scholarly journals Generalized Maugis–Dugdale model of an elastic cylinder in non-slipping adhesive contact with a stretched substrate

2006 ◽  
Vol 97 (5) ◽  
pp. 584-593 ◽  
Author(s):  
Shaohua Chen ◽  
Huajian Gao
Keyword(s):  
Adhesive Contact ◽  
Elastic Cylinder ◽  
Dugdale Model

Robust Strategies for Automated AFM Force Curve Analysis—II: Adhesion-Influenced Indentation of Soft, Elastic Materials

2007 ◽  
Vol 129 (6) ◽  
pp. 904-912 ◽  
Author(s):  
David C. Lin ◽  
Emilios K. Dimitriadis ◽  
Ferenc Horkay
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Full Range ◽  
Soft Materials ◽  
Adhesive Contact ◽  
Colloid Interface ◽  
Inhomogeneous Materials ◽  
Dugdale Model ◽  
Normal Contact ◽  
Adhesive Interactions

In the first of this two-part discourse on the extraction of elastic properties from atomic force microscopy (AFM) data, a scheme for automating the analysis of force-distance curves was introduced and experimentally validated for the Hertzian (i.e., linearly elastic and noninteractive probe-sample pairs) indentation of soft, inhomogeneous materials. In the presence of probe-sample adhesive interactions, which are common especially during retraction of the rigid tip from soft materials, the Hertzian models are no longer adequate. A number of theories (e.g., Johnson–Kendall–Roberts and Derjaguin–Muller–Toporov), covering the full range of sample compliance relative to adhesive force and tip radius, are available for analysis of such data. We incorporated Pietrement and Troyon’s approximation (2000, “General Equations Describing Elastic Indentation Depth and Normal Contact Stiffness Versus Load,” J. Colloid Interface Sci., 226(1), pp. 166–171) of the Maugis–Dugdale model into the automated procedure. The scheme developed for the processing of Hertzian data was extended to allow for adhesive contact by applying the Pietrement–Troyon equation. Retraction force-displacement data from the indentation of polyvinyl alcohol gels were processed using the customized software. Many of the retraction curves exhibited strong adhesive interactions that were absent in extension. We compared the values of Young’s modulus extracted from the retraction data to the values obtained from the extension data and from macroscopic uniaxial compression tests. Application of adhesive contact models and the automated scheme to the retraction curves yielded average values of Young’s modulus close to those obtained with Hertzian models for the extension curves. The Pietrement–Troyon equation provided a good fit to the data as indicated by small values of the mean-square error. The Maugis–Dugdale theory is capable of accurately modeling adhesive contact between a rigid spherical indenter and a soft, elastic sample. Pietrement and Troyon’s empirical equation greatly simplifies the theory and renders it compatible with the general automation strategies that we developed for Hertzian analysis. Our comprehensive algorithm for automated extraction of Young’s moduli from AFM indentation data has been expanded to recognize the presence of either adhesive or Hertzian behavior and apply the appropriate contact model.

Revisiting the Maugis–Dugdale Adhesion Model of Elastic Periodic Wavy Surfaces

2016 ◽  
Vol 83 (10) ◽  
Author(s):  
Fan Jin ◽  
Xu Guo ◽  
Qiang Wan
Keyword(s):  
Flat Surface ◽  
Adhesion Force ◽  
Adhesive Contact ◽  
Interaction Zone ◽  
Dugdale Model ◽  
Full Contact ◽  
Type Contact ◽  
Wavy Surfaces ◽  
Contact Models ◽  
Adhesion Model

The plane strain adhesive contact between a periodic wavy surface and a flat surface has been revisited based on the classical Maugis–Dugdale model. Closed-form analytical solutions derived by Hui et al. [1], which were limited to the case that the interaction zone cannot saturate at a period, have been extended to two additional cases with adhesion force acting throughout the whole period. Based on these results, a complete transition between the Westergaard and the Johnson, Kendall, and Roberts (JKR)-type contact models is captured through a dimensionless transition parameter, which is consistent with that for a single cylindrical contact. Depending on two dimensionless parameters, different transition processes between partial and full contact during loading/unloading stages are characterized by one or more jump instabilities. Rougher surfaces are found to enhance adhesion both by increasing the magnitude of the pull-off force and by inducing more energy loss due to adhesion hysteresis.

Influence of the Tabor Parameter on the Roughness-Induced Adhesion Hysteresis

2012 ◽  
Vol 157-158 ◽  
pp. 1233-1237
Author(s):  
Le Feng Wang ◽  
Wei Bin Rong ◽  
Bing Shao ◽  
Li Ning Sun
Keyword(s):  
Rough Surface ◽  
Rough Surfaces ◽  
Adhesive Contact ◽  
Contact Model ◽  
Dissipation Energy ◽  
Dugdale Model ◽  
Relationship Of ◽  
Special Case ◽  
Tabor Parameter

Influence of the Tabor parameter on the roughness-induced adhesion hysteresis was investigated. To achieve this, the adhesive contact model of single asperities was considered by incorporating the Maugis-dugdale model and its corresponding extension firstly. Further more, the load-approach relationship of adhesive contact between a rough surface and a flat was analyzed. The dissipation energy during a load and unload cycle is derived for general values of the Tabor parameter. It was found that the adhesion hysteresis becomes weaker gradually with the increase of the adhesion parameter, and it becomes stronger with the decrease of the Tabor parameter at the same adhesion parameter. The adhesion hysteresis for a special case that rough surfaces with DMT(Deryagin-Muller-Toporov)-type asperities is also discussed.

scholarly journals A double-Hertz model for adhesive contact between cylinders under inclined forces

2019 ◽  
Vol 475 (2221) ◽  
pp. 20180589
Author(s):  
Ji-Feng Yan ◽  
Gan-Yun Huang
Keyword(s):  
Friction Coefficient ◽  
Half Space ◽  
Adhesive Contact ◽  
Elastic Cylinder ◽  
Elastic Half Space ◽  
Hertz Model ◽  
Shear Traction ◽  
Contact Behaviour ◽  
Normal Traction ◽  
Compressive Pressure

A generalized double-Hertz (D-H) model has been proposed to consider the adhesive contact between an elastic cylinder and an elastic half space under inclined forces. The normal traction is exactly the same as that in the conventional D-H model. The shear traction of finite value is distributed into a slipping zone and a non-slipping zone. In the slipping zone, the shear traction is proportional to the compressive pressure. With the model, adhesive contact behaviour between cylinders has been numerically illustrated. The shear-induced peeling has been demonstrated. The value of the ratio for shear traction to normal traction larger than friction coefficient has been found in part of the non-slipping zone. Those altogether are consistent with experiments.

Non-slipping adhesive contact of an elastic cylinder on stretched substrates

2005 ◽  
Vol 462 (2065) ◽  
pp. 211-228 ◽  
Author(s):  
Shaohua Chen ◽  
Huajian Gao
Keyword(s):  
Contact Region ◽  
Threshold Level ◽  
Adhesive Contact ◽  
Elastic Cylinder ◽  
External Loading ◽  
Applied Loading ◽  
Level Ii ◽  
Substrate Strain ◽  
Cell Reorientation ◽  
Contact Size

The plane strain problem of an elastic cylinder in adhesive contact with a stretched substrate is studied via a generalized JKR model taking into account the transmission of both tangential and normal tractions across the contact interface. The width of the contact region is determined from the Griffith energy balance near the contact edge. In the absence of external loading, the tangential traction is found to have a negligible effect on the contact size. As an external stress is applied to stretch the substrate, the contact solution exhibits three distinct regimes characterized by two threshold strains: (i) the size of the contact region is hardly affected by the applied loading when the substrate strain is below the first threshold level; (ii) the contact size decreases quickly with stretch as the substrate strain increases to between the two threshold levels; (iii) the contact size approaches zero when the substrate strain exceeds the second threshold level. Interestingly, these results share a number of common features with the experimentally observed cell reorientation on a cyclically stretched substrate. An approximate solution is presented in an appendix to represent the numerical results in closed form.

A New Numerical Approach for Adhesive Contacts of Real Engineering Surfaces

2010 ◽  
Vol 44-47 ◽  
pp. 1251-1257 ◽  
Author(s):  
Yu Qi Zheng ◽  
San Min Wang
Keyword(s):  
Elastic Deformation ◽  
Meshless Method ◽  
Adhesive Contact ◽  
Adhesive Force ◽  
Viscous Force ◽  
Rigid Spheres ◽  
Dugdale Model ◽  
Nano Scale ◽  
D Model ◽  
Tabor Parameter

Microelectromechanical system (MEMS) and nanotechnology are important directions on the development of the science in twenty-first century. Some of the effects, such as viscous force, surface force, electrostatic force, friction etc., which can be usually ignored on the traditional scale, have become noticeable when the scale has turn to micro or nano scale. Nanotribology is one of the main areas of the indispensable researches on the basic theory and methodology of the effects. The micro/nano adhesive contact which is the foundation of nanotribology is studied in this paper. The earliest study on adhesive contact was done by Bradley. He presented an expression of adhesive force of two contacting rigid spheres. Derjaguin, Muller and Toprov (DMT) gave the relation of the contact area and the applied load of the adhesive contact of two spheres, but they did not consider the elastic deformation due to the adhesive force of the bodies. Johnson, Keudall and Roberts (JKR) provided a theory of the adhesive contact of two elastic spheres. Tabor gave a parameter (Tabor parameter) to interpret the ratio of the elastic deformation with the adhesive force of two contacting bodies. That is to say the DMT model corresponding to small Tabor parameter(<0.1) and the JKR model to large Tabor parameter(>5). Maguis gave a DMT-JKR transition using the Dugdale model in fracture mechanics (M-D model) in the intermediate region between the DMT model and the JKR model. A numerical algorithm of elastic adhesive contact based on the meshless method is presented in this paper. This make it possible to solve the adhesive contact with more complex surface topography and to consider more intricate factors, such as thermal stress, friction, elasto-plastic deformation etc. in the further studies on micro/nano scale adhesive contact problems. The meshless method seems to be a promising approach for contact analyses because of its flexibility in domain descritization and versatility in node arrangements. It can be used to solve a variety of complicated engineering problems. A numerical example of adhesive contact between a micro elastic cylinder and a rigid half-space is carried out to show the feasibility of the algorithm. In the simulation, an effective method of the M-D model is used to save the cost of computation. Compared with the existed solutions, the results solved by the presented algorithm are reasonable.

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