Tunable Elastic Wave Bandgap and Local Resonances in Single-phase Metamaterial with Applied Deformation

Metamaterial with bandgap tunability is an emerging area in manipulating elastic wave transmission characteristics for next generation phononic devices. Although several attempts are made employing multi-fields such as magnetic, electric and thermal etc., mechanical deformation based tunable bandgap is a major interest. However, achieving tunability in terms of broadening or terminating the bandgap in single-phase metamaterial remains as challenging tasks. In this work, we explore the bandgap of a single-phase star shaped structure with applied deformation. Initially, quasi-static analysis of unit cell has been performed to find the static displacement field under prescribed deformation. Further, a linearized elasto-dynamics is adopted for wave analysis of the predeformed periodic unit cell, and we apply Bloch-Floquet boundary condition. Subsequently, utilizing finite element based framework, an eigenvalue problem is formulated. Accordingly, dispersion responses are predicted and bandgaps are extracted for specified external mechanical deformation. In particular, development of bandgap under equibiaxial tensile deformation is addressed, and underlying local resonances (dipole, quadrupole and monopole) are explained through vibration mode shapes.