Tunable phononic bandgap materials designed via topology optimization. (June 2022)

• Record Type: Journal Article
• Authors: Dalklint, Anna; Wallin, Mathias; Bertoldi, Katia; Tortorelli, Daniel
• Is Part Of: Journal of the mechanics and physics of solids. Volume 163(2022)
• Publication Date: 2022-06
• Subjects: Topology optimization -- Phononic crystal -- Tunable material properties -- Finite strain; Mechanics, Applied -- Periodicals; Solids -- Periodicals; Mechanics -- Periodicals; Mécanique appliquée -- Périodiques; Solides -- Périodiques; Mechanics, Applied; Solids; Periodicals; 531.05
• DOI: 10.1016/j.jmps.2022.104849
• Languages: English
• ISSNs: 0022-5096

Abstract

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.