Yun-Che Wang

Extreme damping in composite materials with negative-stiffness inclusions

When a force deforms an elastic object, practical experience suggests that the resulting displacement will be in the same direction as the force. This property is known as positive stiffness. Less familiar is the concept of negative stiffness, where the deforming force and the resulting displacement are in opposite directions. (Negative stiffness is distinct from negative Poissons ratio, which refers to the occurrence of lateral expansion upon stretching an object.) Negative stiffness can occur, for example, when the deforming object has stored (or is supplied with) energy. This property is usually unstable, but it has been shown theoretically that inclusions of negative stiffness can be stabilized within a positive-stiffness matrix. Here we describe the experimental realization of this composite approach by embedding negative-stiffness inclusions of ferroelastic vanadium dioxide in a pure tin matrix. The resulting composites exhibit extreme mechanical damping and large anomalies in stiffness, as a consequence of the high local strains that result from the inclusions deforming more than the composite as a whole. Moreover, for certain temperature ranges, the negative-stiffness inclusions are more effective than diamond inclusions for increasing the overall composite stiffness. We expect that such composites could be useful as high damping materials, as stiff structural elements or for actuator-type applications.

Extreme stiffness systems due to negative stiffness elements

When an elastic object is pressed, we expect it to resist by exerting a restoring force. A reversal of this force corresponds to negative stiffness. If we combine elements with positive and negative stiffness in a composite, it is possible to achieve stiffness greater than (or less than) that of any of the constituents. This behavior violates established bounds that tacitly assume that each phase has positive stiffness. Extreme composite behavior has been experimentally demonstrated in a lumped system using a buckled tube to achieve negative stiffness and in a composite material in the vicinity of a phase transformation of one of the constituents. In the context of a composite system, extreme refers to a physical property greater than either constituent. We consider a simple spring model with pre-load to achieve negative stiffness. When suitably tuned to balance positive and negative stiffness, the system shows a critical equilibrium point giving rise to extreme overall stiffness. A stability analysis of a viscous damped system containing negative stiffness springs reveals that the system is stable when tuned for high compliance, but metastable when tuned for high stiffness. The metastability of the extreme system is analogous to that of diamond. The frequency response of the viscous damped system shows that the overall stiffness increases with frequency and goes to infinity when one constituent has a suitable negative stiffness.

Extreme thermal expansion, piezoelectricity, and other coupled field properties in composites with a negative stiffness phase

Particulate composites with negative stiffness inclusions in a viscoelastic matrix are shown to have higher thermal expansion than that of either constituent and exceeding conventional bounds. It is also shown theoretically that other extreme linear coupled field properties including piezoelectricity and pyroelectricity occur in layer- and fiber-type piezoelectric composites, due to negative inclusion stiffness effects. The causal mechanism is a greater deformation in and near the inclusions than the composite as a whole. A block of negative stiffness material is unstable, but negative stiffness inclusions in a composite can be stabilized by the surrounding matrix and can give rise to extreme viscoelastic effects in lumped and distributed composites. In contrast to prior proposed composites with unbounded thermal expansion, neither the assumptions of void spaces nor slip interfaces are required in the present analysis.

Stable extremely-high-damping discrete viscoelastic systems due to negative stiffness elements

Systems with negative stiffness constituents can have extreme material properties greatly exceeding those of either constituent. We show that a discrete system with a viscoelastic damping element and a negative stiffness element can be made with overall viscoelastic damping orders of magnitude higher than that of any constituent, or of the system with all elements of positive stiffness. The product of stiffness and damping, important for vibration damping, is also enhanced by orders of magnitude. We show this system is unconditionally stable in the high damping regime. The singularity in damping can be made arbitrarily close to the stability boundary.

Influence of cell size on re-entrant transformation of negative Poisson's ratio reticulated polyurethane foams

Several foams of different cell-size, including Scott Industrial polyurethane foam with large cells (20 pores per inch, ppi, or 1.2 mm per pore, black), medium cells (65 ppi, or 0.4 mm per pore, green), and near-microcellular (100 ppi, 0.25 mm per pore, white), were processed over various time and temperature regimes to ascertain the role of cell size in transformation to negative Poissons ratio materials. These foams were transformed successfully, and exhibited negative Poissons ratio behavior. Poissons ratio was measured using a new laser based setup. For all as-received (unprocessed) foams with different cell sizes, Poissons ratio decreased with compressive axial strain and increased with tensile strain up to a maximum. The maximum Poissons ratio in tension decreased as cell size increases. The strain at which maximum Poissons ratio occurs, increased with cell size. In negative Poissons ratio foams, minimum Poissons ratios of −0.8, −0.5, and −0.4 for 20 ppi, 65 ppi, and 100 ppi foams, respectively were observed. Furthermore, the cell size effects on transformation parameters were also found.

Negative stiffness-induced extreme viscoelastic mechanical properties: stability and dynamics

Use of negative stiffness inclusions allows one to exceed the classic bounds upon overall mechanical properties of composite materials. We here analyse discrete viscoelastic ‘spring’ systems with negative stiffness elements to demonstrate the origin of extreme properties, and analyse the stability and dynamics of the systems. Two different models are analysed: one requires geometrical nonlinear analysis with pre-load as a negative stiffness source and the other is a linearized model with a direct application of negative stiffness. Material linearity is assumed for both models. The metastability is controlled by a viscous element. In the stable regime, extreme high mechanical damping tan δ can be obtained at low frequency. In the metastable regime, singular resonance-like responses occur in tan δ. The pre-stressed viscoelastic system is stable at the equilibrium point with maximal overall compliance and is metastable when tuned for maximal overall stiffness. A reversal in the relationship between the magnitude of complex modulus and frequency is also observed. The experimental observability of the singularities in tan δ is discussed in the context of designed composites and polycrystalline solids with metastable grain boundaries.

Resonant ultrasound spectroscopy in shear mode

We present an enhancement of the resonant ultrasound spectroscopy method for the determination of elastic and viscoelastic properties. By using shear transducers rather than the usual compressional ones, signal strength for the fundamental is enhanced by one to three orders of magnitude. This enables simplified determination of shear modulus and damping tan δ with off-the-shelf electronics. Moreover, the polarization of the shear transducers can be used to identify modes of vibration.

Stability of negative stiffness viscoelastic systems

We analytically investigate the stability of a discrete viscoelastic system with negative stiffness elements both in the time and frequency domains. Parametric analysis was performed by tuning both the amount of negative stiffness in a standard linear solid and driving frequency. Stability conditions were derived from the analytical solutions of the differential governing equations and the Lyapunov stability theorem. High frequency response of the system is studied. Stability of singularities in the dissipation tan 6 is discussed. It was found that stable singular tan δ is achievable. The system with extreme high stiffness analyzed here was metastable. We established an explicit link for the divergent rates of the metastable system between the solutions of differential governing equations in the time domain and the Lyapunov theorem.

Quadraxial probe for high resolution near-field scanning rf/microwave microscopy

The authors propose and demonstrate a miniaturized quadraxial probe that employs a differential feed technique for use in near-field rf/microwave transmission microscopy. Their quadraxial probe’s electric field measurements show higher electric field localization than a conventional coaxial (monopole) probe. The improved spatial resolution and more sensitive phase measurement of the quadraxial probe versus coaxial probe are further validated by a metal line scan experiment.

Localized microwave measurement using AFM-compatible scanning nearfield microwave microscope cantilever with ultra-tall coaxial probe

We have demonstrated localized microwave measurements using SNMM cantilevers integrated with ultra-tall coaxial tips. Our results demonstrate improved electromagnetic field confinement with enhanced immunity to the parasitic capacitive coupling that is typically associated with SNMM imaging using cantilever based probes. Dielectric spectroscopy capabilities at microwave frequencies are currently being pursued for material characterization in nanometer scale.