Advertisement

Acta Mechanica

, Volume 225, Issue 4–5, pp 1391–1417 | Cite as

A micromechanics based multiscale model for nonlinear composites

  • Dianyun Zhang
  • Anthony M. WaasEmail author
Article

Abstract

A micromechanics model for fiber-reinforced composites that can be used at the subscale in a multiscale computational framework is established to predict the effective nonlinear composite response. Using a fiber–matrix concentric cylinder model as the basic repeat unit to represent the composite, micromechanics is used to relate the applied composite strains to the fiber and matrix strains by a six by six transformation matrix. The resolved spatial variations of the matrix fields are found to be in good agreement with corresponding finite element analysis results. The evolution of the composite nonlinear response is assumed to be governed by two scalar, strain-based variables that are related to the extreme value of an appropriately defined matrix equivalent strain, and the matrix secant moduli are used to compute the composite secant moduli for nonlinear analysis. The results from the micromechanics model are compared well with a full finite element analysis. The predictive capability of the proposed model is illustrated by two distinct fiber-reinforced material systems, carbon and glass, for the fiber volume fraction varying from 50 to 70 %. Since fully analytical solutions are utilized for the micromechanical analysis, the proposed method offers a distinct computational advantage in a multiscale analysis and is therefore suitable for large-scale progressive damage and failure analyses of composite material structures.

Keywords

Transverse Shear Multiscale Model Stiffness Tensor Matrix Strain Axial Shear 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Sfantos G.K., Aliabadi M.H.: Multi-scale boundary element modelling of material degradation and fracture. Comput. Methods Appl. Mech. Eng. 196, 1310–1329 (2007)CrossRefzbMATHGoogle Scholar
  2. 2.
    Pineda E.J., Bednarcyk B.A., Waas A.M., Arnold S.M.: Progressive failure of a unidirectional fiber-reinforced composite using the method of cells: discretization objective computational results. Int. J. Solids Struct. 50, 1203–1216 (2013)CrossRefGoogle Scholar
  3. 3.
    Herakovich C.T.: Mechanics of Fibrous Composites. Wiley, New York (1998)Google Scholar
  4. 4.
    Aboudi J., Arnold S.M., Bednarcyk B.A.: Micromechanics of Composite Materials: A Generalized Multiscale Analysis Approach. Elsevier, Amsterdam (2013)Google Scholar
  5. 5.
    Hashin Z., Rosen B.W.: The elastic moduli of fiber-reinforced materials. J. Appl. Mech. 31, 223–232 (1964)CrossRefGoogle Scholar
  6. 6.
    Christensen R.M., Lo K.H.: Solutions for effective shear properties in three phase sphere and cylinder models. J. Mech. Phys. Solids 27, 315–330 (1979)CrossRefzbMATHGoogle Scholar
  7. 7.
    Mori T., Tanaka K.: Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. 21, 571–574 (1973)CrossRefGoogle Scholar
  8. 8.
    Prabhakar P., Waas A.M.: Upscaling from a micro-mechanics model to capture laminate compressive strength due to kink banding instability. Comput. Mater. Sci. 67, 40–47 (2013)CrossRefGoogle Scholar
  9. 9.
    Zhao, Y.H., Weng, G.J.: Theory of plasticity for a class of inclusion and fiber-reinforced composites. In: Weng, G., Taya, M., Abé, H. (eds.) Micromechanics and Inhomogeneity, pp. 599–622. Springer, New York (1990)Google Scholar
  10. 10.
    Qiu Y.P., Weng G.J.: A Theory of plasticity for porous materials and particle-reinforced composites. J. Appl. Mech. 59, 261–268 (1992)CrossRefzbMATHGoogle Scholar
  11. 11.
    Segurado J., Llorca J., González C.: On the accuracy of mean-field approaches to simulate the plastic deformation of composites. Scripta Mater. 46, 525–529 (2002)CrossRefGoogle Scholar
  12. 12.
    Nemat-Nasser S., Iwakuma T., Hejazi M.: On composites with periodic structure. Mech. Mater. 1, 239–267 (1982)CrossRefGoogle Scholar
  13. 13.
    Accorsi M.L., Nemat-Nasser S.: Bounds on the overall elastic and instantaneous elastoplastic moduli of periodic composites. Mech. Mater. 5, 209–220 (1986)CrossRefGoogle Scholar
  14. 14.
    Dvorak G.J., Benveniste Y.: On transformation strains and uniform fields in multiphase elastic media. Proc. Math. Phys. Sci. 437, 291–310 (1992)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Dvorak G.J.: Transformation field analysis of inelastic composite materials. Proc. Math. Phys. Sci. 437, 311–327 (1992)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Michel J.C., Suquet P.: Nonuniform transformation field analysis. Int. J. Solids Struct. 40, 6937–6955 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Aboudi J.: Mechanics of Composite Materials: A Unified Micromechanical Approach. Elsevier, Amsterdam (1991)zbMATHGoogle Scholar
  18. 18.
    Paley M., Aboudi J.: Micromechanical analysis of composites by the generalized cells model. Mech. Mater. 14, 127–139 (1992)CrossRefGoogle Scholar
  19. 19.
    Aboudi J., Pindera M.-J., Arnold S.M.: Linear thermoelastic higher-order theory for periodic multiphase materials. J. Appl. Mech. 68, 697–707 (2001)CrossRefzbMATHGoogle Scholar
  20. 20.
    Aboudi J., Pindera M.-J., Arnold S.M.: Higher-order theory for periodic multiphase materials with inelastic phases. Int. J. Plast. 19, 805–847 (2003)CrossRefzbMATHGoogle Scholar
  21. 21.
    Haj-Ali R., Aboudi J.: Nonlinear micromechanical formulation of the high fidelity generalized method of cells. Int. J. Solids Struct. 46, 2577–2592 (2009)CrossRefzbMATHGoogle Scholar
  22. 22.
    Bednarcyk B.A., Arnold S.M., Aboudi J., Pindera M.-J.: Local field effects in titanium matrix composites subject to fiber-matrix debonding. Int. J Plast. 20, 1707–1737 (2004)CrossRefzbMATHGoogle Scholar
  23. 23.
    Bednarcyk B.A., Aboudi J., Arnold S.M.: Micromechanics modeling of composites subjected to multiaxial progressive damage in the constituents. AIAA J. 48, 1367–1378 (2010)CrossRefGoogle Scholar
  24. 24.
    Haj-Ali R., Aboudi J.: Formulation of the high-fidelity generalized method of cells with arbitrary cell geometry for refined micromechanics and damage in composites. Int. J. Solids Struct. 47, 3447–3461 (2010)CrossRefzbMATHGoogle Scholar
  25. 25.
    Sun C.T., Vaidya R.S.: Prediction of composite properties from a representative volume element. Compos. Sci. Technol. 56, 171–179 (1996)CrossRefGoogle Scholar
  26. 26.
    Xia Z., Zhang Y., Ellyin F.: A unified periodical boundary condition for representative volume elements of composites and applications. Int. J. Solids Struct. 40, 1907–1921 (2003)CrossRefzbMATHGoogle Scholar
  27. 27.
    González C., Lorca J.: Mechanical behavior of unidirectional fiber-reinforced polymers under transverse compression: microscopic mechanisms and modeling. Compos. Sci. Technol. 67, 2795–2806 (2007)CrossRefGoogle Scholar
  28. 28.
    Drugan W.J., Willis J.R.: A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites. J. Mech. Phys. Solids 44, 497–524 (1996)CrossRefzbMATHMathSciNetGoogle Scholar
  29. 29.
    Segurado J., Llorca J.: A numerical approximation to the elastic properties of sphere-reinforced composites. J. Mech. Phys. Solids 50, 2107–2121 (2002)CrossRefzbMATHGoogle Scholar
  30. 30.
    Totry E., Gonzlez C., Lorca J.: Influence of the loading path on the strength of fiber-reinforced composites subjected to transverse compression and shear. Int. J. Solids Struct. 45, 1663–1675 (2008)CrossRefzbMATHGoogle Scholar
  31. 31.
    Heinrich C., Aldridge M., Wineman A.S., Kieffer J., Waas A.M., Shahwan K.: The influence of the representative volume element (RVE) size on the homogenized response of cured fiber composites. Model. Simul. Mater. Sci. Eng. 20, 075007 (2012)CrossRefGoogle Scholar
  32. 32.
    Totry E., Gonzàlez C., Lorca J.: Prediction of the failure locus of C/PEEK composites under transverse compression and longitudinal shear through computational micromechanics. Compos. Sci. Technol. 68, 3128–3136 (2008)CrossRefGoogle Scholar
  33. 33.
    Totry E., Molina-Aldareguía J.M., González C., Lorca J.: Effect of fiber, matrix and interface properties on the in-plane shear deformation of carbon-fiber reinforced composites. Compos. Sci. Technol. 70, 970–980 (2010)CrossRefGoogle Scholar
  34. 34.
    Sicking, D.L.: Mechanical Characterization of Nonlinear Laminated Composites with Transverse Crack Growth, Ph.D. Thesis, Texas A&M University, College Station, TX (1992)Google Scholar
  35. 35.
    Ng W.H., Salvi A.G., Waas A.M.: Characterization of the in-situ non-linear shear response of laminated fiber-reinforced composites. Compos. Sci. Technol. 70, 1126–1134 (2010)CrossRefGoogle Scholar
  36. 36.
    Hyer M.W., Waas A.M.: Micromechanics of Linear Elastic Continuous Fiber Composites, Comprehensive Composite Materials, pp. 345–375. Pergamon, Oxford (2002)Google Scholar
  37. 37.
    Eshelby J.D.: The Determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. A: Math. Phys. Eng. Sci. 241, 376–396 (1957)CrossRefzbMATHMathSciNetGoogle Scholar
  38. 38.
    Pankow, M., Yen, C.-F., Rudolph, M., Justusson, B., Zhang, D., Waas, A.M.: Experimental investigation on the deformation response of hybrid 3D woven composites. In: Proceedings of the 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Honolulu, Hawaii, USA, AIAA, pp. 2012–1572 (2012)Google Scholar
  39. 39.
    Timoshenko S.P., Goodier J.N.: Theory of Elasticity. McGraw-Hill, New York (1970)zbMATHGoogle Scholar
  40. 40.
    Heinrich C., Aldridge M., Wineman A.S., Kieffer J., Waas A.M., Shahwan K.: The influence of the representative volume element (RVE) size on the homogenized response of cured fiber composites. Model. Simul. Mater. Sci. Eng. 20, 075007 (2012)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2014

Authors and Affiliations

  1. 1.Composite Structures Laboratory, Department of Aerospace EngineeringUniversity of MichiganAnn ArborUSA

Personalised recommendations