A numerical simulation capability for electroelastic wave propagation in dielectric elastomer composites: Application to tunable soft phononic crystals

Phononic crystals are periodic, composite solids that exhibit phononic band gaps - frequency ranges in which elastic waves are prohibited. For phononic crystals made from soft elastomers, phononic band gaps may be reversibly manipulated through large elastic deformation of the periodic structure. By using dielectric elastomers, which undergo large, reversible deformations when subjected to an applied electric field, the frequency ranges of band gaps may be adjusted, or new band gaps may be created, through electrical stimuli. In this work, we present our finite-element-based numerical simulation capability for designing electrically-tunable, soft phononic crystals. Our finite-element tools address both nonlinear quasi-electrostatic processes and the linearized dynamics of electroelastic wave propagation through a pre-deformed state and may be applied to general composite unit-cell geometries subjected to arbitrary far-field electromechanical preloading. We apply our simulation capability to electrically-tunable, soft phononic crystals consisting of periodic lattices of aligned circular-cross-section fibers embedded in a matrix and demonstrate the shifting of band gaps with electrical preloading parallel to the fibers and the opening, closing, and shifting of band gaps with electrical preloading perpendicular to the fibers. The roles of large-stretch chain-locking behavior, material parameter contrasts, and fiber volume fraction are also investigated.