Dynamic compressive behaviour of cellular materials: A review of phenomenon, mechanism and modelling

International Journal of Impact Engineering - Tập 112 - Trang 74-115 - 2018
Yongle Sun1, Q.M. Li1,2
1School of Mechanical, Aerospace and Civil Engineering, The University of Manchester, Sackville Street, Manchester M13 9PL, UK
2State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, PR China

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Gibson, 1997

Amran, 2015, Properties and applications of foamed concrete; a review, Constr Build Mater, 101, 990, 10.1016/j.conbuildmat.2015.10.112

Ashby, 2000

Banhart, 2001, Manufacture, characterisation and application of cellular metals and metal foams, Prog Mater Sci, 46, 559, 10.1016/S0079-6425(00)00002-5

Banhart, 2003, Aluminum foams: on the road to real applications, MRS Bull, 28, 290, 10.1557/mrs2003.83

Gama, 2001, Aluminum foam integral armor: a new dimension in armor design, Compos Struct, 52, 381, 10.1016/S0263-8223(01)00029-0

Gibson, 2010

Lefebvre, 2008, Porous metals and metallic foams: current status and recent developments, Adv Eng Mater, 10, 775, 10.1002/adem.200800241

Ryan, 2013, Hypervelocity impact testing of advanced materials and structures for micrometeoroid and orbital debris shielding, Acta Astronaut, 83, 216, 10.1016/j.actaastro.2012.09.012

Ryan, 2010, Honeycomb vs. foam: evaluating potential upgrades to ISS module shielding, Acta Astronaut, 67, 818, 10.1016/j.actaastro.2010.05.021

Zhou, 2015, Design of metal foam cladding subjected to close-range blast, J Perform Constr Facil, 29, 10.1061/(ASCE)CF.1943-5509.0000606

Simone, 1998, Aluminum foams produced by liquid-state processes, Acta Mater, 46, 3109, 10.1016/S1359-6454(98)00017-2

Elnasri, 2007, Shock enhancement of cellular structures under impact loading: part I experiments, J Mech Phys Solids, 55, 2652, 10.1016/j.jmps.2007.04.005

Ruan, 2007, Triaxial compression of aluminium foams, Compos Sci Technol, 67, 1218, 10.1016/j.compscitech.2006.05.005

Liu, 2013, A relationship between the geometrical structure of a nanoporous metal foam and its modulus, Acta Mater, 61, 2390, 10.1016/j.actamat.2013.01.011

Hasan, 2008, Measuring the cell wall mechanical properties of Al-alloy foams using the nanoindentation method, Compos Struct, 83, 180, 10.1016/j.compstruct.2007.04.016

König, 2000, AlVis - an aluminium-foam visualization and investigation tool, 229

Bastawros, 2000, Experimental analysis of deformation mechanisms in a closed-cell aluminum alloy foam, J Mech Phys Solids, 48, 301, 10.1016/S0022-5096(99)00035-6

Bastawros, 2000, Deformation heterogeneity in cellular Al alloys, Adv Eng Mater, 2, 210, 10.1002/(SICI)1527-2648(200004)2:4<210::AID-ADEM210>3.0.CO;2-Z

Zou, 2009, Dynamic crushing of honeycombs and features of shock fronts, Int J Impact Eng, 36, 165, 10.1016/j.ijimpeng.2007.11.008

Sun, 2017, Image-based correlation between the meso-scale structure and deformation of closed-cell foam, Mater Sci Eng, 688, 27, 10.1016/j.msea.2017.01.092

Liao, 2013, Dynamic crushing of 2D cellular structures: local strain field and shock wave velocity, Int J Impact Eng, 57, 7, 10.1016/j.ijimpeng.2013.01.008

Liao, 2014, On the local nature of the strain field calculation method for measuring heterogeneous deformation of cellular materials, Int J Solids Struct, 51, 478, 10.1016/j.ijsolstr.2013.10.019

Jeon, 2010, Finite element simulation of the plastic collapse of closed-cell aluminum foams with X-ray computed tomography, Mech Mater, 42, 227, 10.1016/j.mechmat.2010.01.003

Sun, 2016, Determination of the constitutive relation and critical condition for the shock compression of cellular solids, Mech Mater, 99, 26, 10.1016/j.mechmat.2016.04.004

Sun, 2016, Investigation of strain-rate effect on the compressive behaviour of closed-cell aluminium foam by 3D image-based modelling, Mater Des, 89, 215, 10.1016/j.matdes.2015.09.109

Gibson, 1981

Yu, 2006, Strain-rate effect and micro-structural optimization of cellular metals, Mech Mater, 38, 160, 10.1016/j.mechmat.2005.05.018

Bouix, 2009, Polypropylene foam behaviour under dynamic loadings: strain rate, density and microstructure effects, Int J Impact Eng, 36, 329, 10.1016/j.ijimpeng.2007.11.007

Yu, 2007, Research into the effect of cell diameter of aluminum foam on its compressive and energy absorption properties, Mater Sci Eng, 454–455, 542, 10.1016/j.msea.2006.11.091

Bart-Smith, 1998, Compressive deformation and yielding mechanisms in cellular Al alloys determined using X-ray tomography and surface strain mapping, Acta Mater, 46, 3583, 10.1016/S1359-6454(98)00025-1

Simone, 1998, The effects of cell face curvature and corrugations on the stiffness and strength of metallic foams, Acta Mater, 46, 3929, 10.1016/S1359-6454(98)00072-X

Simone, 1998, Effects of solid distribution on the stiffness and strength of metallic foams, Acta Mater, 46, 2139, 10.1016/S1359-6454(97)00421-7

Sun, 2015, Effect of entrapped gas on the dynamic compressive behaviour of cellular solids, Int J Solids Struct, 63, 50, 10.1016/j.ijsolstr.2015.02.034

Tang, 2014, Effects of statistics of cell's size and shape irregularity on mechanical properties of 2D and 3D Voronoi foams, Acta Mech, 225, 1361, 10.1007/s00707-013-1054-4

Deshpande, 2001, Foam topology: bending versus stretching dominated architectures, Acta Mater, 49, 1035, 10.1016/S1359-6454(00)00379-7

Fleck, 2010, Micro-architectured materials: past, present and future, 466, 2495

Liu, 2009, The influence of cell micro-topology on the in-plane dynamic crushing of honeycombs, Int J Impact Eng, 36, 98, 10.1016/j.ijimpeng.2008.03.001

Alkhader, 2008, Mechanical response of cellular solids: role of cellular topology and microstructural irregularity, Int J Eng Sci, 46, 1035, 10.1016/j.ijengsci.2008.03.012

Chen, 1999, Effect of imperfections on the yielding of two-dimensional foams, J Mech Phys Solids, 47, 2235, 10.1016/S0022-5096(99)00030-7

Jeon, 2005, The effect of structural defects on the compressive behavior of closed-cell Al foam, Acta Mater, 53, 3415, 10.1016/j.actamat.2005.04.010

Ajdari, 2011, Dynamic crushing and energy absorption of regular, irregular and functionally graded cellular structures, Int J Solids Struct, 48, 506, 10.1016/j.ijsolstr.2010.10.018

Li, 2007, Dynamic crushing behavior of honeycomb structures with irregular cell shapes and non-uniform cell wall thickness, Int J Solids Struct, 44, 5003, 10.1016/j.ijsolstr.2006.12.017

Zhang, 2010, Effects of defects on the in-plane dynamic crushing of metal honeycombs, Int J Mech Sci, 52, 1290, 10.1016/j.ijmecsci.2010.06.004

Silva, 1997, The effects of non-periodic microstructure and defects on the compressive strength of two-dimensional cellular solids, Int J Mech Sci, 39, 549, 10.1016/S0020-7403(96)00065-3

Ajdari, 2008, Effect of defects on elastic–plastic behavior of cellular materials, Mater Sci Eng, 487, 558, 10.1016/j.msea.2007.10.050

Wu, 1997, Axial crush of metallic honeycombs, Int J Impact Eng, 19, 439, 10.1016/S0734-743X(97)00004-3

Hou, 2012, Inertia effects on the progressive crushing of aluminium honeycombs under impact loading, Int J Solids Struct, 49, 2754, 10.1016/j.ijsolstr.2012.05.005

Karagiozova, 2017, On the dynamic compression of cellular materials with local structural softening, Int J Impact Eng, 108, 153, 10.1016/j.ijimpeng.2017.04.007

Karagiozova, 2004, Dynamic buckling of elastic–plastic square tubes under axial impact—I: stress wave propagation phenomenon, Int J Impact Eng, 30, 143, 10.1016/S0734-743X(03)00061-7

Karagiozova, 2004, Dynamic buckling of elastic–plastic square tubes under axial impact—II: structural response, Int J Impact Eng, 30, 167, 10.1016/S0734-743X(03)00062-9

Xi, 2017, Meso-scale mechanism of compaction shock propagation in cellular materials, Int J Impact Eng, 109, 321, 10.1016/j.ijimpeng.2017.07.005

Wang, 2017, Stress distribution in graded cellular materials under dynamic compression, Lat Am J Solids Struct, 14, 1251, 10.1590/1679-78253428

Tan, 2005, Dynamic compressive strength properties of aluminium foams. Part I—experimental data and observations, J Mech Phys Solids, 53, 2174, 10.1016/j.jmps.2005.05.007

Tan, 2005, Dynamic compressive strength properties of aluminium foams. Part II—‘shock’ theory and comparison with experimental data and numerical models, J Mech Phys Solids, 53, 2206, 10.1016/j.jmps.2005.05.003

Neville, 2008, Composite metal foams processed through powder metallurgy, Mater Des, 29, 388, 10.1016/j.matdes.2007.01.026

Rabiei, 2009, A comparison of composite metal foam's properties and other comparable metal foams, Mater Lett, 63, 533, 10.1016/j.matlet.2008.11.002

Calladine, 1984, Strain-rate and inertia effects in the collapse of two types of energy-absorbing structure, Int J Mech Sci, 26, 689, 10.1016/0020-7403(84)90021-3

Liu, 2009, A numerical study on the rate sensitivity of cellular metals, Int J Solids Struct, 46, 3988, 10.1016/j.ijsolstr.2009.07.024

Deshpande, 2000, Isotropic constitutive models for metallic foams, J Mech Phys Solids, 48, 1253, 10.1016/S0022-5096(99)00082-4

Shaw, 1966, The plastic behavior of cellular materials, Int J Mech Sci, 8, 469, 10.1016/0020-7403(66)90019-1

Gioux, 2000, Failure of aluminum foams under multiaxial loads, Int J Mech Sci, 42, 1097, 10.1016/S0020-7403(99)00043-0

Zhao, 2004, On the strength enhancement under impact loading of square tubes made from rate insensitive metals, Int J Solids Struct, 41, 6677, 10.1016/j.ijsolstr.2004.05.039

Deshpande, 2000, High strain rate compressive behaviour of aluminium alloy foams, Int J Impact Eng, 24, 277, 10.1016/S0734-743X(99)00153-0

Zhao, 2005, An experimental study on the behaviour under impact loading of metallic cellular materials, Int J Mech Sci, 47, 757, 10.1016/j.ijmecsci.2004.12.012

Ruan, 2003, In-plane dynamic crushing of honeycombs—a finite element study, Int J Impact Eng, 28, 161, 10.1016/S0734-743X(02)00056-8

Zheng, 2005, Dynamic crushing of 2D cellular structures: a finite element study, Int J Impact Eng, 32, 650, 10.1016/j.ijimpeng.2005.05.007

Lee, 2006, Deformation rate effects on failure modes of open-cell Al foams and textile cellular materials, Int J Solids Struct, 43, 53, 10.1016/j.ijsolstr.2005.06.101

Barnes, 2014, Dynamic crushing of aluminum foams: Part I – Experiments, Int J Solids Struct, 51, 1631, 10.1016/j.ijsolstr.2013.11.019

Ma, 2009, Modeling loading rate effect on crushing stress of metallic cellular materials, Int J Impact Eng, 36, 775, 10.1016/j.ijimpeng.2008.11.013

Wang, 2013, On the energy conservation and critical velocities for the propagation of a “steady-shock” wave in a bar made of cellular material, Acta Mech Sin, 1

Hanssen, 2002, Close-range blast loading of aluminium foam panels, Int J Impact Eng, 27, 593, 10.1016/S0734-743X(01)00155-5

Li, 2002, Attenuation or enhancement - A one-dimensional analysis on shock transmission in the solid phase of a cellular material, Int J Impact Eng, 27, 1049, 10.1016/S0734-743X(02)00016-7

Ben-Dor, 1994, Shock wave interaction with cellular materials Part II: open cell foams; experimental and numerical results, Shock Waves, 3, 167, 10.1007/BF01414711

Petel, 2013, The elastic–plastic behaviour of foam under shock loading, Shock Waves, 23, 55, 10.1007/s00193-012-0414-7

Zhou, 2012, Protection against blast load with cellular materials and structures, Int J Aerosp Lightweight Struct, 2, 53, 10.3850/S2010428612000220

Zhu, 2011, Shock enhancement effect of lightweight composite structures and materials, Compos Part B, 42, 1202, 10.1016/j.compositesb.2011.02.014

Ashby, 2006, The properties of foams and lattices, Philos Trans R Soc London. Ser A, 364, 15, 10.1098/rsta.2005.1678

Schaedler, 2016, Architected cellular materials, Annu Rev Mater Res, 46, 187, 10.1146/annurev-matsci-070115-031624

Qiu, 2009, Collapse of periodic planar lattices under uniaxial compression, part I: quasi-static strength predicted by limit analysis, Int J Impact Eng, 36, 1223, 10.1016/j.ijimpeng.2009.05.011

Qiu, 2009, Collapse of periodic planar lattices under uniaxial compression, part II: dynamic crushing based on finite element simulation, Int J Impact Eng, 36, 1231, 10.1016/j.ijimpeng.2009.05.010

He, 2014, Preparation of density-graded aluminum foam, Mater Sci Eng, 618, 496, 10.1016/j.msea.2014.08.087

Zheng, 2016, Impact plastic crushing and design of density-graded cellular materials, Mech Mater, 94, 66, 10.1016/j.mechmat.2015.11.014

Cichocki, 1998, Tailored porosity gradients via colloidal infiltration of compression-molded sponges, J Am Ceram Soc, 81, 1661, 10.1111/j.1151-2916.1998.tb02528.x

Ajdari, 2012, Hierarchical honeycombs with tailorable properties, Int J Solids Struct, 49, 1413, 10.1016/j.ijsolstr.2012.02.029

Yi, 2012, The impact response of clamped sandwich beams with ordinary and hierarchical cellular cores, Int J Impact Eng, 47, 14, 10.1016/j.ijimpeng.2012.03.001

Zheng, 2016, Multiscale metallic metamaterials, Nat Mater, 15, 1100, 10.1038/nmat4694

Song, 2007, Compressive mechanical response of a low-density epoxy foam at various strain rates, J Mater Sci, 42, 7502, 10.1007/s10853-007-1612-z

Tekoğlu, 2011, Size effects in foams: experiments and modeling, Prog Mater Sci, 56, 109, 10.1016/j.pmatsci.2010.06.001

Andrews, 2001, Size effects in ductile cellular solids. Part II: experimental results, Int J Mech Sci, 43, 701, 10.1016/S0020-7403(00)00043-6

Onck, 2001, Size effects in ductile cellular solids. Part I: modeling, Int J Mech Sci, 43, 681, 10.1016/S0020-7403(00)00042-4

Vural, 2003, Dynamic response and energy dissipation characteristics of balsa wood: experiment and analysis, Int J Solids Struct, 40, 2147, 10.1016/S0020-7683(03)00057-X

Li, 2002, Strain measures for rigid crushable foam in uniaxial compression, Strain, 38, 132, 10.1046/j.1475-1305.2002.00029.x

Li, 2000, The crush behaviour of Rohacell-51WF structural foam, Int J Solids Struct, 37, 6321, 10.1016/S0020-7683(99)00277-2

de Sousa, 2008, Microstructure and properties of LZSA glass-ceramic foams, Mater Sci Eng, 476, 89, 10.1016/j.msea.2007.05.098

Sun, 2016, The variation in elastic modulus throughout the compression of foam materials, Acta Mater, 110, 161, 10.1016/j.actamat.2016.03.003

Ahmad Zaidi, 2009, Investigation on penetration resistance of foamed concrete, Proc Inst Civil Eng Struct Build, 162, 77, 10.1680/stbu.2009.162.1.77

Triawan, 2012, The elastic behavior of aluminum alloy foam under uniaxial loading and bending conditions, Acta Mater, 60, 3084, 10.1016/j.actamat.2012.02.013

Flores-Johnson, 2008, Degradation of elastic modulus of progressively crushable foams in uniaxial compression, J Cell Plast, 44, 415, 10.1177/0021955X08095113

Li, 2006, Compressive strain at the onset of densification of cellular solids, J Cell Plast, 42, 371, 10.1177/0021955X06063519

Tan, 2002, Inertia effects in uniaxial dynamic compression of a closed cell aluminium alloy foam, Mater Sci Technol, 18, 480, 10.1179/026708302225002092

Flores-Johnson, 2010, Indentation into polymeric foams, Int J Solids Struct, 47, 1987, 10.1016/j.ijsolstr.2010.03.025

Idris, 2009, Mechanical behaviour and energy absorption of closed-cell aluminium foam panels in uniaxial compression, Mater Sci Eng, 517, 37, 10.1016/j.msea.2009.03.067

Wang, 2011, Compressive behavior of closed-cell aluminum alloy foams at medium strain rates, Mater Sci Eng, 528, 2326, 10.1016/j.msea.2010.12.059

Li, 2014, On crushing response of the three-dimensional closed-cell foam based on Voronoi model, Mech Mater, 68, 85, 10.1016/j.mechmat.2013.08.009

Zheng, 2013, Dynamic crushing of cellular materials: a unified framework of plastic shock wave models, Int J Impact Eng, 53, 29, 10.1016/j.ijimpeng.2012.06.012

Shen, 2010, Compressive behaviour of closed-cell aluminium foams at high strain rates, Compos Part B, 41, 678, 10.1016/j.compositesb.2010.07.005

Xu, 2014, Strength enhancement of aluminium foams and honeycombs by entrapped air under dynamic loadings, Int J Impact Eng, 74, 120, 10.1016/j.ijimpeng.2014.03.007

Wang, 2013, Experimental investigation on dynamic constitutive behavior of aluminum foams by new inverse methods from wave propagation measurements, Int J Impact Eng, 62, 48, 10.1016/j.ijimpeng.2013.06.002

Fang, 2010, On the behaviour characterization of metallic cellular materials under impact loading, Acta Mech Sin, 26, 837, 10.1007/s10409-010-0392-x

Peroni, 2013, Impact behaviour testing of aluminium foam, Int J Impact Eng, 53, 74, 10.1016/j.ijimpeng.2012.07.002

Irausquín, 2013, Evaluation of the effect of the strain rate on the compressive response of a closed-cell aluminium foam using the split Hopkinson pressure bar test, Mater Des, 47, 698, 10.1016/j.matdes.2012.12.050

Zhao, 1997, On the use of a viscoelastic split Hopkinson pressure bar, Int J Impact Eng, 19, 319, 10.1016/S0734-743X(96)00038-3

Wang, 2015, Experimental investigation on the strain-rate effect and inertia effect of closed-cell aluminum foam subjected to dynamic loading, Mater Sci Eng, 620, 253, 10.1016/j.msea.2014.10.026

Montanini, 2005, Measurement of strain rate sensitivity of aluminium foams for energy dissipation, Int J Mech Sci, 47, 26, 10.1016/j.ijmecsci.2004.12.007

Rajendran, 2009, Numerical simulation of drop weight impact behaviour of closed cell aluminium foam, Mater Des, 30, 2823, 10.1016/j.matdes.2009.01.026

Wang, 2011, A new method combining lagrangian analysis with Hopkinson pressure bar technique, Strain, 47, 173, 10.1111/j.1475-1305.2008.00533.x

Koohbor, 2016, Investigation of the dynamic stress–strain response of compressible polymeric foam using a non-parametric analysis, Int J Impact Eng, 91, 170, 10.1016/j.ijimpeng.2016.01.007

Ramamurty, 2004, Variability in mechanical properties of a metal foam, Acta Mater, 52, 869, 10.1016/j.actamat.2003.10.021

Duarte, 2014, Variation of quasi-static and dynamic compressive properties in a single aluminium foam block, Mater Sci Eng, 616, 171, 10.1016/j.msea.2014.08.002

Nagy, 1974, Mechanical behavior of foamed materials under dynamic compression, J Cell Plast, 10, 127, 10.1177/0021955X7401000306

Zhang, 1998, Constitutive modeling of polymeric foam material subjected to dynamic crash loading, Int J Impact Eng, 21, 369, 10.1016/S0734-743X(97)00087-0

Sherwood, 1992, Constitutive modeling and simulation of energy absorbing polyurethane foam under impact loading, Polym Eng Sci, 32, 1138, 10.1002/pen.760321611

Ouellet, 2006, Compressive response of polymeric foams under quasi-static, medium and high strain rate conditions, Polym Test, 25, 731, 10.1016/j.polymertesting.2006.05.005

Kasparek, 2011, Numerical and experimental studies of polyurethane foam under impact loading, Comput Mater Sci, 50, 1353, 10.1016/j.commatsci.2010.11.025

Merrett, 2013, The blast and impact loading of aluminium foam, Mater Des, 44, 311, 10.1016/j.matdes.2012.08.016

Tagarielli, 2008, The high strain rate response of PVC foams and end-grain balsa wood, Compos Part B, 39, 83, 10.1016/j.compositesb.2007.02.005

Park, 2002, Strain rate sensitivity and defects in steel foam, Mater Sci Eng, 323, 358, 10.1016/S0921-5093(01)01372-7

Chakravarty, 2003, Strain rate effects on sandwich core materials: an experimental and analytical investigation, Acta Mater, 51, 1469, 10.1016/S1359-6454(02)00541-4

Mukai, 1999, Experimental study of energy absorption in a close-celled aluminum foam under dynamic loading, Scr Mater, 40, 921, 10.1016/S1359-6462(99)00038-X

Paul, 2000, Strain rate sensitivity of a closed-cell aluminum foam, Mater Sci Eng, 281, 1, 10.1016/S0921-5093(99)00750-9

Ramachandra, 2003, Impact energy absorption in an Al foam at low velocities, Scr Mater, 49, 741, 10.1016/S1359-6462(03)00431-7

Yi, 2001, Strain rate effects on the compressive property and the energy-absorbing capacity of aluminum alloy foams, Mater Charact, 47, 417, 10.1016/S1044-5803(02)00194-8

Peroni, 2008, The mechanical behaviour of aluminium foam structures in different loading conditions, Int J Impact Eng, 35, 644, 10.1016/j.ijimpeng.2007.02.007

Dou, 2007, High strain rate compression of cenosphere-pure aluminum syntactic foams, Scr Mater, 57, 945, 10.1016/j.scriptamat.2007.07.024

Hall, 2000, Crushing of aluminum closed cell foams: density and strain rate effects, Scr Mater, 43, 515, 10.1016/S1359-6462(00)00460-7

Xu, 2012, Experimental study of the out-of-plane dynamic compression of hexagonal honeycombs, Compos Struct, 94, 2326, 10.1016/j.compstruct.2012.02.024

Xu, 2012, Strength enhancement of aluminium honeycombs caused by entrapped air under dynamic out-of-plane compression, Int J Impact Eng, 47, 1, 10.1016/j.ijimpeng.2012.02.008

Zhao, 1998, Crushing behaviour of aluminium honeycombs under impact loading, Int J Impact Eng, 21, 827, 10.1016/S0734-743X(98)00034-7

Xu, 2010, High rate compressive behavior of aluminum foams by modified SHPB technique, 727

Mukai, 2006, Compressive response of a closed-cell aluminum foam at high strain rate, Scr Mater, 54, 533, 10.1016/j.scriptamat.2005.10.062

Cady, 2009, Compressive properties of a closed-cell aluminum foam as a function of strain rate and temperature, Mater Sci Eng, 525, 1, 10.1016/j.msea.2009.07.007

Dannemann, 2000, High strain rate compression of closed-cell aluminium foams, Mater Sci Eng, 293, 157, 10.1016/S0921-5093(00)01219-3

Han, 2005, The strain rate effect of an open cell aluminum foam, Metall Mater Trans A, 36, 645, 10.1007/s11661-005-0180-6

Tan, 2012, On the dynamic mechanical properties of open-cell metal foams – A re-assessment of the ‘simple-shock theory’, Int J Solids Struct, 49, 2744, 10.1016/j.ijsolstr.2012.03.026

Chakravarty, 2010, An investigation on the dynamic response of polymeric, metallic, and biomaterial foams, Compos Struct, 92, 2339, 10.1016/j.compstruct.2010.02.013

Radford, 2005, The use of metal foam projectiles to simulate shock loading on a structure, Int J Impact Eng, 31, 1152, 10.1016/j.ijimpeng.2004.07.012

Lopatnikov, 2003, Dynamics of metal foam deformation during Taylor cylinder-Hopkinson bar impact experiment, Compo Struct, 61, 61, 10.1016/S0263-8223(03)00039-4

Zheng, 2014, Dynamic stress-strain states for metal foams using a 3D cellular model, J Mech Phys Solids, 72, 93, 10.1016/j.jmps.2014.07.013

Wang, 2007

Reid, 1983, Experimental investigation of inertia effects in one-dimensional metal ring systems subjected to end impact — I. Fixed-ended systems, Int J Impact Eng, 1, 85, 10.1016/0734-743X(83)90014-3

Reid, 1983, Structural plastic shock model for one-dimensional ring systems, Int J Impact Eng, 1, 175, 10.1016/0734-743X(83)90005-2

Reid, 1997, Dynamic uniaxial crushing of wood, Int J Impact Eng, 19, 531, 10.1016/S0734-743X(97)00016-X

Harrigan, 2005, High rate crushing of wood along the grain, Int J Mech Sci, 47, 521, 10.1016/j.ijmecsci.2004.12.013

Davison, 2008

Ding, 2016, Dynamic crushing of cellular materials: a unique dynamic stress–strain state curve, Mech Mater, 100, 219, 10.1016/j.mechmat.2016.07.001

Wang, 2017, Dynamic material parameters of closed-cell foams under high-velocity impact, Int J Impact Eng, 99, 111, 10.1016/j.ijimpeng.2016.09.013

Gaitanaros, 2014, Dynamic crushing of aluminum foams: Part II – Analysis, Int J Solids Struct, 51, 1646, 10.1016/j.ijsolstr.2013.11.020

Gaitanaros, 2015, On the effect of relative density on the crushing and energy absorption of open-cell foams under impact, Int J Impact Eng, 82, 3, 10.1016/j.ijimpeng.2015.03.011

Morris, 1991, Shock-wave equation-of-state studies at Los Alamos, Shock Waves, 1, 213, 10.1007/BF01413796

Zaretsky, 2012, Impact response of high density flexible polyurethane foam, Int J Impact Eng, 39, 1, 10.1016/j.ijimpeng.2011.09.004

Meyers, 1994

Hu, 2013, Mechanical behavior of hexagonal honeycombs under low-velocity impact – theory and simulations, Int J Solids Struct, 50, 3152, 10.1016/j.ijsolstr.2013.05.017

Chen, 1989, Dynamic wave dispersion and loss properties of conventional and negative Poisson's ratio polymeric cellular materials, Cell Polym, 8, 343

Kader, 2016, Modelling and characterization of cell collapse in aluminium foams during dynamic loading, Int J Impact Eng, 96, 78, 10.1016/j.ijimpeng.2016.05.020

Toda, 2006, 3-D image-based mechanical simulation of aluminium foams: effects of internal microstructure, Adv Eng Mater, 8, 459, 10.1002/adem.200600035

Li, 2006, About one-dimensional shock propagation in a cellular material, Int J Impact Eng, 32, 1898, 10.1016/j.ijimpeng.2005.04.006

Andrews, 1999, Compressive and tensile behaviour of aluminum foams, Mater Sci Eng A, 270, 113, 10.1016/S0921-5093(99)00170-7

Zheng, 2012, Dynamic crushing of cellular materials: continuum-based wave models for the transitional and shock modes, Int J Impact Eng, 42, 66, 10.1016/j.ijimpeng.2011.09.009

Li, 2016, A numerical study on deformation mode and strength enhancement of metal foam under dynamic loading, Mater Des, 110, 72, 10.1016/j.matdes.2016.07.123

Harrigan, 2010, The correct analysis of shocks in a cellular material, Int J Impact Eng, 37, 918, 10.1016/j.ijimpeng.2009.03.011

Karagiozova, 2012, Propagation of compaction waves in metal foams exhibiting strain hardening, Int J Solids Struct, 49, 2763, 10.1016/j.ijsolstr.2012.03.012

McDonald, 2006, Characterization of the three-dimensional structure of a metallic foam during compressive deformation, J Microsc, 223, 150, 10.1111/j.1365-2818.2006.01607.x

Hönig, 2002, In-plane dynamic crushing of honeycomb. Part I: crush band initiation and wave trapping, Int J Mech Sci, 44, 1665, 10.1016/S0020-7403(02)00060-7

Hönig, 2002, In-plane dynamic crushing of honeycomb. Part II: application to impact, Int J Mech Sci, 44, 1697, 10.1016/S0020-7403(02)00061-9

H.J. Frost, M.F. Ashby, Deformation mechanism maps: the plasticity and creep of metals and ceramics, (1982).

Jones, 2011

Walley, 1994, Strain rate sensitivity of polymers in compression from low to high rates, DYMAT J, 1, 211

Karnes, 1966, Strain rate effects in cold worked high-purity Aluminium, J Mech Phys Solids, 14, 75, 10.1016/0022-5096(66)90038-X

Khan, 1992, Experimental and theoretical study of mechanical behavior of 1100 aluminum in the strain rate range 10−5−104s−1, Int J Plasticity, 8, 397, 10.1016/0749-6419(92)90057-J

Kitazono, 2006, Strain rate sensitivity and energy absorption of Zn–22Al foams, Scr Mater, 55, 501, 10.1016/j.scriptamat.2006.06.001

Miyoshi, 2000, ALPORAS aluminum foam: production process, properties, and applications, Adv Eng Mater, 2, 179, 10.1002/(SICI)1527-2648(200004)2:4<179::AID-ADEM179>3.0.CO;2-G

Islam, 2016, Investigation of microstructural and mechanical properties of cell walls of closed-cell aluminium alloy foams, Mater Sci Eng, 666, 245, 10.1016/j.msea.2016.04.046

Zhou, 2005, Microscale testing of the strut in open cell aluminum foams, J Mater Sci, 40, 429, 10.1007/s10853-005-6100-8

Markaki, 2001, The effect of cell wall microstructure on the deformation and fracture of aluminium-based foams, Acta Mater, 49, 1677, 10.1016/S1359-6454(01)00072-6

Ma, 2010, Modeling strain rate effect of heterogeneous materials using SPH method, Rock Mech Rock Eng, 43, 763, 10.1007/s00603-010-0089-2

Toda, 2006, Quantitative assessment of microstructure and its effects on compression behavior of aluminum foams via high-resolution synchrotron X-ray tomography, Metall Mater Trans A, 37, 1211, 10.1007/s11661-006-1072-0

Koohbor, 2017, Effects of cell-wall instability and local failure on the response of closed-cell polymeric foams subjected to dynamic loading, Mech Mater

Maire, 2014, Quantitative X-ray tomography, Int Mater Rev, 59, 1, 10.1179/1743280413Y.0000000023

Vesenjak, 2012, Analysis of anisotropy and strain rate sensitivity of open-cell metal foam, Mater Sci Eng, 541, 105, 10.1016/j.msea.2012.02.010

Benouali, 2005, Investigation on the influence of cell shape anisotropy on the mechanical performance of closed cell aluminium foams using micro-computed tomography, J Mater Sci, 40, 5801, 10.1007/s10853-005-4994-9

Wang, 2014, Temperature effects on the mechanical behavior of aluminum foam under dynamic loading, Mater Sci Eng, 599, 174, 10.1016/j.msea.2014.01.076

Jeon, 2009, Cell wall mechanical properties of closed-cell Al foam, Mech Mater, 41, 60, 10.1016/j.mechmat.2008.08.002

Hönig, 2000, Dynamic buckling of an imperfect elastic, visco-plastic plate, Int J Impact Eng, 24, 907, 10.1016/S0734-743X(00)00007-5

Su, 1995, Inertia-sensitive impact energy-absorbing structures part I: effects of inertia and elasticity, Int J Impact Eng, 16, 651, 10.1016/0734-743X(94)00061-Z

Su, 1995, Inertia-sensitive impact energy-absorbing structures part II: effect of strain rate, Int J Impact Eng, 16, 673, 10.1016/0734-743X(94)00062-2

Zhang, 1989, A note on a ‘velocity sensitive’ energy-absorbing structure, Int J Impact Eng, 8, 43, 10.1016/0734-743X(89)90030-4

Gao, 2005, A study on type II structures. Part I: a modified one-dimensional mass–spring model, Int J Impact Eng, 31, 895

Zou, 2007, Dynamic crushing of a one-dimensional chain of type II structures, Int J Impact Eng, 34, 303, 10.1016/j.ijimpeng.2005.08.002

Maxwell, 1864, On the calculation of the equilibrium and stiffness of frames, Philos Mag, 27, 294, 10.1080/14786446408643668

Papka, 1998, Experiments and full-scale numerical simulations of in-plane crushing of a honeycomb, Acta Mater, 46, 2765, 10.1016/S1359-6454(97)00453-9

Wilbert, 2011, Buckling and progressive crushing of laterally loaded honeycomb, Int J Solids Struct, 48, 803, 10.1016/j.ijsolstr.2010.11.014

Mohr, 2003, Nucleation and propagation of plastic collapse bands in aluminum honeycomb, J Appl Phys, 94, 2262, 10.1063/1.1592010

Da Silva, 2007, Compressive response and failure of balsa wood, Int J Solids Struct, 44, 8685, 10.1016/j.ijsolstr.2007.07.003

Zhou, 2004, Mechanisms and mechanics of compressive deformation in open-cell Al foams, Mech Mater, 36, 781, 10.1016/j.mechmat.2003.05.004

Jang, 2009, On the crushing of aluminum open-cell foams: Part I. Experiments, Int J Solids Struct, 46, 617, 10.1016/j.ijsolstr.2008.09.008

Jang, 2009, On the crushing of aluminum open-cell foams: part II analysis, Int J Solids Struct, 46, 635, 10.1016/j.ijsolstr.2008.10.016

Tan, 2005, Discussion: “the resistance of clamped sandwich beams to shock loading”, J Appl Mech, 72, 978, 10.1115/1.2040452

Fleck, 2005, Closure to “discussion of ‘the resistance of clamped sandwich beams to shock loading, J Appl Mech, 72, 980, 10.1115/1.2040450

Pattofatto, 2007, Shock enhancement of cellular structures under impact loading: part II analysis, J Mech Phys Solids, 55, 2672, 10.1016/j.jmps.2007.04.004

Edwin Raj, 2009, Comparison of quasi-static and dynamic compression behavior of closed-cell aluminum foam, Mater Sci Eng, 526, 11, 10.1016/j.msea.2009.07.017

Kitazono, 2003, Application of mean-field approximation to elastic-plastic behavior for closed-cell metal foams, Acta Mater, 51, 4823, 10.1016/S1359-6454(03)00322-7

Öchsner, 2009, Modelling of the multiaxial elasto-plastic behaviour of porous metals with internal gas pressure, Finite Elem Anal Des, 45, 104, 10.1016/j.finel.2008.07.007

Zhang, 2009, Effect of inner gas pressure on the elastoplastic behavior of porous materials: a second-order moment micromechanics model, Int J Plast, 25, 1231, 10.1016/j.ijplas.2008.10.001

Xu, 2010, Deformation of closed-cell foams incorporating the effect of inner gas pressure, Int J Appl Mech, 02, 489, 10.1142/S1758825110000627

Schraad, 2006, A multi-field approach to modeling the dynamic response of cellular materials, Int J Mech Sci, 48, 85, 10.1016/j.ijmecsci.2005.09.004

Zhang, 2009, Energy absorption of pressurized thin-walled circular tubes under axial crushing, Int J Mech Sci, 51, 335, 10.1016/j.ijmecsci.2009.03.002

Sadot, 2016, The trapped gas effect on the dynamic compressive strength of light aluminum foams, Mater Sci Eng, 659, 278, 10.1016/j.msea.2016.02.031

Banerjee, 2006, Numerical simulation of the dynamic compression of a 6061-T6 aluminum metallic foam

Fang, 2015, A 3D mesoscopic model for the closed-cell metallic foams subjected to static and dynamic loadings, Int J Impact Eng, 82, 103, 10.1016/j.ijimpeng.2014.10.009

Alvandi-Tabrizi, 2015, High strain rate behavior of composite metal foams, Mater Sci Eng, 631, 248, 10.1016/j.msea.2015.02.027

Stronge, 1988, Microdynamics of crushing in cellular solids, J Eng Mater Technol, 110, 185, 10.1115/1.3226029

Shim, 1990, Dynamic crushing of strain-softening cellular structures—a one-dimensional analysis, J Eng Mater Technol, 112, 398, 10.1115/1.2903349

Shim, 1992, Effects of nonhomogeneity, cell damage and strain-rate on impact crushing of a strain-softening cellular chain, Int J Impact Eng, 12, 585, 10.1016/0734-743X(92)90251-N

Wang, 2010, A study on compressive shock wave propagation in metallic foams, Sci China Phys Mech Astron, 53, 279, 10.1007/s11433-009-0271-2

Daxner, 1999, Mesoscopic simulation of inhomogeneous metallic foams with respect to energy absorption, Comput Mater Sci, 16, 61, 10.1016/S0927-0256(99)00046-4

Roberts, 2001, Elastic moduli of model random three-dimensional closed-cell cellular solids, Acta Mater, 49, 189, 10.1016/S1359-6454(00)00314-1

Li, 2015, Insight into cell size effects on quasi-static and dynamic compressive properties of 3D foams, Mater Sci Eng, 636, 60, 10.1016/j.msea.2015.03.052

Hu, 2014, Analyses on the dynamic strength of honeycombs under the y-directional crushing, Mater Des, 53, 293, 10.1016/j.matdes.2013.06.076

Hu, 2010, Dynamic crushing strength of hexagonal honeycombs, Int J Impact Eng, 37, 467, 10.1016/j.ijimpeng.2009.12.001

Hu, 2014, Undulation of the honeycombs׳ plateau stress under impact and the dynamic enhancement—Theoretical analysis, Mater Sci Eng, 598, 190, 10.1016/j.msea.2014.01.040

Daxner, 2010, Finite element modeling of cellular materials, Cell Porous Mater Struct Processes, 521, 47, 10.1007/978-3-7091-0297-8_2

Petit, 2013, Cellular solids studied by x-ray tomography and finite element modeling – a review, J Mater Res, 28, 2191, 10.1557/jmr.2013.97

Maire, 2012, X-ray tomography applied to the characterization of highly porous materials, Annu Rev Mater Res, 42, 163, 10.1146/annurev-matsci-070511-155106

Caty, 2008, Modeling the properties of closed-cell cellular materials from tomography images using finite shell elements, Acta Mater, 56, 5524, 10.1016/j.actamat.2008.07.023

Bardenhagen, 2005, Insight into the physics of foam densification via numerical simulation, J Mech Phys Solids, 53, 597, 10.1016/j.jmps.2004.09.003

Brydon, 2005, Simulation of the densification of real open-celled foam microstructures, J Mech Phys Solids, 53, 2638, 10.1016/j.jmps.2005.07.007

Veyhl, 2011, Finite element analysis of the mechanical properties of cellular aluminium based on micro-computed tomography, Mater Sci Eng, 528, 4550, 10.1016/j.msea.2011.02.031

Chen, 2017, Finite element analysis of the compressive and shear responses of structural foams using computed tomography, Compos Struct, 159, 784, 10.1016/j.compstruct.2016.09.091

Sun, 2014, In situ investigation and image-based modelling of aluminium foam compression using micro X-Ray computed tomography, 189

Hangai, 2013, Deformation behavior estimation of aluminum foam by X-ray CT image-based finite element analysis, Metall Mater Trans A, 44, 1880, 10.1007/s11661-012-1532-7

Sun, 2015, Strain-rate sensitivity of foam materials: a numerical study using 3D image-based finite element model, 04022

Veyhl, 2013, On the mechanical properties of sintered metallic fibre structures, Mater Sci Eng, 562, 83, 10.1016/j.msea.2012.11.034

Sun, 2013, In-plane crushing and energy absorption performance of multi-layer regularly arranged circular honeycombs, Compos Struct, 96, 726, 10.1016/j.compstruct.2012.10.008

Song, 2010, Dynamic crushing behavior of 3D closed-cell foams based on Voronoi random model, Mater Des, 31, 4281, 10.1016/j.matdes.2010.04.007

Hanssen, 2002, Validation of constitutive models applicable to aluminium foams, Int J Mech Sci, 44, 359, 10.1016/S0020-7403(01)00091-1

Ruan, 2002, Compressive behaviour of aluminium foams at low and medium strain rates, Compos Struct, 57, 331, 10.1016/S0263-8223(02)00100-9

Simulia, ABAQUS analysis user's manual, ABAQUS v6.12 Documentation, (Dassault Systémes, V6.12).

Darvizeh, 2015, A transport approach for analysis of shock waves in cellular materials, Int J Impact Eng, 82, 59, 10.1016/j.ijimpeng.2014.11.006

Lu, 2003

Fleck, 2004, The resistance of clamped sandwich beams to shock loading, J Appl Mech, 71, 386, 10.1115/1.1629109

Ousji, 2017, Air-blast response of sacrificial cladding using low density foams: experimental and analytical approach, Int J Mech Sci, 128, 459, 10.1016/j.ijmecsci.2017.05.024

Ding, 2016, Blast alleviation of cellular sacrificial cladding: a nonlinear plastic shock model, Int J Appl Mech, 08, 10.1142/S1758825116500575

Lopatnikov, 2004, High-velocity plate impact of metal foams, Int J Impact Eng, 30, 421, 10.1016/S0734-743X(03)00066-6

Karagiozova, 2013, Compaction of metal foam subjected to an impact by a low-density deformable projectile, Int J Impact Eng, 62, 196, 10.1016/j.ijimpeng.2013.07.004

Ma, 2007, Analysis of foam claddings for blast alleviation, Int J Impact Eng, 34, 60, 10.1016/j.ijimpeng.2005.10.005

Ma, 2007, Energy absorption of double-layer foam cladding for blast alleviation, Int J Impact Eng, 34, 329, 10.1016/j.ijimpeng.2005.07.012

Aleyaasin, 2015, Air-blast response of cellular material with a face plate: an analytical–numerical approach, Int J Mech Sci, 91, 64, 10.1016/j.ijmecsci.2014.03.027

Zhou, 2013, Mitigating ground shocks with cellular solids, J Eng Mech, 139, 1362, 10.1061/(ASCE)EM.1943-7889.0000585

Karagiozova, 2010, Blast attenuation in Cymat foam core sacrificial claddings, Int J Mech Sci, 52, 758, 10.1016/j.ijmecsci.2010.02.002

Karagiozova, 2014, Compaction of a double-layered metal foam block impacting a rigid wall, Int J Solids Struct, 51, 2424, 10.1016/j.ijsolstr.2014.03.012

Karagiozova, 2015, Primary and reflected compaction waves in a foam rod due to an axial impact by a small mass, Lat Am J Solids Struct, 12, 905, 10.1590/1679-78251300

Askes, 2011, Gradient elasticity in statics and dynamics: an overview of formulations, length scale identification procedures, finite element implementations and new results, Int J Solids Struct, 48, 1962, 10.1016/j.ijsolstr.2011.03.006

Hadjesfandiari, 2011, Couple stress theory for solids, Int J Solids Struct, 48, 2496, 10.1016/j.ijsolstr.2011.05.002

Kumar, 2004, Generalized continuum modeling of 2-D periodic cellular solids, Int J Solids Struct, 41, 7399, 10.1016/j.ijsolstr.2004.06.038

Berezovski, 2013, Dispersive waves in microstructured solids, Int J Solids Struct, 50, 10.1016/j.ijsolstr.2013.02.018

Gibson, 1989, Failure surfaces for cellular materials under multiaxial loads—I. Modelling, Int J Mech Sci, 31, 635, 10.1016/S0020-7403(89)80001-3

Abrate, 2008, Criteria for yielding or failure of cellular materials, J Sandwich Struct Mater, 10, 5, 10.1177/1099636207070997

Drucker, 1952, Soil mechanics and plastic analysis or limit design, Q Appl Math, 10, 157, 10.1090/qam/48291

Maji, 1995, Mechanical properties of polyurethane-foam impact limiters, J Eng Mech, 121, 528, 10.1061/(ASCE)0733-9399(1995)121:4(528)

Doyoyo, 2003, Experimental studies on the yield behavior of ductile and brittle aluminum foams, Int J Plast, 19, 1195, 10.1016/S0749-6419(02)00017-7

Zhang, 1997, Constitutive modeling and material characterization of polymeric foams, J Eng Mater Technol, 119, 284, 10.1115/1.2812258

Miller, 2000, A continuum plasticity model for the constitutive and indentation behaviour of foamed metals, Int J Mech Sci, 42, 729, 10.1016/S0020-7403(99)00021-1

Zhou, 2012, Loading rate effect on yield surface of aluminum alloy foams, Mater Sci Eng, 543, 193, 10.1016/j.msea.2012.02.074

Triantafillou, 1989, Failure surfaces for cellular materials under multiaxial loads—II. Comparison of models with experiment, Int J Mech Sci, 31, 665, 10.1016/S0020-7403(89)80002-5

Hallquist, 2005

Qin, 2009, An analytical solution for the large deflections of a slender sandwich beam with a metallic foam core under transverse loading by a flat punch, Compos Struct, 88, 509, 10.1016/j.compstruct.2008.05.012

Qin, 2009, Large deflections of metallic sandwich and monolithic beams under locally impulsive loading, Int J Mech Sci, 51, 752, 10.1016/j.ijmecsci.2009.08.008

Qin, 2009, A theoretical analysis of the dynamic response of metallic sandwich beam under impulsive loading, Eur J Mech - A/Solids, 28, 1014, 10.1016/j.euromechsol.2009.04.002

Qin, 2011, Low-velocity heavy-mass impact response of slender metal foam core sandwich beam, Compos Struct, 93, 1526, 10.1016/j.compstruct.2010.11.018

Ivañez, 2010, FEM analysis of dynamic flexural behaviour of composite sandwich beams with foam core, Compos Struct, 92, 2285, 10.1016/j.compstruct.2009.07.018

Rajaneesh, 2012, Impact modeling of foam cored sandwich plates with ductile or brittle faceplates, Compos Struct, 94, 1745, 10.1016/j.compstruct.2011.12.021

Zhang, 2016, A theoretical study of low-velocity impact of geometrically asymmetric sandwich beams, Int J Impact Eng, 96, 35, 10.1016/j.ijimpeng.2016.05.011

Zhang, 2015, A theoretical study of plastic analysis of fully clamped geometrical asymmetric sandwich beams with a metal foam core, Int J Mech Sci, 99, 98, 10.1016/j.ijmecsci.2015.04.019

Zhang, 2016, Dynamic response of slender multilayer sandwich beams with metal foam cores subjected to low-velocity impact, Compos Struct, 153, 614, 10.1016/j.compstruct.2016.06.059

Rajendran, 2008, Preliminary investigation of aluminium foam as an energy absorber for nuclear transportation cask, Mater Des, 29, 1732, 10.1016/j.matdes.2008.03.028

Qin, 2013, Low-velocity impact response of fully clamped metal foam core sandwich beam incorporating local denting effect, Compos Struct, 96, 346, 10.1016/j.compstruct.2012.09.024

Wang, 2013, Experimental and numerical study on the low-velocity impact behavior of foam-core sandwich panels, Compos Struct, 96, 298, 10.1016/j.compstruct.2012.09.002

Chung, 2002, Compressive response of circular cell polycarbonate honeycombs under inplane biaxial static and dynamic loading. Part I: experiments, Int J Impact Eng, 27, 729, 10.1016/S0734-743X(02)00011-8

Chung, 2002, Compressive response of circular cell polycarbonate honeycombs under inplane biaxial static and dynamic loading—Part II: simulations, Int J Impact Eng, 27, 1015, 10.1016/S0734-743X(02)00012-X

Hou, 2011, Impact behavior of honeycombs under combined shear-compression. Part I: experiments, Int J Solids Struct, 48, 687, 10.1016/j.ijsolstr.2010.11.005

Hou, 2011, Impact behavior of honeycombs under combined shear-compression. Part II: analysis, Int J Solids Struct, 48, 698, 10.1016/j.ijsolstr.2010.11.004

Zhou, 2016, High velocity impact mitigation with gradient cellular solids, Compos Part B, 85, 93, 10.1016/j.compositesb.2015.09.042

Zhou, 2015, Energy absorption of graded foam subjected to blast: a theoretical approach, Mater Des, 84, 351, 10.1016/j.matdes.2015.06.124

Marx, 2017, Overview of composite metal foams and their properties and performance, Adv Eng Mater, 10.1002/adem.201600776

Compton, 2014, 3D-printing of lightweight cellular composites, Adv Mater, 26, 5930, 10.1002/adma.201401804

Cheung, 2013, Reversibly assembled cellular composite materials, Science, 341, 1219, 10.1126/science.1240889