The Influence of Elastic Nonlinearity on Wave Processes in Media with Dislocations

It has been shown that account of elastic nonlinearity during the propagation of an acoustic wave in a solid lead to the appearance of a quadratic nonlinearity, which in its turn leads to the possibility of generating a wave of double frequency, the interaction of harmonics is asymmetric. The conditions under which nonlinear stationary waves are formed are considered. A phase portrait is constructed, and the dependence of the wavenumber of a nonlinear wave on its amplitude is estimated.

Dynamic Compression Model Incorporating Elastic Nonlinearity of Paperboard

Spring of constant elasticity is a concept from theories of extension while elastic nonlinearity in compressive deformation is a general phenomenon for polymeric materials involved in offset or flexographic printing, paper board, polymer plate, and cushioning tape. This phenomenon needs therefore to be coped with by the model of printing dynamics. We hereby present an extended approach based on the Maxwell material model. In the extended approach, a compression process is subdivided into (or approximated by) sequential subprocesses. The elastic modulus may vary from one subsection to another but remains constant in each of the subprocesses. With the extended approach dynamic behaviours (compression/recovering) of paperboard can be reproduced and predicted. As a concrete example, dynamic behaviours of paper board in the print nip were simulated with satisfactory outcome. The simulation also revealed that viscoelasticity of the board is the origin of mechanical hysteresis of the stress–strain curve. Due to viscoelasticity and nonlinearity of the materials careful design is essential to simulate full-scale printing with a lab press.

Intra-Cycle Elastic Nonlinearity of Nitrogen-Doped Carbon Nanotube/Polymer Nanocomposites under Medium Amplitude Oscillatory Shear (MAOS) Flow

This study seeks to unravel the effect of carbon nanotube’s physical and chemical features on the final electrical and rheological properties of polymer nanocomposites thereof. Nitrogen-doped carbon nanotubes (N-CNTs) were synthesized over two different types of catalysts, i.e., Fe and Ni, employing chemical vapor deposition. Utilizing this technique, we were able to synthesize N-CNTs with significantly different structures. As a result, remarkable differences in the network structure of the nanotubes were observed upon mixing the N-CNTs in a polyvinylidene fluoride (PVDF) matrix, which, in turn, led to drastically different electrical and rheological properties. For instance, no enhancement in the electrical conductivity of poorly-dispersed (N-CNT)Ni/PVDF samples was observed even at high nanotube concentrations, whereas (N-CNT)Fe/PVDF nanocomposites exhibited an insulative behavior at 1.0 wt%, a semi-conductive behavior at 2.0 wt%, and a conductive behavior at 2.7 wt%. In terms of rheology, the most substantial differences in the viscoelastic behavior of the systems were distinguishable in the medium amplitude oscillatory shear (MAOS) region. The stress decomposition method combined with the evaluation of the elastic and viscous third-order Chebyshev coefficients revealed a strong intra-cycle elastic nonlinearity in the MAOS region for the poorly-dispersed systems in small frequencies; however, the well-dispersed systems showed no intra-cycle nonlinearity in the MAOS region. It was shown that the MAOS elastic nonlinearity of poorly-dispersed systems stems from the confinement of N-CNT domains between the rheometer’s plates for small gap sizes comparable with the size of the agglomerates. Moreover, the intra-cycle elastic nonlinearity of poorly-dispersed systems is frequency-dependent and vanished at higher frequencies. The correlation between the microstructure and viscoelastic properties under large shear deformations provides further guidance for the fabrication of high-performance 3D-printed electrically conductive nanocomposites with precisely controllable final properties for engineering applications.

Nonlinear effects of viscoelastic fluid flows and applications in microfluidics: A review

Viscoelastic fluid naturally has both viscous and elastic properties. Therefore, there are two sources of nonlinear effects, namely inertial and elastic nonlinearities. The existence of elastic nonlinearity brings about various interesting flow phenomena in viscoelastic fluid flow, especially in microfluidics where the inertial nonlinearity can be negligible while the elastic nonlinearity can dominate the flow. Specifically, purely elasticity-induced instability and turbulence can occur in microchannels when the elastic nonlinearity is strong enough. Recently, those intriguing properties of viscoelastic fluid flow have motivated lots of researches on taking viscoelastic fluid as working fluid in different types of microfluidic devices, such as micro-mixers, micro heat exchangers, logic microfluidic circuits and particle manipulation. This paper aims to provide a state-of-the-art review of the nonlinear effect of viscoelastic fluids and its applications in the aforementioned microfluidic fields, which may provide a useful guidance for the researchers who are interested in this area.

Flexure Pivot Oscillator With Intrinsically Tuned Isochronism

The most important property for accurate mechanical time bases is isochronism: the independence of period from oscillation amplitude. This paper develops a new concept in isochronism adjustment for flexure-based watch oscillators. Flexure pivot oscillators, which would advantageously replace the traditional balance wheel-spiral spring oscillator used in mechanical watches due to their significantly lower friction, exhibit nonlinear elastic properties that introduce an isochronism defect. Rather than minimizing this defect, we are interested in controlling it to compensate for external defects such as the one introduced by escapements. We show that this can be done by deriving a formula that expresses the change of frequency of the oscillator with amplitude, i.e., isochronism defect, caused by elastic nonlinearity. To adjust the isochronism, we present a new method that takes advantage of the second-order parasitic motion of flexures and embody it in a new architecture we call the co-RCC flexure pivot oscillator. In this realization, the isochronism defect of the oscillator is controlled by adjusting the stiffness of parallel flexures before fabrication through their length Lp, which has no effect on any other crucial property, including nominal frequency. We show that this method is also compatible with post-fabrication tuning by laser ablation. The advantage of our design is that isochronism tuning is an intrinsic part of the oscillator, whereas previous isochronism correctors were mechanisms added to the oscillator. The results of our previous research are also implemented in this mechanism to achieve gravity insensitivity, which is an essential property for mechanical watch time bases. We derive analytical models for the isochronism and gravity sensitivity of the oscillator and validate them by finite element simulation. We give an example of dimensioning this oscillator to reach typical practical watch specifications and show that we can tune the isochronism defect with a resolution of 1 s/day within an operating range of 10% of amplitude. We present a mock-up of the oscillator serving as a preliminary proof-of-concept.