@article{b8a98e7258264e148719edc62d2df42d,
title = "Tunable phononic bandgap materials designed via topology optimization",
abstract = "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.",
keywords = "Finite strain, Phononic crystal, Topology optimization, Tunable material properties",
author = "Anna Dalklint and Mathias Wallin and Katia Bertoldi and Daniel Tortorelli",
note = "Funding Information: This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore Laboratory under Contract DE-AC52-07NA27344. The Swedish energy agency (grant nbr. 48344-1) and eSSENCE: The e-Science Collaboration (grant nbr. 2020 6:1) are also gratefully acknowledged. The computations were enabled by resources provided by LUNARC. Last but not least, the authors would like to thank Dr. Kenneth Swartz and Dr. Seth Watts for helpful discussions throughout the research project. Funding Information: This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore Laboratory under Contract DE-AC52-07NA27344 . The Swedish energy agency (grant nbr. 48344-1 ) and eSSENCE: The e-Science Collaboration (grant nbr. 2020 6:1 ) are also gratefully acknowledged. The computations were enabled by resources provided by LUNARC. Last but not least, the authors would like to thank Dr. Kenneth Swartz and Dr. Seth Watts for helpful discussions throughout the research project. Publisher Copyright: {\textcopyright} 2022 The Authors",
year = "2022",
month = jun,
doi = "10.1016/j.jmps.2022.104849",
language = "English (US)",
volume = "163",
journal = "Journal of the Mechanics and Physics of Solids",
issn = "0022-5096",
publisher = "Elsevier Limited",
}