Computational Mechanics

, Volume 64, Issue 6, pp 1495–1516 | Cite as

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

  • Gianluca AlaimoEmail author
  • Ferdinando Auricchio
  • Sonia Marfia
  • Elio Sacco
Original Paper


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.


RVE Domain subdivision Composite PWUTFA 



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.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Gianluca Alaimo
    • 1
    Email author
  • Ferdinando Auricchio
    • 1
  • Sonia Marfia
    • 2
  • Elio Sacco
    • 3
  1. 1.Dipartimento di Ingegneria Civile e ArchitetturaUniversità di PaviaPaviaItaly
  2. 2.Dipartimento di IngegneriaUniversità di Roma TreRomeItaly
  3. 3.Dipartimento di Strutture per l’Ingegneria e l’ArchitetturaUniversità di Napoli “Federico II”NaplesItaly

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