Modeling of Wave Propagation through Soft Electrically Tunable Metamaterials

In this paper, we present our numerical simulation capability, developed within the Abaqus/Standard environment, for modeling steady-state wave propagation through soft dielectric elastomer composites. Specifically, we will discuss (a) a nonlinear user-element subroutine (UEL) to simulate the coupled electric-displacement response of these soft materials, (b) a user MPC subroutine to enforce complex-valued Bloch-Floquet constraints, as well as to impose appropriate updated Lagrangian boundary conditions on the representative volume element (RVE), and (c) a method within the UEL to lower the dispersion error in the solution by modifying the mass matrix. Through the combination of these methods, we can study how the application of an electric field to these materials results in opening and closing of phononic band-gaps, that is, frequency ranges in which propagating waves through the dielectric elastomer composite are not permitted. This modeling framework is useful to guide the development of phononic metamaterials that cannot be studied analytically and leverages the computational backbone of Abaqus/Standard, which enhances portability and maintainability of our modeling approach. We envision using these electrically-tunable phononic metamaterials to provide vibration isolation for undersea structures. This work is supported through the Naval Undersea Warfare Center In-house Laboratory Independent Research (ILIR) program.