Effective stress-strain relations for two-dimensional cellular sandwich cores: Homogenization, material models, and properties

[+] Author and Article Information
Jörg Hohe, Wilfried Becker

Universität Siegen, Institut für Mechanik und Regelungstechnik, Paul-Bonatz-Str 9-11, D-57068 Siegen, Germany; hohe@imr-sun8.fb5.uni-siegen.de, beck@fb5.uni-siegen.de

Appl. Mech. Rev 55(1), 61-87 (Aug 21, 2001) (27 pages) doi:10.1115/1.1425394 History: Received August 21, 2001
Copyright © 2002 by ASME
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Bitzer TN (1997), Honeycomb Technology, Chapman & Hall, London.
Hoff  NJ and Mautner  SE (1944), Sandwich construction, Aero. Eng. Rev. 3, 29–43.
Bitzer  TN (1994), Honeycomb marine applications, J. Reinf. Plast. Compos. 13, 355–360.
Atkinson  R (1997), Innovative uses for sandwich constructions, Reinf. Plastics 41, 30–33.
Mash  G (1999), The meat in the sandwich, Reinf. Plastics 43, 28–35.
Allen HG (1969), Analysis and Design of Structural Sandwich Panels, Pergamon Press, Oxford.
Corden J (1995), Honeycomb structure, ASM Handbook I. Composites, JR Davis (ed), American Society for Metals, Metals Park OH, 721–728.
Marshall AC (1990), Core composite and sandwich structures, International Encyclopedia of Composites I, SM Lee (ed), VCH Publishers, New York, 488–507.
Vinson JR (1999), The Behavior of Sandwich Structures of Isotropic and Composite Materials, Technomic Publ, Lancaster PA.
Zenkert D (1997), Sandwich Construction, EMAS Publishing, Warley.
Habip  LM (1964), A review of recent Russian work on sandwich structures, Int. J. Mech. Sci. 6, 483–487.
Habip  LM (1965), A survey of modern developments in the analysis of sandwich structures Appl. Mech. Rev. 18, 93–98.
Frostig Y (1998), Inaccuracies and validity of simplified models in the theory of sandwich structures, Sandwich Construction 4 (Ohlsson, KA ed.), Proc of 4th Int Conf Sandwich Construction, (Stockholm, Sweden, 08.-12.06.1998), EMAS Publishing, London, 167–189.
Librescu  L and Hause  T (2000), Recent developments in the modeling and behavior of advanced sandwich constructions: A survey, Compos. Struct. 48, 1–17.
Noor  AK, Burton  WS, and Bert  CW (1996), Computational models for sandwich panels and shells, Appl. Mech. Rev. 49, 155–199.
Noor  AK, Burton  WS, and Peters  JM (1995), Hierarchical adaptive modeling of structural sandwiches and multilayered composite panels, Eng. Fract. Mech. 50, 801–817.
O’Sullivan  HP (1961), Double block shear test for foil honeycomb cores, Aircraft Eng. 33, 64–66.
Smallen  H and Roberts  WF (1961), Properties of stainless steel sandwich using low-density honeycomb cores, Weld. J. (Miami) 40, 90s–96s.
Adams  RD and Maheri  MR (1993), The dynamic shear properties of structural honeycomb materials, Compos. Sci. Technol. 47, 15–23.
Bitzer, TN (1998), Basic sandwich panel tests, Sandwich Construction 4, KA Ohlsson (ed), Proc of 4th Int Conf Sandwich Construction (Stockholm, Sweden, 08.-12.06.1998), EMAS Publ, London, 615–621.
European Space Agency (1994), Structural Materials Handbook, ESA PSS-03-203, European Space Agency, Paris.
Hexcel Co (1987), Mechanical Properties of Hexcel Honeycomb Materials, Report TSB 120, Hexcel Co, Dublin CA.
Voigt  W (1889), On the relation between the elasticity constants of isotropic bodies, Ann. Phys. Chem. 274, 573–587.
Reuss  A (1929), Determination of the yield point of polycrystals based on the yield condition of sigle crystals (German), Z. Angew. Math. Mech. 9, 49–58.
Hill  R (1952), The elastic behaviour of a crystalline aggregate, Proc. R. Soc. London, Ser. A 65, 349–354.
Hashin  Z and Shtrikman  S (1962), On some variational principles in anisotropic and nonhomogeneous elasticity, J. Mech. Phys. Solids 10, 335–342.
Talbot  DRS and Willis  JR (1985), Variational principles for inhomogeneous non-linear media, ASME J. Appl. Mech. 35, 39–54.
Eshelby  JD (1957), The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. R. Soc. London, Ser. A 241, 376–396.
Bakhvalov N and Panasenko G (1989), Homogenisation: Averaging Process in Periodic Media, Kluwer Academic Publ, Dordrecht.
Bensoussan A Lions JL and Papanicolaou G (1978), Asymptotic Analysis for Periodic Structures, North Holland Publ, Amsterdam.
Sanchez-Palencia E and Zaoui A (eds) (1987), Homogenization Techniques for Composite Media, Springer-Verlag, Berlin.
Nemat-Nasser S and Hori M (1993), Micromechanics: Overall Properties of Heterogeneous Materials, North Holland Publ, Amsterdam.
Garrard  A (1949), Theory of sandwich construction I, Br. Plast. 18, 380–388.
Garrard  A (1949), Theory of sandwich construction II, Br. Plast. 18, 451–458.
Horvay  G (1952), Bending of honeycombs and of perforated plates, ASME J. Appl. Mech. 19, 122–123.
Libove C and Hubka RE (1951), Elastic constants for corrugated-core sandwich plates, NACA TN 2289, Washington DC.
Sapowith  AD (1959), Transverse shear stiffness for the double ”V” corrugated-core sandwich panel, J. Aerospace Eng. 18, 53–56.
Akasaka  T and Takagishi  T (1959), The shear modulus of foil honeycomb sandwich structures, Trans. Japan Soc. Aerospace Sci. 2, 83–90.
Chang  CC and Ebcioglu  LK (1961), Effect of cell geometry on the shear modulus and on density of sandwich panel cores, J. Basic Eng. 83, 513–518.
Hoffman  GA (1958), Poisson’s ratio for honeycomb sandwich cores, J. Aerosp. Sci. 25, 534–535.
Kelsey  S, Gellatley  RA, and Clark  BW (1958), The shear modulus of foil honeycomb cores,Aircraft Eng. 30, 294–302.
Nagao H (1959), The shear modulus of honeycomb cores, Proc of 9th Japan Natl Congress for Applied Mechanics, 97–100.
Penzien  J and Didriksson  T (1964), Effective shear modulus of honeycomb cellular structure, AIAA 2, 531–535.
Ponte Castañeda  P and Suquet  P (1995), On the Effective Mechanical Behaviour of Weakly Inhomogeneous Nonlinear Materials, Eur. J. Mech. A/Solids A14, 205–236.
Becker  W (1998), The inplane stiffness of a honeycomb core including the thickness effect, Arch. Appl. Mech. 68, 334–341.
Becker  W (2000), Closed-form analysis of the thickness effect of regular honeycomb core material, Compos. Struct. 48, 67–70.
Hohe  J and Becker  W (1999), Determination of the elasticity tensor of non-orthotropic cellular sandwich cores, Techn. Mech. 19, 259–268.
Hohe  J and Becker  W (2001), A refined analysis of the effective elasticity tensor for general cellular sandwich cores, Int. J. Solids Struct. 38, 3689–3717.
Guedes  JM and Kikuchi  N (1990), Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods, Comput. Methods Appl. Mech. Eng. 83, 143–198.
Kalamkarov AL (1992), Composite and Reinforced Elements of Construction, John Wiley & Sons, Chichester.
Kalamkarov  AL and Kolpakov  AG (1993), Numerical design of thin-walled structural members on account of their strength, Int. J. Numer. Methods Eng. 36, 3441–3449.
Kalamkarov AL and Kolpakov AG (1997), Analysis, Design and Optimization of Composite Structures, John Wiley & Sons, Chichester.
Kolpakov  AG (1985), Determination of the average characteristics of elastic frameworks, J. Appl. Math. Mech. 49, 739–745.
Lee  J, Choi  JB, and Choi  K (1996), Application of homogenization FEM analysis to regular and re-entrant honeycomb structures, J. Mater. Sci. 31, 4105–4110.
Shi  G and Tong  P (1995), Equivalent transverse shear stiffness of honeycomb cores, Int. J. Solids Struct. 32, 1383–1393.
Shi  G and Tong  P (1995), The derivation of equivalent constitutive equations of honeycomb structures by a two-scale method, Comput. Mech. 15, 395–407.
Ueng  CES, Underwood  EE, and Liu  TL (1979), Shear modulus of superplastically formed sandwich cores, Comput. Struct. 10, 393–397.
Ko WL (1980), Comparison of structural behavior of superplastically formed/diffusion bonded sandwich structures and honeycomb core sandwich structures, NASA TM 81348, Washington DC.
Borris PW, Caldwell MS, Castillo JI, and Bitzner TN (1989), Recent honeycomb developments, Tomorrow’s Materials Today, Proc of 34th SAMPE Symp (Reno NV, 08.-11.05.1989), 849–860.
Christensen  RM (2000), Mechanics of cellular and other low-density materials, Int. J. Solids Struct. 37, 93–104.
Kim  B and Christensen  RM (2000), Basic two-dimensional core types for sandwich structures, Int. J. Mech. Sci. 42, 657–676.
Cosserat E and Cosserat F (1909), Theory of Deformable Bodies (French), A Hermann et Fils, Paris.
Lakes  R (1993), Materials with structural hierarchy, Nature (London) 361, 511–515.
Bishop  JFW and Hill  R (1951), A theory of the plastic distortion of a polycrystalline aggregate under combined stress, Philos. Mag. 42, 414–427.
Gibson LJ and Ashby MF (1997), Cellular Solids, Cambridge Univ Press, Cambridge.
Gibson  LJ, Ashby  MF, Schajer  GS, and Robertson  CI (1982), The mechanics of two-dimensional cellular materials, Proc. R. Soc. London, Ser. A 382, 25–42.
Abd El-Sayed  FK, Jones  R, and Burgess  IW (1979), A theoretical approach to the deformation of honeycomb based composite materials, Composites 10, 209–214.
Caddock BD, Evans KE, and Masters IG (1991), Honeycomb cores with a negative Poisson’s ratio for use in composite sandwich panels, Composites: Design Manufacture and Application, BD Caddock, KE Evans, and IG Masters (eds), Proc of 8th Int Conf Composite Materials (Hawaii, 1991), 3-E-1–3-E-10.
Gibson  LJ (1989), Modelling the mechanical behavior of cellular materials, Mater. Sci. Eng., A 110, 1–36.
Meraghni  F, Desrumaux  F, and Benzeggagh  ML (1999), Mechanical behaviour of cellular core for structural sandwich panels, Compos. A 30, 767–779.
Nast E (1997), On the numerical and experimental analysis of shells consisting of sandwich and composite materials, PhD-thesis (German) Univ of the German Forces Hamburg, Dept of Electrical Eng, Hamburg.
Papka  SD and Kyriakides  S (1999), Biaxial crushing of honeycombs – Part II: Analysis, Int. J. Solids Struct. 36, 4397–4423.
Ueng CES, Underwood EE and Liu TL (1979), Shear modulus of new sandwich cores made of superplastic sheet, Proc of 20th Structures, Structural Dynamics and Materials Conf (St Louis MO, 04.-06.04.1979), 176-180.
Ueng  CES, Underwood  EE, and Liu  TL (1980), Shear modulus of new sandwich cores made of superplastic sheet, AIAA J. 18, 721–723.
Burton  WS and Noor  AK(1997), Assessment of continuum models for sandwich panel honeycomb cores, Comput. Methods Appl. Mech. Eng. 145, 341–360.
Chamis CC, Aiello RA, and Murthy PLN (1986), Composite sandwich thermostructural behavior: Computational simulation, Proc of 27th Structures, Structural Mechanics and Materials Conf (San Antonio TX, 19.-21.05.1986) Part I: Structures and Materials, New York, 370–381.
Chamis  CC, Aiello  RA, and Murthy  PLN (1988), Fiber composite sandwich thermostructural behavior: Computational simulation, J. Compos. Technol. Res. 10, 93–99.
Overaker  DW, Cuitiño  AM, and Langrana  NA (1998), Effects of morphology and orientation on the behavior of two-dimensional hexagonal foams and application in a re-entrant foam anchor model, Mech. Mater. 29, 43–52.
Overaker  DW, Cuitiño  AM, and Langrana  NA (1998), Elastoplastic micromechanical modeling of two-dimensional irregular convex and nonconvex (re-entrant) hexagonal foams, ASME J. Appl. Mech. 65, 748–757.
Warren  WE and Kraynik  AM (1987), Foam mechanics: The linear elastic response of two-dimensional spatially periodic cellular materials, Mech. Mater. 6, 27–37.
Warren  WE and Kraynik  AM, and Stone  CM (1989), A constitutive model for two-dimensional nonlinear elastic foams, J. Mech. Phys. Solids 37, 717–733.
Hohe  J and Becker  W (2001), An energetic homogenization procedure for the elastic properties of general cellular sandwich cores, Compos. B 32, 185–197.
Ueng  CES and Kim  TD (1983), Shear modulus of core materials with arbitrary polygonal shape, Comput. Struct. 16, 21–25.
Scholz SP (1992), Continuum mechanical modeling of sandwich grid structures, PhD-thesis (German) Technical Univ of Berlin, Dept of Physical Eng, Berlin.
Vinson JR and Sierakowski RL (1987), The Behavior of Sandwich Structures composed of Composite Materials, Martinus Nijhoff Publ, Dordrecht.
Masters IG and Evans KE (1993), Auxetic honeycombs for composite sandwich panels, Proc of 2nd Canadian and Int Composites Conf, 701–710.
Masters  IG and Evans  KE (1996), Models for the elastic deformation of honeycombs, Compos. Struct. 35, 403–422.
Zhang  J and Ashby  MF (1992), The out-of-plane properties of honeycombs, Int. J. Mech. Sci. 34, 475–489.
Nast E (1997), On honeycomb-type core moduli, Proc of 38th Structures, Structural Dynamics, and Materials Conf (Kissimmee FL, 07.-10.04.1997), 1035–1044.
Torquato  S, Gibianski  LV, Silva  MJ, and Gibson  LJ (1998),Effective mechanical and transport properties of cellular solids, Int. J. Mech. Sci. 40, 71–82.
Fu  M and Yin  J (1999),Equivalent elastic parameters of the honeycomb core (Chinese), Acta Mech. Sin. 31, 113–118.
Ladd  AJC and Kinney  JH (1997), Elastic constants of cellular structures, Physica A A240, 349–360.
Warren  TL (1990), Negative Poisson’s ratio in transversely isotropic foam structure, J. Appl. Phys. 67, 7591–7594.
Hohe  J, Beschorner  C, and Becker  W (1999), Effective elastic properties of hexagonal and quadrilateral grid structures, Compos. Struct. 46, 73–89.
Elspass W and Flemming M (1990), Analysis of precision sandwich structures under thermal loading, Proc of 17th Congress Int Council of Aeronautical Sciences (Stockholm, Sweden, 09.-14.09.1990) 2 , ICAS-90-4.8.1, AIAA, Reston VA, 1513–1518.
Grediac  M (1993), A finite element study of the transverse shear in honeycomb cores, Int. J. Solids Strcut. 30, 1777–1788.
Simone  AE and Gibson  LJ (1998), Effects of solid distribution on the stiffness and strength of metallic foams, Acta Mater. 46, 2139–2150.
Simone  AE and Gibson  LJ (1998), The effect of cell wall curvature and corrugations on the stiffness and strength of metallic foams, Acta Mater. 46, 3929–3935.
Friis  EA, Lakes  RS, and Parks  JB (1988), Negative Poisson’s Ratio Polymeric and Metallic Foams, J. Mater. Sci. 23, 4406–4414.
Lakes  R (1987), Foam structures with negative Poisson’s ratio, Science 235, 1038–1040.
Choi  JB and Lakes  RS (1995), Nonlinear analysis of the Poisson’s ratio of negative Poisson’s ratio foams, J. Compos. Mater. 29, 113–128.
Evans  KE (1991), The design of doubly curved sandwich panels with honeycomb cores, Compos. Struct. 17, 95–111.
Smith  CW, Grima  JN, and Evans  KE (2000), A novel mechanism for generating auxetic behaviour in reticulated foams: Missing rib foam model, Acta Mater. 48, 4349–4356.
Kalamkarov  AL (1987), On the determination of the effective characteristics of cellular plates and shells of periodic structure, Mech. Solids 22, 175–179.
Hohe  J and Becker  W (1999), Effective elastic properties of triangular grid structures, Compos. Struct. 45, 131–145.
Hunt  HEM (1993), The mechanical strength of honeycomb monoliths as determined by simple experiments, Trans. Inst. Chem. Eng. 71, 257–266.
Chen  HJ and Tsai  SW (1996), Analysis and optimum design of composite grid structures, J. Compos. Mater. 30, 503–534.
Sippel R and Helwig G (1991), A High performance sandwich reflector for “’First”’: Design and mechanical analysis of the sandwich core, Proc of Int Conf Spacecraft Structures and Mechanical Testing (Noordwijk, The Netherlands, 24.-26.04.1991), 738–787.
Chung  J and Waas  AM (2000), The inplane elastic properties of circular cell and elliptical cell honeycombs, Acta Mech. 144, 29–42.
Hohe  J and Becker  W (2000), A mechanical model for two-dimensional cellular sandwich cores with general geometry, Comput. Mater. Sci. 19, 108–115.
Kalamkarov  AL (1989), The thermoelasticity problem for structurally non-uniform shells of regular structure, J. Appl. Mech. Tech. Phys. 30, 981–988.
Silva  MJ, Hayes  WC, and Gibson  LJ (1995), The effects of non-periodic microstructure on the elastic properties of two-dimensional cellular solids, Int. J. Mech. Sci. 37, 1161–1177.
Fortes  MA and Ashby  MF (1999), The effect of non-uniformity on the in-plane modulus of honeycombs, Acta Mater. 47, 3469–3473.
Ko WL (1979), Elastic constants for superplastically formed/diffusion bonded sandwich structures, Proc of 20th Structures, Structural Dynamics and Materials Conf (St. Louis MO, 04.-06.04.1979), 188–207.
Ko  WL (1980), Elastic constants for superplastically formed/diffusion bonded sandwich structures, AIAA J. 18, 986–987.
Nordstrand  TM and Carlsson  LA (1997), Evaluation of transverse shear stiffness of structural core sandwich plates, Compos. Struct. 37, 145–153.
Nordstrand  TM, Carlsson  LA, and Allen  HG (1994), Transverse shear stiffness of structural core sandwich, Compos. Struct. 27, 317–329.
Ko  WL (1982), Structural properties of superplastically formed/diffusion bonded orthogonally corrugated core sandwich plates, AIAA J. 20, 536–543.
Kobelev  VN, Ustarkhanov  OM, and Bulgakov  AL (1991), Reduced characteristics of sandwich structure pyramidal filler (Russian), Izvestiya VUZ 34, 3–6.
Jensen DV and Schneller C (1991), Transverse shearing of novel honeycomb cores, Proc of Conf Advanced Composite Materials in Civil Eng (Las Vegas NV, 31.01.-01.02.1991), 394–404.
Grenestedt  JL (1998), Influence of wavy imperfections in cell walls on elastic stiffness of cellular solids, J. Mech. Phys. Solids 46, 29–50.
Guo  XE and Gibson  LJ (1999), Behavior of intact and damaged honeycombs: A finite element study, Int. J. Mech. Sci. 41, 85–105.
Prakash  O, Bichebois  P, Brechet  Y, Louchet  F, and Embury  JD (1996), A note on the deformation behaviour of two-dimensional model cellular structures, Philos. Mag. A73, 739–751.
Elspass W (1990), Design of high precision sandwich structures using analytical and finite element methods, Finite Element Methods in the Design Process, Proc of 6th World Congress on Finite Element (Banff, Canada, 1990).
Carlsson  L, Fellers  C, and Jonsson  P (1985), Bending stiffness of corrugated cardboard with special reference to unsymmetrical and multi-layer constructions, Das Papier 39, 149–156 (German).
Norris CB (1947), An Analysis of the Compressive Strength of Honeycomb Cores, NACA TN 1251, Washington DC.
Werren F and Norris B (1950), Analysis of Shear Strength of Honeycomb Cores for Sandwich Construction, NACA TN 2208, Washington DC.
Wang  Y (1991), Elastic collapse of honeycombs under out-of-plane pressure, Int. J. Mech. Sci. 33, 637–644.
Shi  G and Tong  P (1994), Local buckling of honeycomb sandwich plates under action of transverse shear forces, AIAA J. 32, 1520–1524.
Ogawa  T and Okazaki  N (1993), Compressive strength of various honeycombs, J. Soc. Mater. Sci. Jpn. 42, 823–828 (Japanese).
Gibson  LJ, Ashby  MF, Zhang  J, and Triantafillou  TC (1989), Failure surfaces for cellular materials under multiaxial loads - I. Modelling, Int. J. Mech. Sci. 31, 635–663.
Zhang  J and Ashby  MF (1992), Buckling of honeycombs under in-plane biaxial stresses, Int. J. Mech. Sci. 34, 491–509.
Klintworth  JW and Stronge  WJ (1988), Elasto-plastic yield limits and deformation laws for transversely crushed honeycombs, Int. J. Mech. Sci. 30, 273–292.
Hutzler  S and Weaire  D (1997), Buckling properties of 2D regular elastomeric honeycombs, J. Phys.: Condens. Matter 9, L323–L329.
Huybrechts  S and Tsai  WT (1996), Analysis and behavior of grid structures, Compos. Sci. Technol. 56, 1001–1015.
Kraynik  AM, Reinelt  DA, and Princen  HM (1991), The nonlinear elastic behavior of polydisperse hexagonal foams and concentrated emulsions, J. Rheol. 35, 1235–1253.
Papka  SD and Kyriakides  S (1994), In-plane compressive response and crushing of honeycomb, J. Mech. Phys. Solids 42, 1499–1532.
Zhu  HX and Mills  NJ (2000), The in-plane non-linear compression of regular honeycombs, Int. J. Solids Struct. 37, 1931–1949.
Silva  MJ and Gibson  LJ (1997), The effects of non-periodic microstructure and defects on the compressive strength of two-dimensional cellular solids, Int. J. Mech. Sci. 39, 549–563.
Klintworth  JW and Stronge  WJ (1989), Plane punch indentation of a ductile honeycomb, Int. J. Mech. Sci. 31, 359–378.
Stronge  WJ and Shim  VPW (1988), Microdynamics of crushing in cellular solids, J. Eng. Mat. Tech. 110, 185–190.
Papka  SD and Kyriakides  S (1999), Biaxial crushing of honeycombs – Part I: Experiments, Int. J. Solids Struct. 36, 4367–4396.
Schreyer  HL, Zuo  QH, and Maji  AK (1994), Anisotropic plasticity model for foams and honeycombs, J. Eng. Mech. 120, 1913–1930.
Caddock  BD and Evans  KE (1989), Microporous materials with negative Poisson’s ratios: I. Microstructure and mechanical properties, J. Phys. D 22, 1877–1882.
Onck  PR, Andrews  EW, and Gibson  LJ (2001), Size effects in ductile cellular solids. Part I: Modeling, Int. J. Mech. Sci. 43, 681–699.
Brulin O and Hsieh RKT (eds) (1982), Mechanics of Micropolar Media, World Scientific Publ, Singapore.
Mühlhaus HB (ed) (1995), Continuum Models for Materials with Microstructure, John Wiley & Sons, Chichester.
Warren WE and Byskov E (1997), Micropolar and nonlocal effects in spatially periodic, two-dimensional structures, Report R 37, Technical Univ of Denmark, Dept of Structural Eng and Materials, Lyngby.


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Structural sandwich panel
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Concept of the representative volume element
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Hexagonal honeycomb core
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Effective in-plane engineering constants for equilateral hexagonal honeycomb cores
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Effective transverse engineering constants for equilateral hexagonal honeycomb cores
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General hexagonal sandwich core
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Quadrilateral cell core
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Orthotropic triangular cell core
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Normal and shear components of the effective elasticity tensor for some basic sandwich core geometries 94
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Coupling components of the effective elasticity tensor for some basic sandwich core geometries 94
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Nonlinear material response 137



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