Skip to main content
SpringerLink
Log in

Optimization clustering technique for PieceWise Uniform Transformation Field Analysis homogenization of viscoplastic composites

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

Aim of the present study is to propose an enhanced method for the domain decomposition (clustering) of the representative volume element (RVE) of composite materials to be used with homogenization techniques, based on the PieceWise Uniform Transformation Field Analysis (PWUTFA). With PWUTFA, both constitutive and evolutive equations for the constituents of the composite material are written in terms of averages in each cluster; moreover, it is not required to solve via FEM the nonlinear micro-mechanical problem, allowing to drastically reduce the number of internal variables. PWUTFA is founded on the idea that it is possible to divide the RVE into large subdomains (clusters) that should group together finite elements having, under any applied loading condition, the most similar values of strain. Accordingly, in this study a multi-objective optimization-based approach is proposed with the aim to simultaneously reduce both the error in the approximation of the strain fields and the number of clusters in which the domain is decomposed. Different clustering solutions, obtained through the proposed optimization approach are analyzed, and the corresponding mechanical responses are compared with the ones obtained by the finite element analysis and by uniform transformation field analysis.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28

Similar content being viewed by others

References

  1. Chaboche JL, Kanouté P, Roos A (2005) On the capabilities of mean-field approaches for the description of plasticity in metal matrix composites. Int J Plast 21(7):1409–1434

    Article  Google Scholar 

  2. Covezzi F, de Miranda S, Marfia S, Sacco E (2016) Complementary formulation of the TFA for the elasto-plastic analysis of composites. Compos Struct 156:93–100

    Article  Google Scholar 

  3. Covezzi F, de Miranda S, Marfia S, Sacco E (2017) Homogenization of elastic–viscoplastic composites by the mixed TFA. Comput Methods Appl Mech Eng 318:701–723

    Article  MathSciNet  Google Scholar 

  4. de Souza Neto EA, Perić D, Owen DRJ (2008) Computational methods for plasticity: theory and applications. Wiley, New York

    Book  Google Scholar 

  5. Dvorak GJ (1992) Transformation field analysis of inelastic composite materials. Proc R Soc Lond A 437:311–327

    Article  MathSciNet  Google Scholar 

  6. Dvorak GJ, Bahei-El-Din A (1997) Inelastic composite materials: transformation field analysis and experiments. In: Suquet P (ed) Continuum micromechanics, CISM course and lecture, vol 377. Springer, Vienna, pp 1–59

    Google Scholar 

  7. Franciosi P, Berbenni S (2007) Heterogeneous crystal and poly-crystal plasticity modeling from transformation field analysis within a regularized Schimd law. J Mech Phys Solids 55:2265–2299

    Article  MathSciNet  Google Scholar 

  8. Franciosi P, Berbenni S (2008) Multi-laminate plastic-strain organization for nonuniform TFA modeling of poly-crystal regularized plastic flow. Int J Plast 24:1549–1580

    Article  Google Scholar 

  9. Fritzen F, Hodapp M, Leuschner M (2014) GPU accelerated computational homogenization based on a variational approach in a reduced basis framework. Comput Methods Appl Mech Eng 278:186–217

    Article  MathSciNet  Google Scholar 

  10. Fritzen F, Leuschner M (2013) Reduced basis hybrid computational homogenization based on a mixed incremental formulation. Comput Methods Appl Mech Eng 260:143–154

    Article  MathSciNet  Google Scholar 

  11. Fritzen F, Leuschner M (2015) Nonlinear reduced order homogenization of materials including cohesive interfaces. Comput Mech 56(1):131–151

    Article  MathSciNet  Google Scholar 

  12. Gunst RF (1996) Response surface methodology: process and product optimization using designed experiments. Technometrics 38(3):284–286. https://doi.org/10.1080/00401706.1996.10484509

    Article  Google Scholar 

  13. Liu Z, Bessa MA, Liu WK (2016) Self-consistent clustering analysis: an efficient multi-scale scheme for inelastic heterogeneous materials. Comput Methods Appl Mech Eng 306:319–341

    Article  MathSciNet  Google Scholar 

  14. MathWorks Inc. Matlab software. https://ch.mathworks.com/products/matlab.html. January 2019

  15. Marfia S, Sacco E (2016) Computational homogenization of composites experiencing plasticity, cracking and debonding phenomena. Comput Methods Appl Mech Eng 304:319–341

    Article  MathSciNet  Google Scholar 

  16. Marfia S, Sacco E (2018) Multiscale technique for nonlinear analysis of elastoplastic and viscoplastic composites. Compos Part B 136:241–253

    Article  Google Scholar 

  17. Michel JC, Suquet P (2003) Nonuniform transformation field analysis. Int J Solids Struct 40:6937–6955

    Article  MathSciNet  Google Scholar 

  18. Michel JC, Suquet P (2004) Computational analysis of nonlinear composite structures using the nonuniform transformation field analysis. Comput Methods Appl Mech Eng 193:5477–5502

    Article  MathSciNet  Google Scholar 

  19. Perzyna P (1968) Fundamental problems in viscoplasticity. Adv Appl Mech 9(1):243–377

    Google Scholar 

  20. Roussette S, Michel JC, Suquet P (2009) Nonuniform transformation field analysis of elastic–viscoplastic composites. Compos Sci Technol 69:22–27

    Article  Google Scholar 

  21. Seber George AF (2009) Multivariate observations, vol 252. Wiley, New York

    MATH  Google Scholar 

  22. Sepe V, Marfia S, Sacco E (2013) A nonuniform TFA homogenization technique based on piecewise interpolation functions of the inelastic field. Int J Solids Struct 50:725–742

    Article  Google Scholar 

  23. Ward JH Jr, Joe H (1963) Hierarchical grouping to optimize an objective function. J Am Stat Assoc 58(301):236–244

    Article  MathSciNet  Google Scholar 

  24. Wulfinghoff S, Cavaliere F, Reese S (2018) Model order reduction of nonlinear homogenization problems using a hashin-shtrikman type finite element method. Comput Methods Appl Mech Eng 330:149–179

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This study was funded by Italian Ministry of Education, Project PRIN2015 Multi-scale mechanical models for the design and optimization of micro-structured smart materials and metamaterials (CUP H32F15000090005) and Project PRIN2017 3D Printing: a bridge to the future: computational methods, innovative applications, experimental validations of new materials and technologies (CUP Project number 2017L7X3CS) that is gratefully acknowledged. This work was also partially supported by Regione Lombardia through the Project MADE4LO - Metal ADditivE for LOmbardy (No. 240963) within the POR FESR 2014–2020 program.

Author information

Authors and Affiliations

  1. Dipartimento di Ingegneria Civile e Architettura, Università di Pavia, Via A. Ferrata 1, Pavia, Italy

    Gianluca Alaimo & Ferdinando Auricchio

  2. Dipartimento di Ingegneria, Università di Roma Tre, Via Vito Volterra 62, 00146, Rome, Italy

    Sonia Marfia

  3. Dipartimento di Strutture per l’Ingegneria e l’Architettura, Università di Napoli “Federico II”, Via Claudio 21, 80125, Naples, Italy

    Elio Sacco

Authors
  1. Gianluca Alaimo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ferdinando Auricchio
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sonia Marfia
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Elio Sacco
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gianluca Alaimo.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Alaimo, G., Auricchio, F., Marfia, S. et al. Optimization clustering technique for PieceWise Uniform Transformation Field Analysis homogenization of viscoplastic composites. Comput Mech 64, 1495–1516 (2019). https://doi.org/10.1007/s00466-019-01730-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-019-01730-2

Keywords

Search

Navigation