Tunable phononic bandgap materials designed via topology optimization

Anna Dalklint, Mathias Wallin, Katia Bertoldi, Daniel Tortorelli

Research output: Contribution to journalArticlepeer-review


Topology optimization is used to design phononic bandgap materials that are tunable by mechanical deformation. A periodic media is considered, which due to the assumption of length scale separation, allows the dispersion relations to be obtained by analyzing a single unit cell subjected to Floquet–Bloch boundary conditions. A finite macroscopic deformation is applied to the unit cell to affect its geometry and hence dispersion. We tune the dispersion–deformation relation to our liking by solving a topology optimization problem using nonlinear programming. The adjoint method is employed to compute the sensitivities, and the non-differentiability of degenerate eigenvalues is avoided using symmetric polynomials. Several tunable phononic crystal designs are presented. Also, a verification analysis is performed, wherein the optimized design is interpreted and analyzed using a conforming finite element mesh.

Original languageEnglish (US)
Article number104849
JournalJournal of the Mechanics and Physics of Solids
StatePublished - Jun 2022


  • Finite strain
  • Phononic crystal
  • Topology optimization
  • Tunable material properties

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


Dive into the research topics of 'Tunable phononic bandgap materials designed via topology optimization'. Together they form a unique fingerprint.

Cite this