A multi-material level set-based topology optimization of flexoelectric composites

Hamid Ghasemi, Harold S. Park, Timon Rabczuk

Research output: Contribution to journalArticlepeer-review

209 Citations (Scopus)


We present a computational design methodology for topology optimization of multi-material-based flexoelectric composites. The methodology extends our recently proposed design methodology for a single flexoelectric material. We adopt the multi-phase vector level set (LS) model which easily copes with various numbers of phases, efficiently satisfies multiple constraints and intrinsically avoids overlap or vacuum among different phases. We extend the point wise density mapping technique for multi-material design and use the B-spline elements to discretize the partial differential equations (PDEs) of flexoelectricity. The dependence of the objective function on the design variables is incorporated using the adjoint technique. The obtained design sensitivities are used in the Hamilton–Jacobi (H–J) equation to update the LS function. We provide numerical examples for two, three and four phase flexoelectric composites to demonstrate the flexibility of the model as well as the significant enhancement in electromechanical coupling coefficient that can be obtained using multi-material topology optimization for flexoelectric composites.

Original languageEnglish
Pages (from-to)47-62
Number of pages16
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 2018 Apr 15


  • B-spline elements
  • Flexoelectricity
  • Level set
  • Multi-material
  • Topology optimization

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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