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A generalised formulation for computing the microbuckling load in periodic layered materials

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Abstract

The present paper develops a generalised approach to instability of layered materials for numerical realisation of the method as applied to various constitutive equations of the layers (elastic, hyperelastic, elastic–plastic), different loading schemes (uniaxial or biaxial loading) and different precritical conditions (large or small precritical deformations). It contains many examples of calculations of critical controlled parameters for particular model materials as well as the analysis of different buckling modes.

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References

  1. Budiansky B, Fleck NA (1994) Compressive kinking of fibre composites: a topical review. Appl Mech Rev 47(6):S246–S270

    Article  ADS  Google Scholar 

  2. Soutis C, Turkmen D (1995) Influence of shear properties and fibre imperfections on the compressive behaviour of CFRP laminates. Appl Compos Mater 2(6):327–342

    Article  ADS  Google Scholar 

  3. Schultheisz C, Waas A (1996) Compressive failure of composites, Parts I and II. Prog Aerosp Sci 32(1):1–78

    Article  Google Scholar 

  4. Niu K, Talreja R (2000) Modelling of compressive failure in fiber reinforced composites. Int J Solids Struct 37(17):2405–2428

    Article  MATH  Google Scholar 

  5. Dow NF, Grunfest IJ (1960) Determination of most needed potentially possible improvements in materials for ballistic and space vehicles. General Electric Co., Space Sci. Lab. TISR 60 SD389

  6. Biot MA (1965) Mechanics of incremental deformations. Wiley, New York

    Google Scholar 

  7. Kouri JV, Atluri SN (1993) Analytical modelling of laminated composites. Compos Sci Technol 46(4):335–344

    Article  Google Scholar 

  8. Guz AN (1969) On setting up a stability theory of unidirectional fibrous materials. Sov Appl Mech 5(2):156–162

    Article  ADS  Google Scholar 

  9. Babich IY, Guz AN (1969) Deformation instability of laminated materials. Sov Appl Mech 5(3):53–57

    Google Scholar 

  10. Babich IY, Guz AN (1972) On the theory of elastic stability of compressible and incompressible composite media. Polym Mech 5

  11. Guz AN (ed) (1992) Micromechanics of composite materials: focus on Ukrainian Research. Appl Mech Rev 45(2):15–101

  12. Guz IA (1989) Spatial nonaxisymmetric problems of the theory of stability of laminar highly elastic composite materials. Sov Appl Mech 25(11):1080–1085

    Article  MATH  ADS  Google Scholar 

  13. Guz IA (1989) Three-dimensional nonaxisymmetric problems of the theory of stability of composite materials with a metallic matrix. Sov Appl Mech 25(12):1196–1201

    Article  MATH  ADS  Google Scholar 

  14. Guz IA (1998) Composites with interlaminar imperfections: substantiation of the bounds for failure parameters in compression. Composites Part B 29(4):343–350

    Article  MathSciNet  Google Scholar 

  15. Guz IA, Soutis C (2001) A 3-D stability theory applied to layered rocks undergoing finite deformations in biaxial compression. Eur J Mech A/Solids 20(1):139–153

    Article  MATH  Google Scholar 

  16. Guz IA, Soutis C (2001) Compressive fracture of non-linear composites undergoing large deformations. Int J Solids Struct 38(21):3759–3770

    Article  MATH  Google Scholar 

  17. Guz IA, Herrmann KP (2003) On the lower bounds for critical loads under large deformations in non-linear hyperelastic composites with imperfect interlaminar adhesion. Eur J Mech, A/Solids 22(6):837–849

    Article  MATH  Google Scholar 

  18. Menshykova MV, Guz IA, Menshykov OV (2009) A unified computational approach to instability of periodic laminated materials. Comput Model Eng Sci (CMES) 51(3):239–259

    MATH  Google Scholar 

  19. Guz IA (2005) The effect of the multi-axiality of compressive loading on the accuracy of a continuum model for layered materials. Int J Solids Struct 42(2):439–453

    Article  MATH  Google Scholar 

  20. Rosen BW (1965) Mechanics of composite strengthening. In: Fiber composite materials, chap. 3. American Society of Metals, Metals Park, pp 37–75

  21. Schuerch H (1966) Prediction of compressive strength in uniaxial boron fibre-metal matrix composite materials. AIAA J 4(1):102–106

    Article  ADS  Google Scholar 

  22. Sadovsky MA, Pu SL, Hussain MA (1967) Buckling of microfibers. J Appl Mech 34(12):1011–1016

    Article  Google Scholar 

  23. Guz IA, Soutis C (2000) Critical strains in layered composites with interfacial defects loaded in uniaxial or biaxial compression. Plast Rubber Compos 29(9):489–495

    Article  Google Scholar 

  24. Soutis C, Guz IA (2001) Predicting fracture of layered composites caused by internal instability. Composites, Part A 32(9):1243–1253

    Article  Google Scholar 

  25. Guynn EG, Bradley WL, Ochoa O (1992) A parametric study of variables that affect fibre microbuckling initiation in composite laminates: Part 1-Analyses. J Compos Mater 26(11):1594–1616

  26. Guynn EG, Bradley WL, Ochoa O (1992) A parametric study of variables that affect fibre microbuckling initiation in composite laminates: Part 2-Experiments. J Compos Mater 26(11):1617–1643

  27. Moran P, Liu L, Shih C (1995) Kinking band formation and band broadening in fibre composites under compressive loading. Acta Metall Mater 43(8):2943–2958

    Article  Google Scholar 

  28. Berbinau P, Soutis C, Guz IA (1999) Compressive failure of \(0^\circ \) unidirectional carbon-fibre-reinforced plastic (CFRP) laminates by fibre microbuckling. Compos Sci Technol 59(9):1451–1455

    Article  Google Scholar 

  29. Winiarski B, Guz IA (2008) The effect of fibre volume fraction on the onset of fracture in laminar materials with an array of coplanar interface cracks. Compos Sci Technol 68(12):2367–2375

    Article  Google Scholar 

  30. Guz AN (1999) Fundamentals of the three-dimensional theory of stability of deformable bodies. Springer, Berlin

    Book  MATH  Google Scholar 

  31. Aboudi J (1987) Damage in composites—modelling of imperfect bonding. Compos Sci Technol 28(2):103–128

    Article  Google Scholar 

  32. Librescu L, Schmidt R (2001) A general linear theory of laminated composite shells featuring interlaminar bonding imperfections. Int J Solids Struct 38(19):3355–3375

    Article  MATH  Google Scholar 

  33. Soutis C, Guz IA (2006) Fracture of layered composites by internal fibre instability: effect of interfacial adhesion. Aeronaut J 110(1105):185–195

    Google Scholar 

  34. Ling XW, Atluri SN (2007) A hyperelastic description of single wall carbon nanotubes at moderate strains and temperatures. Comput Model Eng Sci (CMES) 21(1):81–91

    Google Scholar 

  35. Treloar LRG (1975) The physics of rubber elasticity. Oxford University Press, England

  36. Honeycombe RWK (1968) The plastic deformation of metals. Edward Arnold, London

    Google Scholar 

  37. Pinnel MR, Lawley A (1970) Correlation of yielding and structure in aluminium–stainless steel composites. Metall Trans 1(5):1337–1348

    Google Scholar 

  38. Kashtalyan M, Soutis C (2001) Strain energy release rate for off-axis ply cracking in laminated composites. Int J Fract 112(2):L3–L8

    Article  Google Scholar 

  39. Kashtalyan M, Soutis C (2006) Modelling off-axis ply matrix cracking in continuous fibre-reinforced polymer matrix composite laminates. J Mater Sci 41(20):6789–6799

    Article  ADS  Google Scholar 

  40. Zhuk Y, Soutis C, Guz IA (2001) Behaviour of thin-skin stiffened CFRP panels with a stress concentrator under in-plane compression. Composites Part B 32(8):697–709

    Article  Google Scholar 

  41. Zhuk Y, Soutis C, Guz IA (2002) Stiffened composite panels with a stress concentrator under in-plane compression. Int Appl Mech 38(2):240–252

    Article  Google Scholar 

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Acknowledgments

The financial support of the part of this research by The Royal Society, The Royal Academy of Engineering and The Carnegie Trust for the Universities of Scotland is gratefully acknowledged.

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Authors and Affiliations

  1. Centre for Micro- and Nanomechanics (CEMINACS), School of Engineering, University of Aberdeen, Aberdeen, AB24 3UE, Scotland

    I. A. Guz, M. V. Menshykova & O. V. Menshykov

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  1. I. A. Guz
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  2. M. V. Menshykova
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  3. O. V. Menshykov
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Correspondence to I. A. Guz.

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Guz, I.A., Menshykova, M.V. & Menshykov, O.V. A generalised formulation for computing the microbuckling load in periodic layered materials. J Eng Math 95, 155–171 (2015). https://doi.org/10.1007/s10665-014-9753-y

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  • DOI: https://doi.org/10.1007/s10665-014-9753-y

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