Lubricated steady sliding of a rigid sphere on a soft elastic substrate: hydrodynamic friction in the Hertz limit

Soft Matter ◽  
2020 ◽  
Vol 16 (11) ◽  
pp. 2760-2773 ◽  
Author(s):  
Haibin Wu ◽  
Nichole Moyle ◽  
Anand Jagota ◽  
Chung-Yuen Hui
Keyword(s):  
Rigid Sphere ◽  
Elastic Substrate ◽  
Hydrodynamic Friction ◽  
Elastic Substrates ◽  
Lubricated Sliding

Lubricated sliding on soft elastic substrates occurs in a variety of natural and technological settings.

Lubricated Soft Normal Elastic Contact of a Sphere: A New Numerical Method and Experiment

Soft Matter ◽  
2022 ◽  
Author(s):  
Zezhou Liu ◽  
Hao Dong ◽  
Anand Jagota ◽  
Chung-Yuen Hui
Keyword(s):  
Liquid Film ◽  
Numerical Solution ◽  
Numerical Method ◽  
Thin Liquid Film ◽  
Rigid Sphere ◽  
Elastic Contact ◽  
Elastic Substrate ◽  
Normal Contact

An important problem in lubrication is the squeezing of a thin liquid film between a rigid sphere and an elastic substrate under normal contact. Numerical solution of this problem typically...

Elastohydrodynamic Lubrication Analysis of Pure Squeeze Motion on an Elastic Coating/Elastic Substrate System

2015 ◽  
Vol 137 (1) ◽  
Author(s):  
Li-Ming Chu ◽  
Chi-Chen Yu ◽  
Qie-Da Chen ◽  
Wang-Long Li
Keyword(s):  
Young’S Modulus ◽  
Elastic Deformation ◽  
Maximum Stress ◽  
Young's Modulus ◽  
Elastohydrodynamic Lubrication ◽  
Operating Conditions ◽  
Von Mises Stress ◽  
Rigid Sphere ◽  
Elastic Substrate ◽  
Asymptotic Value

A rigid sphere approaching a lubricated flat surface with a layer of elastic coating on the elastic substrate is explored under constant load conditions. The transient pressure profiles, film shapes, elastic deformation, von Mises stress (σvon) during the pure squeeze process under various operating conditions in the elastohydrodynamic lubrication (EHL) regime are discussed. The simulation results reveal that the greater the Young's modulus of coating is, the greater the pressure distribution is, the smaller the contact area is, and the greater the maximum stress (σvon) value is. As the Young’s modulus of coating decreases, the central elastic deformation at the surface (Z = 0) increases and the deformation at the interface of coating/substrate (Z = −1) decreases. For hard coating cases, the maximum central pressure increases to an asymptotic value and minimum film thickness decreases to an asymptotic value as the coating thickness increases. For soft coating cases, this phenomenon reverses. A thicker and stiffer coating leads to a higher maximum stress. At the deformation recovery stage, the positions of the maximum stress would begin to offset downwards and closer to the coating/substrate interface. Moreover, the position of maximum stress varies from the coating to the subsurface as the Young’s modulus of coating increases. The EHL with stress analysis can prevent the chance of fracture in coating or substrate. These characteristics are important for the lubrication design of mechanical elements with coatings.

scholarly journals Indentation of a rigid sphere into an elastic substrate with surface tension and adhesion

2015 ◽  
Vol 471 (2175) ◽  
pp. 20140727 ◽  
Author(s):  
Chung-Yuen Hui ◽  
Tianshu Liu ◽  
Thomas Salez ◽  
Elie Raphael ◽  
Anand Jagota
Keyword(s):  
Surface Tension ◽  
Small Strain ◽  
Work Of Adhesion ◽  
Contact Radius ◽  
Rigid Sphere ◽  
Elastic Substrate ◽  
Indentation Force ◽  
Resistance To Deformation ◽  
Sphere Radius ◽  
Force Displacement

The surface tension of compliant materials such as gels provides resistance to deformation in addition to and sometimes surpassing that owing to elasticity. This paper studies how surface tension changes the contact mechanics of a small hard sphere indenting a soft elastic substrate. Previous studies have examined the special case where the external load is zero, so contact is driven by adhesion alone. Here, we tackle the much more complicated problem where, in addition to adhesion, deformation is driven by an indentation force. We present an exact solution based on small strain theory. The relation between indentation force (displacement) and contact radius is found to depend on a single dimensionless parameter: ω = σ ( μR ) −2/3 ((9 π /4) W ad ) −1/3 , where σ and μ are the surface tension and shear modulus of the substrate, R is the sphere radius and W ad is the interfacial work of adhesion. Our theory reduces to the Johnson–Kendall–Roberts (JKR) theory and Young–Dupre equation in the limits of small and large ω , respectively, and compares well with existing experimental data. Our results show that, although surface tension can significantly affect the indentation force, the magnitude of the pull-off load in the partial wetting liquid-like limit is reduced only by one-third compared with the JKR limit and the pull-off behaviour is completely determined by ω .

A Refined JKR Model for Adhesion of a Rigid Sphere on a Soft Elastic Substrate

2019 ◽  
Vol 86 (5) ◽  
Author(s):  
Lei Zhang ◽  
C. Q. Ru
Keyword(s):  
Surface Energy ◽  
Contact Zone ◽  
Essential Role ◽  
Present Model ◽  
Recent Literature ◽  
Soft Materials ◽  
Detailed Comparison ◽  
Rigid Sphere ◽  
Elastic Substrate ◽  
Adhesion Mechanics

Surface energy outside the contact zone, which is ignored in the classical Johnson–Kendall–Roberts (JKR) model, can play an essential role in adhesion mechanics of soft bodies. In this work, based on a simple elastic foundation model for a soft elastic half space with constant surface tension, an explicit expression for the change of surface energy outside the contact zone is proposed for a soft elastic substrate indented by a rigid sphere in terms of two JKR-type variables (δ, a), where a is the radius of the contact zone and δ is the indentation depth of the rigid sphere. The derived expression is added to the classical JKR model to achieve two explicit equations for the determination of the two JKR variables (δ, a). The results given by the present model are demonstrated with detailed comparison with known results reported in recent literature, which verified the validity and robust accuracy of the present method. In particular, the present model confirms that the change of surface energy of the substrate can play an essential role in micro/nanoscale contact of soft materials (defined by W/(E*R)≥0.1, where W is the adhesive energy, E* is the substrate elasticity, and R is the rigid sphere radius). The present model offers a simpler analytical method for adhesion mechanics of a rigid sphere on a soft elastic substrate when compared with several existing methods proposed in recent literature that request more substantial numerical calculations.

scholarly journals Soft-lubrication interactions between a rigid sphere and an elastic wall

2021 ◽  
Vol 933 ◽  
Author(s):  
Vincent Bertin ◽  
Yacine Amarouchene ◽  
Elie Raphaël ◽  
Thomas Salez
Keyword(s):  
Stress Field ◽  
Viscous Fluid ◽  
Thin Layers ◽  
Reciprocal Theorem ◽  
Rigid Sphere ◽  
Hydrodynamic Stress ◽  
Soft Surface ◽  
Elastic Wall ◽  
Elastic Substrates ◽  
Small Deformations

The motion of an object within a viscous fluid and in the vicinity of a soft surface induces a hydrodynamic stress field that deforms the latter, thus modifying the boundary conditions of the flow. This results in elastohydrodynamic interactions experienced by the particle. Here, we derive a soft-lubrication model, in order to compute all the forces and torque applied on a rigid sphere that is free to translate and rotate near an elastic wall. We focus on the limit of small deformations of the surface with respect to the fluid-gap thickness, and perform a perturbation analysis in dimensionless compliance. The response is computed in the framework of linear elasticity, for planar elastic substrates in the limiting cases of thick and thin layers. The EHD forces are also obtained analytically using the Lorentz reciprocal theorem.

scholarly journals A minimal mechanosensing model predicts keratocyte evolution on flexible substrates

2020 ◽  
Vol 17 (166) ◽  
pp. 20200175
Author(s):  
Zhiwen Zhang ◽  
Phoebus Rosakis ◽  
Thomas Y. Hou ◽  
Guruswami Ravichandran
Keyword(s):  
Cell Shape ◽  
Travelling Waves ◽  
Leading Edge ◽  
Flexible Substrates ◽  
Shape Evolution ◽  
Mechanical Stimuli ◽  
Rigid Substrate ◽  
Elastic Substrate ◽  
Elastic Substrates ◽  
Contractile Forces

A mathematical model is proposed for shape evolution and locomotion of fish epidermal keratocytes on elastic substrates. The model is based on mechanosensing concepts: cells apply contractile forces onto the elastic substrate, while cell shape evolution depends locally on the substrate stress generated by themselves or external mechanical stimuli acting on the substrate. We use the level set method to study the behaviour of the model numerically, and predict a number of distinct phenomena observed in experiments, such as (i) symmetry breaking from the stationary centrosymmetric to the well-known steadily propagating crescent shape, (ii) asymmetric bipedal oscillations and travelling waves in the lamellipodium leading edge, (iii) response to remote mechanical stress externally applied to the substrate (tensotaxis) and (iv) changing direction of motion towards an interface with a rigid substrate (durotaxis).

METHOD FOR LUBRICATED SLIDING WEAR PARTICLE CHARACTERIZATION

2019 ◽  
Author(s):  
Alessandro Augusto Olimpio Ferreira Vittorino ◽  
Túlio Alves Rodrigues ◽  
Marco Aurélio Freitas Santos Júnior ◽  
Washington Martins da Silva Jr.
Keyword(s):  
Sliding Wear ◽  
Wear Particle ◽  
Particle Characterization ◽  
Lubricated Sliding

scholarly journals Design of 3D Additively Manufactured Hybrid Structures for Cranioplasty

Materials ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 181
Author(s):  
Roberto De Santis ◽  
Teresa Russo ◽  
Julietta V. Rau ◽  
Ida Papallo ◽  
Massimo Martorelli ◽  
...  
Keyword(s):  
Physical Models ◽  
Cranial Bone ◽  
Head Model ◽  
Rigid Sphere ◽  
Element Analysis ◽  
Aliphatic Polyesters ◽  
Hybrid Device ◽  
Wide Range ◽  
Hybrid Devices ◽  
Technical Solutions

A wide range of materials has been considered to repair cranial defects. In the field of cranioplasty, poly(methyl methacrylate) (PMMA)-based bone cements and modifications through the inclusion of copper doped tricalcium phosphate (Cu-TCP) particles have been already investigated. On the other hand, aliphatic polyesters such as poly(ε-caprolactone) (PCL) and polylactic acid (PLA) have been frequently investigated to make scaffolds for cranial bone regeneration. Accordingly, the aim of the current research was to design and fabricate customized hybrid devices for the repair of large cranial defects integrating the reverse engineering approach with additive manufacturing, The hybrid device consisted of a 3D additive manufactured polyester porous structures infiltrated with PMMA/Cu-TCP (97.5/2.5 w/w) bone cement. Temperature profiles were first evaluated for 3D hybrid devices (PCL/PMMA, PLA/PMMA, PCL/PMMA/Cu-TCP and PLA/PMMA/Cu-TCP). Peak temperatures recorded for hybrid PCL/PMMA and PCL/PMMA/Cu-TCP were significantly lower than those found for the PLA-based ones. Virtual and physical models of customized devices for large cranial defect were developed to assess the feasibility of the proposed technical solutions. A theoretical analysis was preliminarily performed on the entire head model trying to simulate severe impact conditions for people with the customized hybrid device (PCL/PMMA/Cu-TCP) (i.e., a rigid sphere impacting the implant region of the head). Results from finite element analysis (FEA) provided information on the different components of the model.

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