Mechanism of Surface Wrinkle Modulation for a Stiff Film on Compliant Substrate

2017 ◽  
Vol 84 (5) ◽  
Author(s):  
Yilun Liu ◽  
Mengjie Li ◽  
Jingran Liu ◽  
Xi Chen
Keyword(s):  
Soft Materials ◽  
Stretchable Electronics ◽  
Cosmetic Products ◽  
Modulus Ratio ◽  
Surface Wrinkle ◽  
Theoretical Predictions ◽  
Parallel Finite Element ◽  
And Performance ◽  
Film Substrate ◽  
Good Agreement

In this work, the surface wrinkle modulation of the film/substrate system caused by eigenstrain in the film is studied. A theoretical model is proposed which shows the change of the wrinkle amplitude is completely determined by four dimensionless parameters, i.e., the eigenstrain in the film, the plane strain modulus ratio between the film and the substrate, the film thickness to wrinkle wavelength ratio, and the initial wrinkle amplitude to wavelength ratio. The surface wrinkle amplitude becomes smaller (even almost flat) for the contraction eigenstrain in the film, while for the expansion eigenstrain it becomes larger. If the expansion eigenstrain exceeds a critical value, secondary wrinkling on top of the existing one is observed for some cases. In general, the deformation diagram of the wrinkled film/substrate system can be divided into three regions, i.e., the change of surface wrinkle amplitude, the irregular wrinkling, and the secondary wrinkling, governed by the four parameters above. Parallel finite element method (FEM) simulations are carried out which have good agreement with the theoretical predictions. The findings may be useful to guide the design and performance of stretchable electronics, cosmetic products, biomedical engineering, soft materials, and devices.

Mechanism of Three-Dimensional Surface Wrinkle Manipulation on a Compliant Substrate

2018 ◽  
Vol 85 (7) ◽  
Author(s):  
Mengjie Li ◽  
Huasong Qin ◽  
Jingran Liu ◽  
Yilun Liu
Keyword(s):  
Three Dimensional ◽  
Film Plane ◽  
Stretchable Electronics ◽  
Complex Structures ◽  
Cosmetic Products ◽  
Modulus Ratio ◽  
Surface Wrinkle ◽  
Theoretical Predictions ◽  
Parallel Finite Element ◽  
Film Substrate

In this work, the surface wrinkle modulation mechanism of the three-dimensional (3D) film/substrate system caused by biaxial eigenstrains in the films is studied. A theoretical model based on the energy minimization of the 3D wrinkled film/substrate system is proposed which shows that the change of the surface wrinkle amplitude is determined by four dimensionless parameters, i.e., the eigenstrain in the film, plane strain modulus ratio between the film and substrate, film thickness to wrinkle wavelength ratio, and initial wrinkle amplitude to wavelength ratio. The surface wrinkle amplitude decreases (even almost flat) upon contraction eigenstrain in the film, while increases for that of expansion eigenstrain. Parallel finite element method (FEM) simulations are carried out which have good agreements with the theoretical predictions, and experimental verifications are also presented to verify the findings. Besides, different patterns of 3D surface wrinkles are studied and the similar surface wrinkle modulation is also observed. The findings presented herein may shed useful insights for the design of complex stretchable electronics, cosmetic products, soft devices and the fabrication of 3D complex structures.

scholarly journals A Generalized Approach for Evaluating the Mechanical Properties of Polymer Nanocomposites Reinforced with Spherical Fillers

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 830
Author(s):  
Julio Cesar Martinez-Garcia ◽  
Alexandre Serraïma-Ferrer ◽  
Aitor Lopeandía-Fernández ◽  
Marco Lattuada ◽  
Janak Sapkota ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Polymeric Nanocomposites ◽  
Mechanical Reinforcement ◽  
Future Studies ◽  
Three Phase ◽  
Theoretical Predictions ◽  
Filler Network ◽  
New Research ◽  
Good Agreement ◽  
Research Avenue

In this work, the effective mechanical reinforcement of polymeric nanocomposites containing spherical particle fillers is predicted based on a generalized analytical three-phase-series-parallel model, considering the concepts of percolation and the interfacial glassy region. While the concept of percolation is solely taken as a contribution of the filler-network, we herein show that the glassy interphase between filler and matrix, which is often in the nanometers range, is also to be considered while interpreting enhanced mechanical properties of particulate filled polymeric nanocomposites. To demonstrate the relevance of the proposed generalized equation, we have fitted several experimental results which show a good agreement with theoretical predictions. Thus, the approach presented here can be valuable to elucidate new possible conceptual routes for the creation of new materials with fundamental technological applications and can open a new research avenue for future studies.

The Reduction of Bias Error in Transfer Function Estimates Using FFT-Based Analyzers

1984 ◽  
Vol 106 (1) ◽  
pp. 29-35 ◽  
Author(s):  
P. Cawley
Keyword(s):  
Transfer Function ◽  
Random Excitation ◽  
Analogue Computer ◽  
Bias Error ◽  
Testing Time ◽  
Theoretical Predictions ◽  
Set Up ◽  
Modal Mass ◽  
Time Required ◽  
Good Agreement

The susceptibility to bias error of two methods for computing transfer (frequency response) functions from spectra produced by FFT-based analyzers using random excitation has been investigated. Results from tests with an FFT analyzer on a single degree-of-freedom system set up on an analogue computer show good agreement with the theoretical predictions. It has been shown that, around resonance, the bias error in the transfer function estimate H2 (Syy/Sxy*) is considerably less than that in the more commonly used estimate, H1 (Sxy/Sxx). The record length, and hence the testing time, required for a given accuracy is reduced by over 50 percent if the H2 calculation procedure is used. The analysis has also shown that if shaker excitation is used on lightly damped structures with low modal mass, it is important to minimize the mass of the force gage and the moving element of the shaker.

scholarly journals Novel Hexagonal Dual-Mode Substrate Integrated Waveguide Filter with Source-Load Coupling

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Ziqiang Xu ◽  
Gen Zhang ◽  
Hong Xia ◽  
Meijuan Xu
Keyword(s):  
Center Frequency ◽  
Substrate Integrated Waveguide ◽  
Fractional Bandwidth ◽  
Dual Mode ◽  
Transmission Zeros ◽  
Cavity Structure ◽  
Waveguide Filter ◽  
And Performance ◽  
Single Cavity ◽  
Good Agreement

Hexagonal dual-mode cavity and its application to substrate integrated waveguide (SIW) filter are presented. The hexagonal SIW resonator which can combine flexibility of rectangular cavity and performance of circular cavity is convenient for dual-mode bandpass filters design. By introducing coupling between source and load, the filter not only has good selectivity due to two controllable transmission zeros, but also has a small size by the virtue of its single-cavity structure. A demonstration filter with a center frequency of 10 GHz and a 3 dB fractional bandwidth of 4% is designed and fabricated to validate the proposed structure. Measured results are in good agreement with simulated ones.

Theoretical Prediction of Motions of High-Speed Planing Boats in Waves

1978 ◽  
Vol 22 (03) ◽  
pp. 140-169
Author(s):  
Milton Martin
Keyword(s):  
High Speed ◽  
Damping Ratio ◽  
Nonlinear Effects ◽  
Theoretical Method ◽  
Valuable Insight ◽  
Response Characteristics ◽  
Theoretical Predictions ◽  
Response Amplitude Operators ◽  
Phase Angles ◽  
Good Agreement

A theoretical method is derived for predicting the linearized response characteristics of constant deadrise high-speed planing boats in head and following waves. Comparisons of the theoretical predictions of the pitch and heave response amplitude operators and phase angles with existing experimental data show reasonably good agreement for a wide variety of conditions of interest. It appears that nonlinear effects are more severe at a speed to length ratio of 6 than of, say, 4 or less, principally because of the reduction of the damping ratio of the boat with increasing speed, and the consequent increase in motions in the vicinity of the resonant encounter frequency. However, it is concluded that the linear theory can provide a simple and fast means of determining the effect of various parameters such as trim angle, deadrise, loading, and speed on the damping, natural frequency, and linearized response in waves, and that this can furnish valuable insight into the actual boat dynamics, even though the accurate predictions of large motions and peak accelerations would require a nonlinear analysis.

On Wall Effects in Cavity Flows

1984 ◽  
Vol 28 (01) ◽  
pp. 70-75
Author(s):  
C. C. Hsu
Keyword(s):  
Numerical Results ◽  
Cavity Flows ◽  
Two Dimensional ◽  
Wall Effects ◽  
Free Jet ◽  
Theoretical Predictions ◽  
Experimental Findings ◽  
Good Agreement

Simple wall correction rules for two-dimensional and nearly two-dimensional cavity flows in closed or free jet water tunnels, based on existing linearized analyses, are made. Numerical results calculated from these expressions are compared with existing experimental findings. The present theoretical predictions are, in general, in good agreement with data.

Modelling double diffusion in soils and materials

2018 ◽  
Vol 27 (5-6) ◽  
Author(s):  
Ariadne-Αnne Tsambali ◽  
Avraam A. Konstantinidis ◽  
Elias C. Aifantis
Keyword(s):  
Double Diffusion ◽  
Chloride Diffusion ◽  
Theoretical Predictions ◽  
Sandy Aquifers ◽  
Good Agreement

AbstractThe double diffusivity model proposed earlier by Aifantis and co-workers was applied in this work for modelling the diffusion of metals in sandy aquifers, as well as chloride diffusion in concrete specimens. The theoretical predictions are in very good agreement with the measured concentrations in all cases, showing that the model is capable of dealing with a large variety of double diffusivity problems.

scholarly journals Multimodal Surface Instabilities in Curved Film–Substrate Structures

2017 ◽  
Vol 84 (8) ◽  
Author(s):  
Ruike Zhao ◽  
Xuanhe Zhao
Keyword(s):  
Thin Films ◽  
Mechanical Properties ◽  
Numerical Simulation ◽  
Period Doubling ◽  
Tubular Structures ◽  
Modulus Ratio ◽  
Future Design ◽  
Mismatch Strain ◽  
Curved Structures ◽  
Film Substrate

Structures of thin films bonded on thick substrates are abundant in biological systems and engineering applications. Mismatch strains due to expansion of the films or shrinkage of the substrates can induce various modes of surface instabilities such as wrinkling, creasing, period doubling, folding, ridging, and delamination. In many cases, the film–substrate structures are not flat but curved. While it is known that the surface instabilities can be controlled by film–substrate mechanical properties, adhesion and mismatch strain, effects of the structures’ curvature on multiple modes of instabilities have not been well understood. In this paper, we provide a systematic study on the formation of multimodal surface instabilities on film–substrate tubular structures with different curvatures through combined theoretical analysis and numerical simulation. We first introduce a method to quantitatively categorize various instability patterns by analyzing their wave frequencies using fast Fourier transform (FFT). We show that the curved film–substrate structures delay the critical mismatch strain for wrinkling when the system modulus ratio between the film and substrate is relatively large, compared with flat ones with otherwise the same properties. In addition, concave structures promote creasing and folding, and suppress ridging. On the contrary, convex structures promote ridging and suppress creasing and folding. A set of phase diagrams are calculated to guide future design and analysis of multimodal surface instabilities in curved structures.

scholarly journals Asymptotic analysis for personalized Web search

2010 ◽  
Vol 42 (02) ◽  
pp. 577-604 ◽  
Author(s):  
Yana Volkovich ◽  
Nelly Litvak
Keyword(s):  
Web Search ◽  
Power Laws ◽  
User Preference ◽  
Importance Measure ◽  
Web Documents ◽  
Original Definition ◽  
Theoretical Predictions ◽  
Heavy Tailed ◽  
Definition Of ◽  
Good Agreement

PageRank with personalization is used in Web search as an importance measure for Web documents. The goal of this paper is to characterize the tail behavior of the PageRank distribution in the Web and other complex networks characterized by power laws. To this end, we model the PageRank as a solution of a stochastic equationwhere theRis are distributed asR. This equation is inspired by the original definition of the PageRank. In particular,Nmodels the number of incoming links to a page, andBstays for the user preference. Assuming thatNorBare heavy tailed, we employ the theory of regular variation to obtain the asymptotic behavior ofRunder quite general assumptions on the involved random variables. Our theoretical predictions show good agreement with experimental data.

Some Limitations in Applying Classical EHD Film Thickness Formulas to a High-Speed Bearing

1981 ◽  
Vol 103 (2) ◽  
pp. 295-301 ◽  
Author(s):  
J. J. Coy ◽  
E. V. Zaretsky
Keyword(s):  
Film Thickness ◽  
High Speed ◽  
Heating Effects ◽  
Theoretical Predictions ◽  
Traction Fluid ◽  
Shear Heating ◽  
Thickness Measurements ◽  
Inner Race ◽  
Maximum Stresses ◽  
Good Agreement

Elastohydrodynamic film thickness was measured for a 20-mm ball bearing using the capacitance technique. The bearing was thrust loaded to 90, 448, and 778 N (20, 100, and 175 lb). The corresponding maximum stresses on the inner race were 1.28, 2.09, and 2.45 GPa (185,000, 303,000, and 356,000 psi). Test speeds ranged from 400 to 14,000 rpm. Film thickness measurements were taken with four different lubricants: (a) synthetic paraffinic, (b) synthetic paraffinic with additives, (c) neopentylpolyol (tetra) ester meeting MIL-L-23699A specifications, and (d) synthetic cycloaliphatic hydrocarbon traction fluid. The test bearing was mist lubricated. Test temperatures were 300, 338, and 393 K. The measured results were compared to theoretical predictions using the formulae of Grubin, Archard and Cowking, Dowson and Higginson, and Hamrock and Dowson. There was good agreement with theory at low dimensionless speed, but the film was much smaller than theory predicts at higher speeds. This was due to kinematic starvation and inlet shear heating effects. Comparisons with Chiu’s theory on starvation and Cheng’s theory on inlet shear heating were made.

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