An Atomistically Enriched Continuum Model for Nanoscale Contact Mechanics and Its Application to Contact Scaling

2008 ◽  
Vol 8 (7) ◽  
pp. 3757-3773
Author(s):  
Roger A. Sauer ◽  
Shaofan Li
Keyword(s):  
Contact Mechanics ◽  
Scaling Laws ◽  
Coarse Graining ◽  
Contact Model ◽  
Geometrically Nonlinear ◽  
Lattice Statics ◽  
Mechanics Model ◽  
Contact Formulation ◽  
Wide Range ◽  
Length Scaling

This work provides a comprehensive exposition and extension of an atomistically enriched contact mechanics model initially proposed by the present authors. The contact model is based on the coarse-graining of the interaction occurring between the molecules of the contacting bodies. As these bodies may be highly compliant, a geometrically nonlinear kinematical description is chosen. Thus a large deformation continuum contact formulation is obtained which reflects the attractive and repulsive character of intermolecular interactions. Further emphasis is placed on the efficiency of the proposed atomistic-continuum contact model in numerical simulations. Therefore three contact formulations are discussed and validated by lattice statics computations. Demonstrated by a simple benchmark problem the scaling of the proposed contact model is investigated and some of the important scaling laws are obtained. In particular, the length scaling, or size effect, of the contact model is studied. Due to its formal generality and its numerical efficiency over a wide range of length scales, the proposed contact formulation can be applied to a variety of multiscale contact phenomena. This is illustrated by several numerical examples.

Are elastic moduli of biological cells depth dependent or not? Another explanation using a contact mechanics model with surface tension

Soft Matter ◽  
2018 ◽  
Vol 14 (36) ◽  
pp. 7534-7541 ◽  
Author(s):  
Yue Ding ◽  
Jian Wang ◽  
Guang-Kui Xu ◽  
Gang-Feng Wang
Keyword(s):  
Surface Tension ◽  
Elastic Modulus ◽  
Contact Mechanics ◽  
Elastic Moduli ◽  
Contact Model ◽  
Biological Cells ◽  
Mechanics Model ◽  
Afm Indentation ◽  
A Cell ◽  
Indent Depth

Contrary to the existing reports that the apparent elastic modulus of a cell depends strongly on the indent depth in many AFM indentation experiments, we present a contact model with surface effects, and show that the actual elastic modulus of cell materials could be independent of the indent depth if surface tension is taken into account.

scholarly journals Predicting specific impulse distributions for spherical explosives in the extreme near-field using a Gaussian function

2021 ◽  
pp. 204141962199349
Author(s):  
Jordan J Pannell ◽  
George Panoutsos ◽  
Sam B Cooke ◽  
Dan J Pope ◽  
Sam E Rigby
Keyword(s):  
Scaling Laws ◽  
Near Field ◽  
Specific Impulse ◽  
Gaussian Function ◽  
Data Driven ◽  
Blast Load ◽  
Structural Deformation ◽  
Load Prediction ◽  
Validation Data ◽  
Wide Range

Accurate quantification of the blast load arising from detonation of a high explosive has applications in transport security, infrastructure assessment and defence. In order to design efficient and safe protective systems in such aggressive environments, it is of critical importance to understand the magnitude and distribution of loading on a structural component located close to an explosive charge. In particular, peak specific impulse is the primary parameter that governs structural deformation under short-duration loading. Within this so-called extreme near-field region, existing semi-empirical methods are known to be inaccurate, and high-fidelity numerical schemes are generally hampered by a lack of available experimental validation data. As such, the blast protection community is not currently equipped with a satisfactory fast-running tool for load prediction in the near-field. In this article, a validated computational model is used to develop a suite of numerical near-field blast load distributions, which are shown to follow a similar normalised shape. This forms the basis of the data-driven predictive model developed herein: a Gaussian function is fit to the normalised loading distributions, and a power law is used to calculate the magnitude of the curve according to established scaling laws. The predictive method is rigorously assessed against the existing numerical dataset, and is validated against new test models and available experimental data. High levels of agreement are demonstrated throughout, with typical variations of <5% between experiment/model and prediction. The new approach presented in this article allows the analyst to rapidly compute the distribution of specific impulse across the loaded face of a wide range of target sizes and near-field scaled distances and provides a benchmark for data-driven modelling approaches to capture blast loading phenomena in more complex scenarios.

scholarly journals A Simple Contact Mechanics Model for Highly Strained Aqueous Surface Gels

2021 ◽  
Author(s):  
A. L. Chau ◽  
M. K. Cavanaugh ◽  
Y.-T. Chen ◽  
A. A. Pitenis
Keyword(s):  
Simple Model ◽  
Contact Mechanics ◽  
Contact Lenses ◽  
Radius Of Curvature ◽  
Winkler Foundation ◽  
Surface Layers ◽  
Mechanics Model ◽  
Soft Surface ◽  
Simple Contact ◽  
Highly Strained

Abstract Background Soft, biological, and bio-inspired materials are often compositionally heterogeneous and structurally anisotropic, and they frequently feature graded or layered organizations. This design complexity enables exceptional ranges in properties and performance yet complicates a fundamental understanding of the contact mechanics. Recent studies of soft gel layers have relied on Hertzian or Winkler foundation (“bed-of-springs”) models to characterize the mechanics but have found neither satisfactory. Objective The contact mechanics of soft gel layers are not yet fully understood. The aim of this work is to develop a simple contact mechanics model tailored for compositionally-graded materials with soft surface layers under high strains and deformations. Methods Concepts from polymer physics, fluid draining, and Winkler foundation mechanics are combined to develop a simple contact mechanics model which relates the applied normal force to the probe radius of curvature, elastic modulus, and thickness of soft surface layers subjected to high strains. Results This simple model was evaluated with two examples of graded surface gel layers spanning multiple length-scales, including commercially available contact lenses and stratified hydrogels. The model captures the nonlinear contact mechanics of highly strained soft aqueous gel layers more closely than either Hertz or Winkler foundation theory while simultaneously enabling a prediction for the thickness of the surface gel layer. Conclusion These results indicate that this simple model can adequately characterize the contact mechanics of highly strained soft aqueous gel layers.

Aerodynamic Similarity Principles and Scaling Laws for Windmilling Fans

2018 ◽  
Author(s):  
Dilip Prasad
Keyword(s):  
Rotational Speed ◽  
Pressure Loss ◽  
Scaling Laws ◽  
Dynamic Pressure ◽  
Stagnation Pressure ◽  
Design Parameters ◽  
Similarity Parameter ◽  
Wide Range ◽  
Simulation Results ◽  
Good Agreement

Windmilling requirements for aircraft engines often define propulsion and airframe design parameters. The present study is focused is on two key quantities of interest during windmill operation: fan rotational speed and stage losses. A model for the rotor exit flow is developed, that serves to bring out a similarity parameter for the fan rotational speed. Furthermore, the model shows that the spanwise flow profiles are independent of the throughflow, being determined solely by the configuration geometry. Interrogation of previous numerical simulations verifies the self-similar nature of the flow. The analysis also demonstrates that the vane inlet dynamic pressure is the appropriate scale for the stagnation pressure loss across the rotor and splitter. Examination of the simulation results for the stator reveals that the flow blockage resulting from the severely negative incidence that occurs at windmill remains constant across a wide range of mass flow rates. For a given throughflow rate, the velocity scale is then shown to be that associated with the unblocked vane exit area, leading naturally to the definition of a dynamic pressure scale for the stator stagnation pressure loss. The proposed scaling procedures for the component losses are applied to the flow configuration of Prasad and Lord (2010). Comparison of simulation results for the rotor-splitter and stator losses determined using these procedures indicates very good agreement. Analogous to the loss scaling, a procedure based on the fan speed similarity parameter is developed to determine the windmill rotational speed and is also found to be in good agreement with engine data. Thus, despite their simplicity, the methods developed here possess sufficient fidelity to be employed in design prediction models for aircraft propulsion systems.

Aerodynamic Similarity Principles and Scaling Laws for Windmilling Fans

2018 ◽  
Vol 140 (12) ◽  
Author(s):  
Dilip Prasad
Keyword(s):  
Rotational Speed ◽  
Pressure Loss ◽  
Scaling Laws ◽  
Dynamic Pressure ◽  
Stagnation Pressure ◽  
Design Parameters ◽  
Similarity Parameter ◽  
Wide Range ◽  
Simulation Results ◽  
Good Agreement

Windmilling requirements for aircraft engines often define propulsion and airframe design parameters. The present study is focused on two key quantities of interest during windmill operation: fan rotational speed and stage losses. A model for the rotor exit flow is developed that serves to bring out a similarity parameter for the fan rotational speed. Furthermore, the model shows that the spanwise flow profiles are independent of the throughflow, being determined solely by the configuration geometry. Interrogation of previous numerical simulations verifies the self-similar nature of the flow. The analysis also demonstrates that the vane inlet dynamic pressure is the appropriate scale for the stagnation pressure loss across the rotor and splitter. Examination of the simulation results for the stator reveals that the flow blockage resulting from the severely negative incidence that occurs at windmill remains constant across a wide range of mass flow rates. For a given throughflow rate, the velocity scale is then shown to be that associated with the unblocked vane exit area, leading naturally to the definition of a dynamic pressure scale for the stator stagnation pressure loss. The proposed scaling procedures for the component losses are applied to the flow configuration of Prasad and Lord (2010). Comparison of simulation results for the rotor-splitter and stator losses determined using these procedures indicates very good agreement. Analogous to the loss scaling, a procedure based on the fan speed similarity parameter is developed to determine the windmill rotational speed and is also found to be in good agreement with engine data. Thus, despite their simplicity, the methods developed here possess sufficient fidelity to be employed in design prediction models for aircraft propulsion systems.

scholarly journals A scaled MP-PIC method for bubbling fluidization

2021 ◽  
Author(s):  
Xing Zhao ◽  
Yong Jiang ◽  
Fei Li ◽  
Wei Wang
Keyword(s):  
Fluidized Beds ◽  
Volume Fraction ◽  
Phase Particle ◽  
Scaling Law ◽  
Coarse Graining ◽  
Coarse Grained ◽  
Particle In Cell ◽  
Wide Range ◽  
Pic Method ◽  
Multi Phase

Coarse-grained methods have been widely used in simulations of gas-solid fluidization. However, as a key parameter, the coarse-graining ratio, and its relevant scaling law is still far from reaching a consensus. In this work, a scaling law is developed based on a similarity analysis, and then it is used to scale the multi-phase particle-in-cell (MP-PIC) method, and validated in the simulation of two bubbling fluidized beds. The simulation result shows this scaled MP-PIC can reduce the errors of solids volume fraction and velocity distributions over a wide range of coarse-graining ratios. In future, we expect that a scaling law with consideration of the heterogeneity inside a parcel or numerical particle will further improve the performance of coarse-grained modeling in simulation of fluidized beds.

scholarly journals Exploiting scaling laws for designing polymeric bottle brushes: a theoretical coarse-graining for homopolymeric branched polymers

2019 ◽  
Vol 21 (27) ◽  
pp. 14873-14878 ◽  
Author(s):  
Pietro Corsi ◽  
Elia Roma ◽  
Tecla Gasperi ◽  
Fabio Bruni ◽  
Barbara Capone
Keyword(s):  
Scaling Laws ◽  
Star Polymers ◽  
Coarse Graining ◽  
Branched Polymers ◽  
Coarse Grain ◽  
Multiscale Approach ◽  
Bottle Brushes

Scaling multiscale approach to coarse grain bottle brushes polymeric macromolecules as effective chains of tethered star polymers.

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