  The recent progress of non-Hermitian physics and the notion of exceptional
point (EP) degeneracies in elastodynamics has led to the development of novel
metamaterials for the control of elastic wave propagation, hypersensitive
sensors, and actuators. The emergence of EPs in a Parity-Time symmetric system
relies on judiciously engineered balanced gain and loss mechanisms. Creating
gain requires complex circuits and amplification mechanisms, making engineering
applications challenging. Here, we report strategies to achieve EPs in passive
non-Hermitian elastodynamic systems with differential loss derived from
viscoelastic materials. We compare different viscoelastic material models and
show that the EP emerges only when the frequency-dependent loss-tangent of the
viscoelastic material remains nearly constant in the frequency range of
operation. Such type of loss tangent occurs in materials that undergo
stress-relaxation over a broad spectrum of relaxation times, for example,
materials that follow the Kelvin-Voigt fractional derivative (KVFD) model.
Using dynamic mechanical analysis, we show that a few common viscoelastic
elastomers such as Polydimethylsiloxane (PDMS) and polyurethane rubber follow
the KVFD behavior such that the loss tangent becomes almost constant after a
particular frequency. The material models we present and the demonstration of
the potential of a widely available material system in creating EPs pave the
way for developing non-Hermitian metamaterials with hypersensitivity to
perturbations or enhanced emissivity.
