Truss Metamaterials: Multi-Physics Modeling for Band Gap Tuning

Periodic elastic metamaterials (EMMs) display the capability to forbid the transmission of elastic waves for certain frequency ranges, leading to band gaps. If topology optimization strategies are exploited to tune the band gaps of EMMs, the said band gaps cannot be modified in real-time. This limitation can be overcome by allowing for active materials in the design of EMMs. In this work, a hyperelastic piezoelectric composite was considered to assess the coupled effects of material and geometric nonlinearities on the behavior of sculptured microstructures featuring a three-dimensional periodicity. Specifically, it was assumed that the composite material is obtained by embedding piezo nanoparticles into a soft polymeric matrix. In this way, piezoelectricity and instability-induced pattern transformation could be fully exploited to actively tune the band gaps. A thermodynamically consistent multi-physics model for the active composite material is discussed and implemented in a general-purpose finite-element code. The reported results of the simulations showed how the band gaps are affected by the aforementioned nonlinearities and by a feature of the architected periodic cell linked to its topology.