Skip to main content

Testing of Foams

  • Living reference work entry
  • First Online:
Handbook of Mechanics of Materials

Abstract

Foams are lightweight cellular materials that are widely used in applications such as packaging, thermal insulation, sound absorption, underwater vehicle structures, and as the core in sandwich structures used in aircraft. Testing of foams to obtain reliable properties that are relevant to a given application is a significant challenge. High damping, high compressive or tensile strain, and high volume of air in the structure are among the challenges that make it difficult to apply the common test methods to these materials. For example, use of strain gauges for tensile or compression testing is usually not possible because bonding the strain gauges to the surface of a cellular material may not be possible, the small measurement range of a strain gauge may not be enough to capture the strain in the entire loading range, and microscopic material structure may dominate the measurement. This chapter discusses test techniques that include quasi-static compression, high strain rate compression, impact, dynamic mechanical analysis, vibration methods, and imaging techniques that are relevant to testing of foams. The imaging methods include ultrasonic imaging and microCT-scanning. Test techniques are described and results on representative foam materials are presented to understand the test outcomes.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

References

  1. Stevenson P, editor. Foam engineering: fundamentals and applications. New York: Wiley; 2012.

    Google Scholar 

  2. Daoud A. Effect of fly ash addition on the structure and compressive properties of 4032–fly ash particle composite foams. J Alloys Compd. 2009;487(1–2):618–25.

    Article  Google Scholar 

  3. Gladysz GM, Chawla KK. Voids in materials: from unavoidable defects to designed cellular materials. New York: Elsevier; 2014.

    Google Scholar 

  4. Gibson LJ, Ashby MF. Cellular solids: structure and properties. Cambridge: Cambridge University Press; 1999.

    MATH  Google Scholar 

  5. Mills NJ, Zhu HX. The high strain compression of closed-cell polymer foams. J Mech Phys Solids. 1999;47(3):669–95.

    Article  MATH  Google Scholar 

  6. Rodriguez-Perez MA, Hidalgo F, Solórzano E, de Saja JA. Measuring the time evolution of the gas pressure in closed cell polyolefin foams produced by compression moulding. Polym Test. 2009;28(2):188–95.

    Article  Google Scholar 

  7. Ruiz-Herrero JL, Rodríguez-Pérez MA, de Saja JA. Effective diffusion coefficient for the gas contained in closed cell polyethylene-based foams subjected to compressive creep tests. Polymer. 2005;46(9):3105–10.

    Article  Google Scholar 

  8. Liu X, Zhang J, Fang Q, Wu H, Zhang Y. Response of closed-cell aluminum foams under static and impact loading: experimental and mesoscopic numerical analysis. Int J Impact Eng. 2017;110:382. https://doi.org/10.1016/j.ijimpeng.2016.11.004.

    Article  Google Scholar 

  9. Pang X, Du H. Investigation on dynamic penetration of closed-cell aluminium foam using in situ deceleration measurement. Compos Part B. 2016;100:78–90.

    Article  Google Scholar 

  10. Zhao M, Fan X, Wang TJ. Fatigue damage of closed-cell aluminum alloy foam: modeling and mechanisms. Int J Fatigue. 2016;87:257–65.

    Article  Google Scholar 

  11. Chen Y, Das R, Battley M. Effects of cell size and cell wall thickness variations on the stiffness of closed-cell foams. Int J Solids Struct. 2015;52:150–64.

    Article  Google Scholar 

  12. Zhang Z, Ding J, Xia X, Sun X, Song K, Zhao W, Liao B. Fabrication and characterization of closed-cell aluminum foams with different contents of multi-walled carbon nanotubes. Mater Des. 2015;88:359–65.

    Article  Google Scholar 

  13. Li Q, Chen L, Li X, Zhang J, Zhang X, Zheng K, Fang F, Zhou H, Tian X. Effect of multi-walled carbon nanotubes on mechanical, thermal and electrical properties of phenolic foam via in-situ polymerization. Compos A: Appl Sci Manuf. 2016;82:214–25.

    Article  Google Scholar 

  14. Atturan UA, Nandam SH, Murty BS, Sankaran S. Deformation behaviour of in-situ TiB2 reinforced A357 aluminium alloy composite foams under compressive and impact loading. Mater Sci Eng A. 2017;684:178–85.

    Article  Google Scholar 

  15. Duarte I, Ventura E, Olhero S, Ferreira JMF. A novel approach to prepare aluminium-alloy foams reinforced by carbon-nanotubes. Mater Lett. 2015;160:162–6.

    Article  Google Scholar 

  16. Jung A, Pullen AD, Proud WG. Strain-rate effects in Ni/Al composite metal foams from quasi-static to low-velocity impact behaviour. Compos A: Appl Sci Manuf. 2016;85:1–11.

    Article  Google Scholar 

  17. Hosseini SM, Habibolahzadeh A, Králík V, Petráňová V, Němeček J. Nano-SiCp effects on the production, microstructural evolution and compressive properties of highly porous Al/CaCO3 foam fabricated via continual annealing and roll-bonding process. Mater Sci Eng A. 2017;680:157–67.

    Article  Google Scholar 

  18. Moradi MR, Moloodi A, Habibolahzadeh A. Fabrication of Nano-composite Al-B4C foam via powder metallurgy-space holder technique. Proc Mater Sci. 2015;11:553–9.

    Article  Google Scholar 

  19. Salehi A, Babakhani A, Zebarjad SM. Microstructural and mechanical properties of Al–SiO2 nanocomposite foams produced by an ultrasonic technique. Mater Sci Eng A. 2015;638:54–9.

    Article  Google Scholar 

  20. Zeltmann SE, Poveda RL, Gupta N. Accelerated environmental degradation and residual flexural analysis of carbon nanofiber reinforced composites. Polym Degrad Stab. 2015;121:348–58.

    Article  Google Scholar 

  21. Gupta N, Woldesenbet E. Hygrothermal studies on syntactic foams and compressive strength determination. Compos Struct. 2003;61(4):311–20.

    Article  Google Scholar 

  22. Gupta N, Pinisetty D, Shunmugasamy VC. Reinforced polymer matrix syntactic foams: effect of nano and micro-scale reinforcement. New York: Springer Science & Business Media; 2013.

    Book  Google Scholar 

  23. Gupta N, Zeltmann SE, Shunmugasamy VC, Pinisetty D. Applications of polymer matrix syntactic foams. JOM. 2013;66(2):245–54.

    Article  Google Scholar 

  24. Gupta N, Ricci W. Comparison of compressive properties of layered syntactic foams having gradient in microballoon volume fraction and wall thickness. Mater Sci Eng A. 2006;427(1–2):331–42.

    Article  Google Scholar 

  25. Gupta N. A functionally graded syntactic foam material for high energy absorption under compression. Mater Lett. 2007;61(4–5):979–82.

    Article  Google Scholar 

  26. Bharath Kumar BR, Doddamani M, Zeltmann SE, Gupta N, Ramesh MR, Ramakrishna S. Processing of cenosphere/HDPE syntactic foams using an industrial scale polymer injection molding machine. Mater Des. 2015;92:414–23.

    Article  Google Scholar 

  27. Bharath Kumar BR, Doddamani M, Zeltmann SE, Gupta N, Uzma, Gurupadu S, Sailaja RRN. Effect of surface treatment and blending method on flexural properties of injection molded cenosphere/HDPE syntactic foams. J Mater Sci. 2015;51(8):3793–805.

    Article  Google Scholar 

  28. Shunmugasamy VC, Gupta N, Nguyen NQ, Coelho PG. Strain rate dependence of damage evolution in syntactic foams. Mater Sci Eng A. 2010;527(23):6166–77.

    Article  Google Scholar 

  29. Zeltmann SE, Chen B, Gupta N. Thermal expansion and dynamic mechanical analysis of epoxy matrix-borosilicate glass hollow particle syntactic foams. J Cell Plast. 2017. Accepted, in press. https://doi.org/10.1177/0021955X17691566.

  30. Anantharaman H, Shunmugasamy VC, Strbik Iii OM, Gupta N, Cho K. Dynamic properties of silicon carbide hollow particle filled magnesium alloy (AZ91D) matrix syntactic foams. Int J Impact Eng. 2015;82:14–24.

    Article  Google Scholar 

  31. Májlinger K, Bozóki B, Kalácska G, Keresztes R, Zsidai L. Tribological properties of hybrid aluminum matrix syntactic foams. Tribol Int. 2016;99:211–23.

    Article  Google Scholar 

  32. Myers K, Katona B, Cortes P, Orbulov IN. Quasi-static and high strain rate response of aluminum matrix syntactic foams under compression. Compos A: Appl Sci Manuf. 2015;79:82–91.

    Article  Google Scholar 

  33. Gupta N, Rohatgi PK. Metal matrix syntactic foams: processing, microstructure, properties and applications. Lancaster: DEStech Publications; 2014.

    Google Scholar 

  34. Luong DD, Shunmugasamy VC, Gupta N, Lehmhus D, Weise J, Baumeister J. Quasi-static and high strain rates compressive response of iron and Invar matrix syntactic foams. Mater Des. 2015;66:516–31.

    Article  Google Scholar 

  35. Peroni L, Scapin M, Fichera C, Lehmhus D, Weise J, Baumeister J, Avalle M. Investigation of the mechanical behaviour of AISI 316L stainless steel syntactic foams at different strain-rates. Compos Part B. 2014;66:430–42.

    Article  Google Scholar 

  36. Taherishargh M, Belova IV, Murch GE, Fiedler T. The effect of particle shape on mechanical properties of perlite/metal syntactic foam. J Alloys Compd. 2017;693:55–60.

    Article  Google Scholar 

  37. Corigliano A, Rizzi E, Papa E. Experimental characterization and numerical simulations of a syntactic-foam/glass-fibre composite sandwich. Compos Sci Technol. 2000;60(11):2169–80.

    Article  Google Scholar 

  38. Lamanna E, Gupta N, Cappa P, Strbik OM III, Cho K. Evaluation of the dynamic properties of an aluminum syntactic foam core sandwich. J Alloys Compd. 2017;695:2987–94.

    Article  Google Scholar 

  39. Rahmani O, Khalili SMR, Malekzadeh K, Hadavinia H. Free vibration analysis of sandwich structures with a flexible functionally graded syntactic core. Compos Struct. 2009;91(2): 229–35.

    Article  Google Scholar 

  40. Omar MY, Xiang C, Gupta N, Strbik OM III, Cho K. Syntactic foam core metal matrix sandwich composite: compressive properties and strain rate effects. Mater Sci Eng A. 2015;643:156–68.

    Article  Google Scholar 

  41. Mills NJ. Polymer foams handbook: engineering and biomechanics applications and design guide. Oxford: Butterworth-Heinemann; 2007.

    Google Scholar 

  42. Al Jahwari F, Huang Y, Naguib HE, Lo J. Relation of impact strength to the microstructure of functionally graded porous structures of acrylonitrile butadiene styrene (ABS) foamed by thermally activated microspheres. Polymer. 2016;98:270–81.

    Article  Google Scholar 

  43. Fang J, Gao Y, Sun G, Zhang Y, Li Q. Parametric analysis and multiobjective optimization for functionally graded foam-filled thin-wall tube under lateral impact. Comput Mater Sci. 2014;90:265–75.

    Article  Google Scholar 

  44. Koohbor B, Kidane A. Design optimization of continuously and discretely graded foam materials for efficient energy absorption. Mater Des. 2016;102:151–61.

    Article  Google Scholar 

  45. Shimazaki Y, Nozu S, Inoue T. Shock-absorption properties of functionally graded EVA laminates for footwear design. Polym Test. 2016;54:98–103.

    Article  Google Scholar 

  46. Xiao Z, Fang J, Sun G, Li Q. Crashworthiness design for functionally graded foam-filled bumper beam. Adv Eng Softw. 2015;85:81–95.

    Article  Google Scholar 

  47. Porfiri M, Gupta N. Effect of volume fraction and wall thickness on the elastic properties of hollow particle filled composites. Compos Part B. 2009;40(2):166–73.

    Article  Google Scholar 

  48. Meyers MA. Dynamic behavior of materials. New York: Wiley; 1994.

    Book  MATH  Google Scholar 

  49. Colloca M, Dorogokupets G, Gupta N, Porfiri M. Mechanical properties and failure mechanisms of closed-cell PVC foams. Int J Crashworthiness. 2012;17(3):327–36.

    Article  Google Scholar 

  50. Gupta N, Woldesenbet E, Mensah P. Compression properties of syntactic foams: effect of cenosphere radius ratio and specimen aspect ratio. Compos A: Appl Sci Manuf. 2004;35(1): 103–11.

    Article  Google Scholar 

  51. Gupta N, Ye R, Porfiri M. Comparison of tensile and compressive characteristics of vinyl ester/glass microballoon syntactic foams. Compos Part B. 2010;41(3):236–45.

    Article  Google Scholar 

  52. Luong DD, Strbik OM III, Hammond VH, Gupta N, Cho K. Development of high performance lightweight aluminum alloy/SiC hollow sphere syntactic foams and compressive characterization at quasi-static and high strain rates. J Alloys Compd. 2013;550:412–22.

    Article  Google Scholar 

  53. Bharath Kumar BR, Singh AK, Doddamani M, Luong DD, Gupta N. Quasi-static and high strain rate compressive response of injection-molded cenosphere/HDPE syntactic foam. JOM. 2016;68(7):1861–71.

    Article  Google Scholar 

  54. Kolsky H. An investigation of the mechanical properties of materials at very high rates of loading. Proc Phys Soc B. 1949;62:676.

    Article  Google Scholar 

  55. Luong DD, Pinisetty D, Gupta N. Compressive properties of closed-cell polyvinyl chloride foams at low and high strain rates: experimental investigation and critical review of state of the art. Compos Part B. 2013;44(1):403–16.

    Article  Google Scholar 

  56. Chen WW, Song B. Split Hopkinson (Kolsky) bar: design, testing and applications. New York: Springer Science & Business Media; 2010.

    MATH  Google Scholar 

  57. Follansbee PS, Frantz C. Wave propagation in the split Hopkinson pressure bar. J Eng Mater Technol. 1983;105(1):61–6.

    Article  Google Scholar 

  58. Zhao H, Gary G, Klepaczko JR. On the use of a viscoelastic split hopkinson pressure bar. Int J Impact Eng. 1997;19(4):319–30.

    Article  Google Scholar 

  59. Peroni M, Solomos G, Babcsan N. Development of a Hopkinson bar apparatus for testing soft materials: application to a closed-cell aluminum foam. Materials. 2016;9(1):27.

    Article  Google Scholar 

  60. Chen W, Lu F, Frew DJ, Forrestal MJ. Dynamic compression testing of soft materials. J Appl Mech. 2002;69(3):214–23.

    Article  MATH  Google Scholar 

  61. Nie X, Song B, Ge Y, Chen WW, Weerasooriya T. Dynamic tensile testing of soft materials. Exp Mech. 2009;49(4):451–8.

    Article  Google Scholar 

  62. Van Sligtenhorst C, Cronin DS, Wayne Brodland G. High strain rate compressive properties of bovine muscle tissue determined using a split Hopkinson bar apparatus. J Biomech. 2006;39(10):1852–8.

    Article  Google Scholar 

  63. Shunmugasamy VC, Gupta N, Coelho PG. High strain rate response of rabbit femur bones. J Biomech. 2010;43(15):3044–50.

    Article  Google Scholar 

  64. Kajberg J, Sundin KG. Material characterisation using high-temperature split Hopkinson pressure bar. J Mater Process Technol. 2013;213(4):522–31.

    Article  Google Scholar 

  65. Gómez-del Río T, Barbero E, Zaera R, Navarro C. Dynamic tensile behaviour at low temperature of CFRP using a split Hopkinson pressure bar. Compos Sci Technol. 2005;65(1):61–71.

    Article  Google Scholar 

  66. Tanimura S, Kimura N, Kaizu K, Isuzugawa K. Modified split Hopkinson bar method for low temperatures. Trans Jpn Soc Mech Eng Ser A. 1990;56(529):2040–4.

    Article  Google Scholar 

  67. Shunmugasamy VC, Anantharaman H, Pinisetty D, Gupta N. Unnotched Izod impact characterization of glass hollow particle/vinyl ester syntactic foams. J Compos Mater. 2015;49(2):185–97.

    Article  Google Scholar 

  68. Mrlík M, Al-Ali Al-Maadeed M. Tailoring of the thermal, mechanical and dielectric properties of the polypropylene foams using gamma-irradiation. Polym Degrad Stab. 2016;133:234–42.

    Article  Google Scholar 

  69. Gedler G, Antunes M, Velasco JI. Viscoelastic properties of polycarbonate-graphene nanoplatelets nanocomposite foams. Compos Part B. 2016;93:143–52.

    Article  Google Scholar 

  70. Rodríguez-Pérez MA, Rodríguez-Llorente S, De Saja JA. Dynamic mechanical properties of polyolefin foams studied by DMA techniques. Polym Eng Sci. 1997;37(6):959–65.

    Article  Google Scholar 

  71. Wolska A, Goździkiewicz M, Ryszkowska J. Thermal and mechanical behaviour of flexible polyurethane foams modified with graphite and phosphorous fillers. J Mater Sci. 2012;47(15): 5627–34.

    Article  Google Scholar 

  72. Haines PJ. Thermal methods of analysis: principles, applications and problems. New York: Springer Science & Business Media; 2012.

    Google Scholar 

  73. Menard KP. Dynamic mechanical analysis: a practical introduction. New York: CRC press; 2008.

    Book  Google Scholar 

  74. Kloosterboer JG, Lijten GFCM. Thermal and mechanical analysis of a photopolymerization process. Polymer. 1987;28(7):1149–55.

    Article  Google Scholar 

  75. Calleja G, Jourdan A, Ameduri B, Habas J-P. Where is the glass transition temperature of poly(tetrafluoroethylene)? A new approach by dynamic rheometry and mechanical tests. Eur Polym J. 2013;49(8):2214–22.

    Article  Google Scholar 

  76. Rieger J. The glass transition temperature Tg of polymers – comparison of the values from differential thermal analysis (DTA, DSC) and dynamic mechanical measurements (torsion pendulum). Polym Test. 2001;20(2):199–204.

    Article  Google Scholar 

  77. Ning X, Ishida H. Phenolic materials via ring-opening polymerization of benzoxazines: effect of molecular structure on mechanical and dynamic mechanical properties. J Polym Sci B Polym Phys. 1994;32(5):921–7.

    Article  Google Scholar 

  78. Wang H, Aubuchon SR, Thompson DG, Osborn JC, Marsh AL, Nichols WR, Schoonover JR, Palmer RA. Temperature-dependent dynamic mechanical analysis–Fourier transform infrared study of a poly(ester urethane) copolymer. Macromolecules. 2002;35(23):8794–801.

    Article  Google Scholar 

  79. Delebecq E, Hermeline N, Flers A, Ganachaud F. Looking over liquid silicone rubbers: (2) mechanical properties vs network topology. ACS Appl Mater Interfaces. 2012;4(7): 3353–63.

    Article  Google Scholar 

  80. Jose S, Thomas S, Parameswaranpillai J, Aprem AS, Karger-Kocsis J. Dynamic mechanical properties of immiscible polymer systems with and without compatibilizer. Polym Test. 2015;44:168–76.

    Article  Google Scholar 

  81. Ljungberg N, Wesslén B. The effects of plasticizers on the dynamic mechanical and thermal properties of poly(lactic acid). J Appl Polym Sci. 2002;86(5):1227–34.

    Article  Google Scholar 

  82. Zeltmann SE, Kumar BB, Doddamani M, Gupta N. Prediction of strain rate sensitivity of high density polyethylene using integral transform of dynamic mechanical analysis data. Polymer. 2016;101:1–6.

    Article  Google Scholar 

  83. Zeltmann SE, Prakash KA, Doddamani M, Gupta N. Prediction of modulus at various strain rates from dynamic mechanical analysis data for polymer matrix composites. Compos Part B. 2017;120:27–34.

    Article  Google Scholar 

  84. Shunmugasamy VC, Pinisetty D, Gupta N. Viscoelastic properties of hollow glass particle filled vinyl ester matrix syntactic foams: effect of temperature and loading frequency. J Mater Sci. 2013;48(4):1685–701.

    Article  Google Scholar 

  85. Zeltmann SE. Prediction of strain rate sensitivity of polymers from integral transform of dynamic mechanical data. In: Mechanical and aerospace engineering. New York: New York University; 2016.

    Google Scholar 

  86. Williams ML, Landel RF, Ferry JD. The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. J Am Chem Soc. 1955;77(14):3701–7.

    Article  Google Scholar 

  87. Christensen RM. Theory of viscoelasticity: an intoduction. New York: Academic; 1982.

    Google Scholar 

  88. Tagliavia G, Porfiri M, Gupta N. Vinyl ester – glass hollow particle composites: dynamic mechanical properties at high inclusion volume fraction. J Compos Mater. 2009;43(5):561–82.

    Article  Google Scholar 

  89. Gibson RF. Modal vibration response measurements for characterization of composite materials and structures. Compos Sci Technol. 2000;60(15):2769–80.

    Article  Google Scholar 

  90. Timoshenko S, Young D, Weaver W. Vibration problems in engineering. New York: Wiley; 1974.

    Google Scholar 

  91. Priest EM. Free vibration response comparison of composite beams with fluid structure interaction. In: Mechanical engineering. Monterey: Naval Postgraduate School; 2012. p. 95.

    Google Scholar 

  92. Schultz AB, Tsai SW. Dynamic moduli and damping ratios in fiber-reinforced composites. J Compos Mater. 1968;2(3):368–79.

    Article  Google Scholar 

  93. Assarar M, El Mahi A, Berthelot J-M. Damping analysis of sandwich composite materials. J Compos Mater. 2009;43(13):1461–85.

    Article  Google Scholar 

  94. Barbieri N, Barbieri R, Winikes LC, Oresten LF. Estimation of parameters of a three-layered sandwich beam. J Mech Mater Struct. 2008;3(3):527–44.

    Article  Google Scholar 

  95. Li C, Pain D, Wilcox PD, Drinkwater BW. Imaging composite material using ultrasonic arrays. NDT & E Int. 2013;53:8–17.

    Article  Google Scholar 

  96. Gong W, Chen J, Patterson EA. Buckling and delamination growth behaviour of delaminated composite panels subject to four-point bending. Compos Struct. 2016;138:122–33.

    Article  Google Scholar 

  97. Yang C, Oyadiji SO. Delamination detection in composite laminate plates using 2D wavelet analysis of modal frequency surface. Comput Struct. 2017;179:109–26.

    Article  Google Scholar 

  98. Liu Z, Yu H, He C, Wu B. Delamination damage detection of laminated composite beams using air-coupled ultrasonic transducers. Sci China Phys Mech Astron. 2013;56(7):1269–79.

    Article  Google Scholar 

  99. Kidd TH, Zhuang S, Ravichandran G. In situ mechanical characterization during deformation of PVC polymeric foams using ultrasonics and digital image correlation. Mech Mater. 2012;55:82–8.

    Article  Google Scholar 

  100. Saadatfar M, Garcia-Moreno F, Hutzler S, Sheppard AP, Knackstedt MA, Banhart J, Weaire D. Imaging of metallic foams using X-ray micro-CT. Colloids Surf A Physicochem Eng Asp. 2009;344(1–3):107–12.

    Article  Google Scholar 

  101. Zhang Q, Lee PD, Singh R, Wu G, Lindley TC. Micro-CT characterization of structural features and deformation behavior of fly ash/aluminum syntactic foam. Acta Mater. 2009;57(10):3003–11.

    Article  Google Scholar 

Download references

Acknowledgments

Support provided by Office of Naval Research grant N00014-10-1-0988 is acknowledged. The authors thank the NYU-AD Dean of Engineering for providing partial funding for visit of MRD to NYU-AD to work on the manuscript. Dr. Dirk Lehmhus, Fraunhofer IFAM, Bremen, Germany, is acknowledged for providing several specimens for imaging and for useful discussions. Funding from DAAD (grant # P91583818) and NYU for visit of Dr. Lehmhus to NYU is acknowledged to facilitate discussions. The views expressed in this article are those of the authors, not of funding agencies.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nikhil Gupta .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Gupta, N., Zeltmann, S.E., Luong, D.D., Doddamani, M. (2018). Testing of Foams. In: Schmauder, S., Chen, CS., Chawla, K., Chawla, N., Chen, W., Kagawa, Y. (eds) Handbook of Mechanics of Materials. Springer, Singapore. https://doi.org/10.1007/978-981-10-6855-3_50-1

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-6855-3_50-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-6855-3

  • Online ISBN: 978-981-10-6855-3

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

Publish with us

Policies and ethics