Table 2 Overview of the recent progress in the theoretical, simulation and experimental approaches of multiscale mechanics
| Â | Experimental approaches | Theoretical approaches | Simulation approaches | ||||
|---|---|---|---|---|---|---|---|
Method | Apparatus | Characterization parameters | Hierarchical | Concurrent | Hierarchical | Concurrent | |
Macro-scale (m~mm) | Electrical, Optical, Mechanical measurement; Digital Image Correlation (DIC) … | Strain sensor; Electronic speckle pattern interferometry (ESPI); High-speed camera … | Modulus, Stress, strain, Bending stiffness, Strength … | Cohesive zone model; Shear-lag methods; Voigt-Reuss-Hill (VRH) approximation; Hashin–Shtrikman (HS) bounds; Mori–Tanaka method; Sparse methods; Self-consistent method; Differential method; Interaction direct derivative (IDD) method; … | The current knowledge of the authors has not yet acknowledged any unified mechanical theories that can encompass all-length scales for concurrent multiscale analysis. | Finite element method (FEM); Extended finite element method (XFEM); Boundary element method (BEM); Finite volume method (FVM); Discrete element method (DEM); Meshless method; Cell-based method; Voronoi cell finite element method (VCFEM) … | Finite-Element combined with Atomistic modeling method; Coupled atomistic and discrete dislocation (CADD) method; Meta-Surface Antenna Array Decoupling (MAAD) method; Continuum-molecular dynamics overlap method; Micro-macro molecular dynamics method (MMMD); Quasi-continuum method (QC); Hybrid molecular/cluster statistical thermodynamics method (HMST); Heterogeneous multiscale method (HMM) … |
Micro-scale (μm~mm) | Micro tensile testing; Microbeam bending; Microdroplet detachment; X-ray inspection; Microwave detection; Digital Image Correlation (DIC) … | Fiber tensile tester; Laser profilometer; X-ray diffraction instrument (XRD); Computed tomography (CT); Optical microscope (OM); Scanning electron microscope (SEM) … | Porosity; Cracks; Damage; Elongation; Material microstructure … | ||||
Meso-and nano-scale (nm ~ μm) | Nanoindentation; Microbeam bending; Raman spectroscopy; Bubble testing; Nanoprobe extraction; Nanospeckle method … | Nanoindentation; Transmission electron microscope (TEM); Scanning electron microscope (SEM); Scanning tunneling microscope (STM); Atomic force microscope (AFM) … | Modulus; Strength; Fracture toughness; Interfacial adhesion energy; Interfacial shear strength … | Cauchy-born rule; Nonlocal theory … | Density functional theory (DFT); Ab initio molecular dynamics (AIMD); Molecular dynamics (MD); Monte Carlo simulation (MC); Peridynamics (PD); Coarse-grained (CG) modeling; Cluster statistical thermodynamics (CST); Generalized homogenization (GMH) … | ||
