A Review on Mechanical Models for Cellular Media: Investigation on Material Characterization and Numerical Simulation
Abstract
:1. Introduction
2. Characterization of Cellular Medium Mechanical Properties
2.1. QuasiStatic Mechanical Properties
2.2. Dynamic Mechanical Properties
3. The Constitutive Relationship of Cellular Medium
3.1. Phenomenological Constitutive Model
3.2. Homogenization Algorithm Model
4. Microstructure Mechanical Models of Cellular Medium
4.1. Single Cell Model
4.2. MultiCell Model
5. Discussion
 The effects of cell size, matrix, relative density, strain rate and testing methods on the mechanical properties of cellular media were systematically investigated through quasistatic mechanical testing and dynamic mechanical testing. The investigation on mechanical properties of cellular media under explosive loading and ultrahigh strain rates involves complex stress waves, and systematic analysis methods and influence laws have not yet been obtained.
 The constitutive model can quickly and accurately describe the stressstrain relationship of a cellular medium, and obtain mechanical parameters (elastic modulus, plateau stress, densification strain, etc.). However, it cannot explain the microstructure deformation mechanism during stretching or compressing. The constitutive model with cell parameters (cell size and cell shape), high strain rate (greater than 10^{4} s^{−1}) and explosive loading needs further study.
 The microstructure model can not only obtain the stressstrain curve, but also explain the microstructure deformation mechanism of cellular media, such as cell deformation, weak parts of the material, stress concentration and local deformation. However, most of the models are based on various algorithms and describe the local microstructure (RVE) of cellular media, which is greatly affected by random factors and is not stable. It is a great challenge to establish a stable, lowcost, real and effective microstructure model of cellular media.
 Molecular dynamics, phase field method and peridynamics can be used to establish nanoscopic models to investigate the structural evolution and properties of molecules and atoms in cellular media. Due to these methods involve nanoscale, simulation results and experimental characterization results are not comparable, and the scale range is small and the calculation amount is large, so they are not introduced in this paper.
 The deformation mode and failure mechanism of cellular media under explosive loading and ultrahigh strain rates, gradient cellular material (gradient mode) structural design and performance optimization [18,57,71,154,155,156,157,158,159], and functional foam composite materials (e.g., doped metal particles, carbon nanotubes, and graphene) [21,160,161,162,163] are the keys to future research on cellular media.
 Expand the mechanical constitutive models of cellular media to suitable for various complex loads, and propose more constitutive models to understand the multifunctional performance of cellular media.
 Multifunctional applications for potential industrial applications, such as: highperformance wave absorption characteristics [175,176,177], electromagnetic interference shielding [162,178,179,180], adsorption thermodynamics and dynamics characteristics [181], and can be used in medical care, satellite communications, electronic equipment, national defense security and other fields in the future [180,182,183,184,185]. And conduct more experiments to verify potential industrial applications.
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Models  Advantages  Disadvantages 

Phenomenological constitutive model 


Homogenization algorithm model 


Single cell model 


Multicell model 


Cellular Medium  Relative Density  Cell Size  Strain Rate  Modulus  Strength  Toughness  Performance  Ref. 

Brittle carbon foam  0.029–0.04  0.49–4.9 mm    45–62 MPa    0.04–0.05 MPa$\sqrt{\mathrm{m}}$ 
 [35] 
Polycarbonate (PC) foam  0.56  2.8–37.1 μm    836–978 MPa  25.6–29.8 MPa  7.02–10.22 J/cm^{3}  [36]  
Polyetherimide (PEI) foam  0.75–0.9  2–4 μm 30–120 nm    1929–2628 MPa  64.1–87.7 MPa  17.6–103.1 J/cm^{3}  [37]  
Polyurethane (PU) foam  0.98  0–800 μm      0.06–0.11 MPa   
 [38] 
3D hierarchical foam    0–55 nm    0.5–1 GPa  0.8–13 MPa   
 [39] 
Polymethyl methacrylate (PMMA) foam  0.5  0.2–11μm    577–791 MPa    0.13–0.44 J/cm^{3}  [40]  
Aluminum (Al) foam  0.02–0.2  3–25 mm  10^{−4}–10^{3} s^{−1}  1–700 MPa  1.5 MPa   
 [41,42] 
Expanded polystyrene (EPS) foam  0.04–0.11  130–320 μm    6.5–32.3 MPa  0.19–0.7 MPa    [43]  
Al foam  0.15–0.29  0.8 mm  10^{−3}–2600 s^{−1}    5–22 MPa   
 [44,45,46] 
Expanded polypropylene (EPP) foam  0.03–0.17  0–0.4 mm  10^{−2}–1500 s^{−1}  0.2–4 MPa  0.2–2.7 MPa    [47]  
Polyvinyl chloride (PVC) foam  0.04–0.18  300–450 μm  10^{−4}–2000 s^{−1}  74–400 MPa  1.08–8.65 MPa    [31]  
EPS foam  0.021–0.044    2.68–280 s^{−1}  2.7–4.8 MPa  0.171–0.478 MPa    [48] 
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Luo, G.; Zhu, Y.; Zhang, R.; Cao, P.; Liu, Q.; Zhang, J.; Sun, Y.; Yuan, H.; Guo, W.; Shen, Q.; et al. A Review on Mechanical Models for Cellular Media: Investigation on Material Characterization and Numerical Simulation. Polymers 2021, 13, 3283. https://doi.org/10.3390/polym13193283
Luo G, Zhu Y, Zhang R, Cao P, Liu Q, Zhang J, Sun Y, Yuan H, Guo W, Shen Q, et al. A Review on Mechanical Models for Cellular Media: Investigation on Material Characterization and Numerical Simulation. Polymers. 2021; 13(19):3283. https://doi.org/10.3390/polym13193283
Chicago/Turabian StyleLuo, Guoqiang, Yuxuan Zhu, Ruizhi Zhang, Peng Cao, Qiwen Liu, Jian Zhang, Yi Sun, Huan Yuan, Wei Guo, Qiang Shen, and et al. 2021. "A Review on Mechanical Models for Cellular Media: Investigation on Material Characterization and Numerical Simulation" Polymers 13, no. 19: 3283. https://doi.org/10.3390/polym13193283