Immersed boundary enriched finite element analysis

Phononic crystals (PnCs) are materials with periodic structure that can be designed to prevent the propagation of mechanical waves, e.g., sound or vibration. This phenomenon, which is known as a band gap, can be exploited in many engineering applications, such as vibration isolation and energy harvesting. In order to characterize and even design PnCs, accurate and efficient modeling techniques are invaluable. This work focuses on developing enriched finite element technology for the analysis of PnCs with finite element discretizations that are completely decoupled from the PnC's geometry.

The performance of PnCs depends on both the topology of the inclusion and the lattice type, which is reflected in the shape of the periodic unit cell (PUC). Therefore, both the exterior and the interior boundaries are decoupled from the FE mesh. The PUC is thus analyzed in a fully immersed boundary setting, and Bloch-Floquet periodic boundary conditions are prescribed strongly on non-matching edges. With this approach the same performance as in standard FEM is achieved, while the geometry can be changed without changing the underlying analysis mesh. We use this flexibility also in the design of PnCs with topology optimization—e.g., to maximize bandgaps!

Wave propagating through the 3D cell

Related publications

  • S. J. van den Boom, A. M. Aragón, and F. van Keulen. "Mesh-Independent Design of Phononic Crystals Using an Advanced Finite Element Formulation." Proceedings of the ASME 2016 International Mechanical Engineering Congress and Exposition 13: Acoustics, Vibration, and Wave Propagation. Phoenix, Arizona, USA. November 11–17, 2016.  
  • S. J. van den Boom, F. van Keulen, and A. M. Aragón. "Fully decoupling geometry from discretization in the Bloch–Floquet finite element analysis of phononic crystals." Computer Methods in Applied Mechanics and Engineering 382 (2021), p. 113848.