Skip to main content
SpringerLink
Log in

Shakedown and Optimization Analysis of Periodic Composites

  • Conference paper
Limit State of Materials and Structures

Abstract

In this work, non-conforming three-dimensional finite elements are used for the limit and shakedown analysis of periodic metal-matrix composites. The optimal design variables, such as fiber distribution and various volume fractions are investigated. Combined with homogenization theory, the global safe loading domains for the composites, as well as the global homogenized material parameters are determined, which opens the way for global structural design.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Akoa, F., Hachemi, A., Le Thi Hai An, Mouhtamid, S., Tao, P.D.: Application of lower bound direct method to engineering structures. Special Issue of J. Global Optim. 37(4), 609–630 (2007)

    MATH  Google Scholar 

  2. Andrianov, I., Awrejcewicz, J., Manevitch, L.I.: Asymptotical Mechanics of Thin-Walled Structures. Springer, Berlin (2004)

    Google Scholar 

  3. Banabic, D., Bunge, H.-J., Pöhlandt, K., Tekkaya, A.E.: Formability of Metallic Materials. Springer, New York (2000)

    Google Scholar 

  4. Banabic, D., Kuwabara, T., Balan, T., Comsa, D.S.: An anisotropic yield criterion for sheet metals. J. Mater. Process. Technol. 157–158, 462–465 (2004)

    Article  Google Scholar 

  5. Belytschko, T.: Plane stress shakedown analysis by finite elements. Int. J. Mech. Sci. 14, 619–625 (1972)

    Article  Google Scholar 

  6. Bourgeois, S., Magoariec, H., Débordes, O.: A direct method for determination of effective strength domains for periodic elastic-plastic media. In: Weichert, D., Ponter, A. (eds.) Limit States of Materials and Structures, pp. 179–190 (2009)

    Google Scholar 

  7. Byrd, R.H., Lu, P.H., Nocedal, J., Zhu, C.Y.: A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Stat. Comput. 16(5), 1190–1208 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  8. Carvelli, V.: Shakedown analysis of unidirectional fiber reinforced metal matrix composites. Comput. Mater. Sci. 31, 24–32 (2004)

    Article  Google Scholar 

  9. Carvelli, V., Maier, G., Taliercio, A.: Shakedown analysis of periodic heterogeneous materials by a kinematic approach. J. Mech. Eng. 50(4), 229–240 (1999)

    Google Scholar 

  10. Carvelli, V., Taliercio, A.: A micromechanical model for the analysis of unidirectional elastoplastic composites subjected to 3d stresses. Mech. Res. Commun. 26(5), 547–553 (1999)

    Article  MATH  Google Scholar 

  11. Chen, M., Zhang, L.L., Weichert, D., Tang, W.C.: Shakedown and limit analysis of periodic composites. Proc. Appl. Math. Mech. 9(1), 415–416 (2009)

    Article  Google Scholar 

  12. Débordes, O.: Homogenization computations in the elastic or plastic collapse range applications to unidirectional composites and perforated sheets. In: Proceedings of the 4th International Symposium Innovative Numerical Methods in Engineering, Computational Mechanics Publications, pp. 453–458 (1986)

    Google Scholar 

  13. Daniel, I.M., Ishai, O.: Engineering Mechanics of Composite Materials, 2nd edn. Oxford University Press, London (2006)

    Google Scholar 

  14. Döbert, C., Mahnken, R., Stein, E.: Numerical simulations of interface debonding with a combined damage/friction constitutive model. Comput. Mech. 25, 456–467 (2000)

    Article  MATH  Google Scholar 

  15. Du, Z.-Z., McMeeking, R.M., Schmauder, S.: Transverse yielding and matrix flow past the fibers in metal matrix composites. Mech. Mater. 21, 159–167 (1995)

    Article  Google Scholar 

  16. Forsgren, A., Gill, P.E., Wright, M.H.: Interior methods for nonlinear optimization. SIAM Rev. 44(4), 525–597 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  17. Gould, N.I.M., Orban, D., Toint, P.L.: Numerical methods for large-scale nonlinear optimization. Technical report, Library and Information Services, CCLRC Rutherford Appleton Laboratory (2004)

    Google Scholar 

  18. Hachemi, A., Chen, M., Weichert, D.: Plastic design of composites by direct methods. In: Simos, T.E., Psihoyios, G., Tsitouras, Ch. (eds.) Numerical Analysis and Applied Mathematics, International Conference, pp. 319–323 (2009)

    Google Scholar 

  19. Hachemi, A., Mouthamid, S., Weichert, D.: Progress in shakedown analysis with applications to composites. Arch. Appl. Mech. 74, 762–772 (2005)

    Article  MATH  Google Scholar 

  20. Hachemi, A., Weichert, D.: On the problem of interfacial damage in fibre-reinforced composites under variable loads. Mech. Res. Commun. 32, 15–23 (2005)

    Article  MATH  Google Scholar 

  21. Hill, R.: A theory of yielding and plastic flow of anisotropic solids. Proc. R. Soc. A 193, 281–297 (1948)

    Article  MATH  Google Scholar 

  22. Krishnamoorthy, C.S.: Finite Element Analysis: Theory and Programming, 2nd edn. Tata McGraw-Hill, Naveen Shahdara (2007)

    Google Scholar 

  23. Lankford, W.T., Snyder, S.C., Bausher, J.A.: New criteria for predicting the press performance of deep drawing sheets. Trans. Am. Soc. Mech. Eng. 42, 1197–1205 (1950)

    Google Scholar 

  24. Magoariec, H.: Adaptation élastoplastique et homogénéisation périodique. PhD thesis, France: Mecanique Solides, Université de la Méditerranée—Aix Marseille II (2003)

    Google Scholar 

  25. Magoariec, H., Bourgeois, S., Débordes, O.: Elastic plastic shakedown of 3d periodic heterogenous media: a direct numerical approach. Int. J. Plast. 20, 1655–1675 (2004)

    Article  MATH  Google Scholar 

  26. Michael, J.C., Moulinec, H., Suquet, P.: Effective properties of composite materials with periodic microstructure: a computational approach. Comput. Methods Appl. Math. 172, 109–143 (1999)

    Google Scholar 

  27. Mouhtamid, S.: Anwendung direkter Methoden zur industriellen Berechnung von Grenzlasten mechanischer Komponeten. PhD thesis, Germany: Institut für Allgemeine Mechanik, RWTH-Aachen (2008)

    Google Scholar 

  28. Nguyen, A.D.:: Lower-bound shakedown analysis of pavements by using the interior point method. PhD thesis, Germany: Institut für Allgemeine Mechanik, RWTH-Aachen (2007)

    Google Scholar 

  29. Pelissou, C., Baccou, J., Monerie, Y., Perales, F.: Determination of the size of the representative volume element for random quasi-brittle composites. Int. J. Solids Struct. 46, 2842–2855 (2009)

    Article  MATH  Google Scholar 

  30. Plunkett, B., Cazacu, O., Barlat, F.: Orthotropic yield criteria for description of the anisotropy in tension and compression of sheet metals. Int. J. Plast. 24, 847–866 (2008)

    Article  MATH  Google Scholar 

  31. Ponter, A.R.S., Leckie, F.A.: Bounding properties of metal-matrix composites subjected to cyclic thermal loading. J. Mech. Phys. Solids 46, 697–717 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  32. Ponter, A.R.S., Leckie, F.A.: On the behaviour of metal matrix composites subjected to cyclic thermal loading. J. Mech. Phys. Solids 46, 2183–2199 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  33. Schwabe, F.: Einspieluntersuchungen von Verbundwerkstoffen mit periodischer Mikrostruktur. PhD thesis, Institut für Allgemeine Mechanik, RWTH-Aachen (2000)

    Google Scholar 

  34. Shan, Z.H., Gokhale, A.M.: Representative volume element for non-uniform micro-structure. Comput. Mater. Sci. 24, 361–379 (2002)

    Article  Google Scholar 

  35. Sun, C.T., Vaidya, R.S.: Prediction of composite properties from a representative volume element. Compos. Sci. Technol. 56, 171–179 (1996)

    Article  Google Scholar 

  36. Sun, E.Q.: Shear locking and hourglassing in Msc Nastran, Abaqus and Ansys.in Msc software users meeting (2006)

    Google Scholar 

  37. Suquet, P.: Plasticité et homogénéisation. PhD thesis, France: Université Pierre et Marie Curie (1982)

    Google Scholar 

  38. Taiebat, H.H., Carter, J.P.: Three-dimensional non-conforming elements. Technical report, The University of Sydney, Department of Civil Engineering (2001)

    Google Scholar 

  39. Taliercio, A.: Lower and upper bounds to the macroscopic strength domain of a fiber-reinforced composite material. Int. J. Plast. 8(6), 741–762 (1992)

    Article  MATH  Google Scholar 

  40. Taliercio, A.: Generalized plane strain finite element model for the analysis of elastoplastic composites. Int. J. Solids Struct. 42, 2842–2855 (2005)

    Article  Google Scholar 

  41. Taliercio, A.: Macroscopic strength estimates for metal matrix composites embedding a ductile interphase. Int. J. Solids Struct. 44, 7213–7238 (2007)

    Article  MATH  Google Scholar 

  42. Wächter, A.: An interior point algorithm for large-scale nonlinear optimization with applications in process engineering. PhD thesis, Pennsylvania: Chemical Engineering, Carnegie Mellon University (2002)

    Google Scholar 

  43. Wächter, A.: Short tutorial: getting started with ipopt in 90 minutes. Technical report, IBM Research Report (2009)

    Google Scholar 

  44. Wächter, A., Biegler, L.T.: On the implementation of a primal-dual interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106(1), 25–57 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  45. Weichert, D., Hachemi, A.: Influence of geometrical nonlinearities on the shakedown of damaged structures. Int. J. Plast. 14(9), 891–907 (1999)

    Article  Google Scholar 

  46. Weichert, D., Hachemi, A., Schwabe, F.: Shakedown analysis of composites. Mech. Res. Commun. 26(3), 309–318 (1999)

    Article  MATH  Google Scholar 

  47. Weichert, D., Hachemi, A., Schwabe, F.: Application of shakedown analysis to the plastic design of composites. Arch. Appl. Mech. 69, 623–633 (1999)

    Article  MATH  Google Scholar 

  48. Wilson, E.L., Taylor, R.L., Doherty, W.P., Ghaboussi, J.: Incompatible displacement models. In: Fenves, S.J. (ed.) Numerical and Computer Methods in Structural Mechanics, pp. 43–57 (1973)

    Google Scholar 

  49. You, J.-H., Kim, B.Y., Miskiewicz, M.: Shakedown analysis of fiber-reinforced copper matrix composites by direct and incremental approaches. Mech. Mater. 41(7), 857–867 (2009)

    Article  Google Scholar 

  50. Zahl, D.B., Schmauder, S.: Transverse strength of continuous fiber metal matrix composites. Comput. Mater. Sci. 3, 293–299 (1994)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Southeast University, Nanjing, China

    M. Chen

  2. Institut für Allgemeine Mechanik, RWTH-Aachen, Templergraben 64, 52062, Aachen, Germany

    M. Chen, A. Hachemi & D. Weichert

Authors
  1. M. Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Hachemi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. Weichert
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Chen .

Editor information

Editors and Affiliations

  1. Laboratoire de Mécanique de Lille, Bd Paul Langevin, Villeneuve d'Ascq, 59655, France

    Géry de Saxcé

  2. Laboratoire de Mécanique de Lille, Bd Paul Langevin, Villeneuve d'Ascq, 59655, France

    Abdelbacet Oueslati

  3. Laboratoire de Mécanique de Lille, Bd Paul Langevin, Villeneuve d'Ascq, 59655, France

    Eric Charkaluk

  4. Laboratoire de Mécanique de Lille, Bd Paul Langevin, Villeneuve d'Ascq, 59655, France

    Jean-Bernard Tritsch

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media Dordrecht

About this paper

Cite this paper

Chen, M., Hachemi, A., Weichert, D. (2013). Shakedown and Optimization Analysis of Periodic Composites. In: de Saxcé, G., Oueslati, A., Charkaluk, E., Tritsch, JB. (eds) Limit State of Materials and Structures. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5425-6_3

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-5425-6_3

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-5424-9

  • Online ISBN: 978-94-007-5425-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation