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.

scholarly journals Insect adhesion on rough surfaces: analysis of adhesive contact of smooth and hairy pads on transparent microstructured substrates

2014 ◽  
Vol 11 (98) ◽  
pp. 20140499 ◽  
Author(s):  
Yanmin Zhou ◽  
Adam Robinson ◽  
Ullrich Steiner ◽  
Walter Federle
Keyword(s):  
Sharp Increase ◽  
Rough Surfaces ◽  
Adhesive Contact ◽  
Gradual Transition ◽  
Flat Plates ◽  
Shear Forces ◽  
Partial Contact ◽  
Full Contact ◽  
Contact Models ◽  
Simple Contact

Insect climbing footpads are able to adhere to rough surfaces, but the details of this capability are still unclear. To overcome experimental limitations of randomly rough, opaque surfaces, we fabricated transparent test substrates containing square arrays of 1.4 µm diameter pillars, with variable height (0.5 and 1.4 µm) and spacing (from 3 to 22 µm). Smooth pads of cockroaches ( Nauphoeta cinerea ) made partial contact (limited to the tops of the structures) for the two densest arrays of tall pillars, but full contact (touching the substrate in between pillars) for larger spacings. The transition from partial to full contact was accompanied by a sharp increase in shear forces. Tests on hairy pads of dock beetles ( Gastrophysa viridula ) showed that setae adhered between pillars for larger spacings, but pads were equally unable to make full contact on the densest arrays. The beetles' shear forces similarly decreased for denser arrays, but also for short pillars and with a more gradual transition. These observations can be explained by simple contact models derived for soft uniform materials (smooth pads) or thin flat plates (hairy-pad spatulae). Our results show that microstructured substrates are powerful tools to reveal adaptations of natural adhesives for rough surfaces.

Design of a wheeled wall climbing robot based on the performance of bio-inspired dry adhesive material

Robotica ◽  
2021 ◽  
pp. 1-14
Author(s):  
Hongkai Li ◽  
Xianfei Sun ◽  
Zishuo Chen ◽  
Lei Zhang ◽  
Hongchao Wang ◽  
...  
Keyword(s):  
Flat Surface ◽  
Thrust Force ◽  
Adhesion Force ◽  
Structure Design ◽  
Design Parameters ◽  
Climbing Robot ◽  
Adhesive Material ◽  
Ducted Fan ◽  
The Stability ◽  
Belt System

Abstract Inspired by gecko’s adhesive feet, a wheeled wall climbing robot is designed in this paper with the synchronized gears and belt system acting as the wheels by considering both motion efficiency and adhesive capability. Adhesion of wheels is obtained by the bio-inspired adhesive material wrapping on the outer surface of wheels. A ducted fan mounted on the back of the robot supplies thrust force for the adhesive material to generate normal and shear adhesion force whilemoving on vertical surfaces. Experimental verification of robot climbing on vertical flat surface was carried out. The stability and the effect of structure design parameters were analyzed.

scholarly journals Adhesion of Individual Attachment Setae of the Spider Cupiennius salei to Substrates With Different Roughness and Surface Energy

2021 ◽  
Vol 7 ◽  
Author(s):  
Bastian Poerschke ◽  
Stanislav N. Gorb ◽  
Clemens F. Schaber
Keyword(s):  
Surface Energy ◽  
Glass Substrate ◽  
Adhesion Force ◽  
Adhesive System ◽  
Adhesive Contact ◽  
Contact Angles ◽  
Individual Variability ◽  
Van Der Waals Interactions ◽  
Smooth Surfaces ◽  
Cupiennius Salei

Dynamic adhesion is a key ability for animals to climb smooth surfaces. Spiders evolved, convergent to geckos, a dry adhesive system made of setae branching into smaller microtrichia ending as spatulae. Several previous studies concentrated either on the whole adhesive claw tuft on the spider´s foot that consists of attachment setae or on the single adhesive contact elements, the microtrichia with spatula-shaped tips. Here, the adhesion of single setae of the spider Cupiennius salei was examined and the morphology of the pretarsus and the fine structure of the setae were studied in further detail. Using individual setae fixed to force sensing cantilevers, their adhesion at different contact angles with a glass substrate was measured as well as their adhesive performance on substrates with different roughness and on smooth surfaces with different surface energies. The results show an individual variability of the adhesive forces corresponding to the seta morphology and especially to the seta tip shape. The tip shapes of the setae vary largely even in neighboring setae of the pretarsal claw tuft that comprises approximately 2,400 setae. Regarding surface energy of the substrate, the adhesion force on hydrophobic polytetrafluoroethylene was 30% of that on a hydrophilic glass substrate, which points to the importance of both van der Waals interactions and hydrogen bonds in spider adhesion.

A Generalized Model for Adhesive Contact Between a Rigid Cylinder and a Transversely Isotropic Substrate

2012 ◽  
Vol 80 (1) ◽  
Author(s):  
Haimin Yao
Keyword(s):  
Adhesion Force ◽  
Transversely Isotropic ◽  
Generalized Solution ◽  
Adhesive Contact ◽  
Equilibrium Conditions ◽  
Space Problem ◽  
Rigid Cylinder ◽  
Adhesion Behavior ◽  
Griffith’S Criterion ◽  
Resistant Moment

In this paper, a solution to the quasi-static adhesive contact problem between a rigid cylinder and a transversely isotropic substrate is extended to the most general case by taking adhesion hysteresis into account. An analytical solution to the contact stress is obtained by solving the integral equations established on the basis of the Green's function for the two-dimensional transversely isotropic half-space problem. By using equilibrium conditions and Griffith's criterion, the adhesion force and resistant moment to rolling are determined as functions of contact geometries and material properties of the contacting solids. Detailed discussions on the adhesion force and resistant moment are presented for some specific cases, revealing adhesion behaviors that have not been predicted by previous models. As the most generalized solution to the discussed problem, our results would have extensive applications in predicting the adhesion behavior between solids undergoing sophisticated mechanical loadings.

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.

scholarly journals Local-solution approach to quasistatic rate-independent mixed-mode delamination

2015 ◽  
Vol 25 (07) ◽  
pp. 1337-1364 ◽  
Author(s):  
Tomáš Roubíček ◽  
Christos G. Panagiotopoulos ◽  
Vladislav Mantič
Keyword(s):  
Mixed Mode ◽  
Solution Concept ◽  
Adhesive Contact ◽  
Mathematical Methods ◽  
Solution Approach ◽  
Homogeneous Potential ◽  
Internal Parameters ◽  
Contact Models ◽  
Local Solutions ◽  
The One

The model of quasistatic rate-independent evolution of a delamination at small strains in the so-called mixed mode, i.e. distinguishing opening (Mode I) from shearing (Mode II), devised in [Delamination and adhesive contact models and their mathematical analysis and numerical treatment, Chap. 9, in Mathematical Methods and Models in Composites, ed. V. Mantič (Imperial College Press, 2014), pp. 349–400; and in Quasistatic mixed-mode delamination model, Discrete Contin. Dynam. Syst. Ser. S 6 (2013) 591–610], is rigorously analyzed in the context of a concept of stress-driven local solutions. The model has separately convex stored energy and is associative, namely the one-homogeneous potential of dissipative forces driving the delamination depends only on rates of internal parameters. An efficient fractional-step-type semi-implicit discretization in time is shown to converge to (specific, stress-driven like) local solutions that may approximately obey the maximum-dissipation principle. Making still a spatial discretization, this convergence as well as relevancy of such solution concept are demonstrated on a nontrivial two-dimensional example.

An Adhesion Model for Elastic-Contacting Fractal Surfaces in the Presence of Meniscus

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Y. F. Peng ◽  
Y. B. Guo ◽  
Y. Q. Hong
Keyword(s):  
Relative Humidity ◽  
Thin Liquid Film ◽  
Surface Model ◽  
Fractal Surface ◽  
Fractal Function ◽  
Adhesive Interaction ◽  
Dugdale Model ◽  
Fractal Surfaces ◽  
Fractal Parameters ◽  
Adhesion Model

The strong stiction of adjacent surfaces with meniscus is a major design concern in the devices with a microsized interface. The present research concerns the elastic adhesion of rough fractal surfaces in the presence of a thin liquid film. A rough fractal surface is characterized with a two-variable Weierstrass–Mandelbrot fractal function. The microcontact model of the single asperity is established in terms of the fractal parameters. The adhesion model from meniscus is developed with the Dugdale approximation of the Laplace pressure to consider the adhesive interaction within/outside the contact area. Then the Maugis–Dugdale model and its extension are used to solve the elastic adhesive interaction for the two approaching fractal surfaces by incorporating the fractal surface model. Simulations of the external force versus the interface stiffness, surface roughness, and relative humidity are performed, respectively. The simulation results show that the interface stiffness, surface topography, and relative humidity can heavily influence the interface adhesion of rough surfaces with meniscus.

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