mechanical fish abstractions. (...

Fig. 3 Representative examples of reduced-order models. Schools of finite-length vortex dipoles interacting ( a ) freely and ( b ) subject to behavioral rules. ( c ) A pair of zero-thickness heaving plates. ( d ) A lattice of flapping hydrofoils. Subfigures ( a )–( d ) are adapted with permission ... More about this image found in Representative examples of reduced-order models. Schools of finite-length v...

Fig. 4 Representative examples of high-fidelity CFD simulations. ( a ) Multiple undulating plates driven by their heaving and pitching heads. ( b ) A hydrofoil undergoing prescribed heaving in a periodic domain. ( c ) A generic fish-like swimmer traveling in isolation and in a group. Collective sw... More about this image found in Representative examples of high-fidelity CFD simulations. ( a ) Multiple un...

Fig. 5 Schematics outlining common formations considered in collective swimming studies. ( a ) and ( b ) depict rectangular and diamond configurations, and their respective derivatives. More about this image found in Schematics outlining common formations considered in collective swimming st...

Fig. 1 Schematics of three ML approaches based on available physics and data: (I) PINNs; (II) physics-based data-driven; and (III) purely data-driven (Reproduced with permission from Ref. [ 62 ]. Copyright 2021 by Hanxun Jin). Figure idea from Karniadakis et al. [ 61 ]. More about this image found in Schematics of three ML approaches based on available physics and data: (I) ...

Fig. 2 Applications of ML in characterizing fracture cohesive properties. ( a ) ML solutions can predict accurate fracture toughness comparable to simulations when an analytical solution is not available due to sample complexity: (i) ML framework for engineering problems; (ii) NNs-based prediction... More about this image found in Applications of ML in characterizing fracture cohesive properties. ( a ) ML...

Fig. 3 Applications of ML in crack/flaw detection. ( a ) PINNs can identify internal voids/inclusions for linear and nonlinear solids: (i) general setup for geometric and material property identification; (ii) architectures of PINNs for continuum solid mechanics. (iii) inference of deformation pat... More about this image found in Applications of ML in crack/flaw detection. ( a ) PINNs can identify intern...

Fig. 4 Applications of ML in constitutive parameter inversion for biomaterials. ( a ) A hybrid DL framework to identify unknown material parameters of arteries with high coefficient of determination: (i) hybrid model architecture; (ii) predicted stress–stretch curves from standard fitting method c... More about this image found in Applications of ML in constitutive parameter inversion for biomaterials. ( ...

Fig. 5 Applications of neural operator in constitutive modeling of biomaterials. ( a ) A DeepONet-based DL framework to infer biomechanical response and associated genotype of tissues: (i) the DL framework; (ii) reconstructed stress–stretch relationships compared with their true values (Reproduced... More about this image found in Applications of neural operator in constitutive modeling of biomaterials. (...

Fig. 6 Applications of ML in nano-indentation. ( a ) DL methods including single-fidelity NNs, multifidelity NNs, and residual multifidelity NNs to identify material parameters from instrumented indentation: (i) architectures of these NNs; (ii) Mean absolute percentage error as a function of train... More about this image found in Applications of ML in nano-indentation. ( a ) DL methods including single-f...

Fig. 7 Applications of ML in designing shape-programmable kirigami metamaterials. ( a ) The ML framework to inverse design kirigami metamaterials. ( b ) Schematics of the tandem network employed for inverse design. ( c ) Experimental verification of inverse design from shadow Moiré method (Reprodu... More about this image found in Applications of ML in designing shape-programmable kirigami metamaterials. ...