Constitutive modeling of strain-dependent bond breaking and healing kinetics of chemical polyampholyte (PA) gel.

A finite strain nonlinear viscoelastic constitutive model is used to study the uniaxial tension behaviour of chemical polyampholyte (PA) gel. This PA gel is cross-linked by chemical and physical bonds. Our constitutive model attempts to capture the time and strain dependent breaking and healing kinetics of physical bonds. We compare model prediction by uniaxial tension, cyclic and relaxation tests. Material parameters in our model are obtained by least squares optimization. These parameters gave fits that are in good agreement with the experiments.

Time dependent fracture of soft materials: linear versus nonlinear viscoelasticity.

Toughness of soft materials such as elastomers and gels depends on their ability to dissipate energy and to reduce stress concentration at the crack tip. The primary energy dissipation mechanism is viscoelasticity. Most analyses and models of fracture are based on linear viscoelastic theory (LVT) where strains are assumed to be small and the relaxation mechanisms are independent of stress or strain history. A well-known paradox is that the size of the dissipative zone predicted by LVT is unrealistically small. Here we use a physically based nonlinear viscoelastic model to illustrate why the linear theory breaks down. Using this nonlinear model and analogs of crack problems, we give a plausible resolution to this paradox. In our model, viscoelasticity arises from the breaking and healing of physical cross-links in the polymer network. When the deformation is small, the kinetics of bond breaking and healing are independent of the strain/stress history and the model reduces to the standard linear theory. For large deformations, localized bond breaking damages the material near the crack tip, reducing stress concentration and dissipating energy at the same time. The damage zone size is a new length scale which depends on the strain required to accelerate bond breaking kinetics. These effects are illustrated by considering two cases with stress concentrations: the evolution of spherical damage in a viscoelastic body subjected to internal pressure, and a zero degree peel test.

Nondegenerate Parametric Resonance in Large Ensembles of Coupled Micromechanical Cantilevers with Varying Natural Frequencies.

We investigate the collective dynamics and nondegenerate parametric resonance (NPR) of coplanar, interdigitated arrays of microcantilevers distinguished by their cantilevers having linearly expanding lengths and thus varying natural frequencies. Within a certain excitation frequency range, the resonators begin oscillating via NPR across the entire array consisting of 200 single-crystal silicon cantilevers. Tunable coupling generated from fringing electrostatic fields provides a mechanism to vary the scope of the NPR. Our experimental results are supported by a reduced-order model that reproduces the leading features of our data including the NPR band. The potential for tailoring the coupled response of suspended mechanical structures using NPR presents new possibilities in mass, force, and energy sensing applications, energy harvesting devices, and optomechanical systems.

Actuation of higher harmonics in large arrays of micromechanical cantilevers for expanded resonant peak separation.

A large array of elastically coupled micro cantilevers of variable length is studied experimentally and numerically. Full-scale finite element modal analysis is implemented to determine the spectral behavior of the array and to extract a global coupling matrix. A compact reduced order model is used for numerical investigation of the array's dynamic response. Our model results show that at a given excitation frequency within a propagation band, only a finite number of beams respond. Spectral characteristics of individual cantilevers, inertially excited by an external piezoelectric actuator, were measured in vacuum using laser interferometry. The theoretical and experimental results collectively show that the resonant peaks corresponding to individual beams are clearly separated when operating in vacuum at the 3rd harmonic. Distinct resonant peak separation, coupled with the spatially-confined modal response, make higher harmonic operation of tailored, variable-length cantilever arrays well suited for a variety of resonant based sensing applications.

The stress field near the tip of a plane stress crack in a gel consisting of chemical and physical cross-links.

We study the time-dependent asymptotic stress fields near the tip of a mode I plane stress crack in a hydrogel. The analysis is based on a three-dimensional continuum model which describes the viscoelastic behaviour of a hydrogel gel with permanent and transient cross-links. The viscoelasticity results from the breaking and healing of the transient cross-links in the gel network. We show that the crack tip fields satisfy a local correspondence principle-that is, the spatial singularities of these fields are identical to a hyperelastic cracked body with the same but undamaged networks. Asymptotic results compare very well with finite-element simulations on a single-edge crack specimen loaded under constant stretch rate. We also compare the theoretical results (crack opening profile and crack tip strain field) with experiments and find excellent agreement.

Accurate spring constant calibration for very stiff atomic force microscopy cantilevers.

There are many atomic force microscopy (AFM) applications that rely on quantifying the force between the AFM cantilever tip and the sample. The AFM does not explicitly measure force, however, so in such cases knowledge of the cantilever stiffness is required. In most cases, the forces of interest are very small, thus compliant cantilevers are used. A number of methods have been developed that are well suited to measuring low stiffness values. However, in some cases a cantilever with much greater stiffness is required. Thus, a direct, traceable method for calibrating very stiff (approximately 200 N/m) cantilevers is presented here. The method uses an instrumented and calibrated nanoindenter to determine the stiffness of a reference cantilever. This reference cantilever is then used to measure the stiffness of a number of AFM test cantilevers. This method is shown to have much smaller uncertainty than previously proposed methods. An example application to fracture testing of nanoscale silicon beam specimens is included.