scholarly journals Effect of surface bending and stress on the transmission of line force to an elastic substrate

2018 ◽  
Vol 474 (2215) ◽  
pp. 20170775 ◽  
Author(s):  
Chung Yuen Hui ◽  
Zezhou Liu ◽  
Anand Jagota
Keyword(s):  
Elastic Modulus ◽  
Surface Stress ◽  
Broad Class ◽  
Local Stress ◽  
Soft Materials ◽  
Elastic Substrate ◽  
Capillary Length ◽  
Singular Stress ◽  
Line Load ◽  
Line Force

For a broad class of soft materials their surface stress can strongly influence mechanical behaviour. For example, a line force applied to the surface of an elastic substrate is locally supported by surface stress over an elasto-capillary length l c (surface stress/elastic modulus). Surface stress regularizes the otherwise highly singular stress and strain fields. However, surface such as lipid bilayer interfaces can also resist deformation by bending. This has not been studied either by experiments or theories. We analyse a theoretical model of the response of a half-space to a line force when the surface carries both a stress and resistance to bending. We find that surface bending further regularizes the singular fields. The local stress field near the line load can be separated into three regions. Region 1 occupies distances from the line load smaller than an elasto-capillary bending length l b (bending stiffness/elastic modulus to the 1/3 power) where surface bending dominates and the elastic stress and strains are continuous. Region 2 occupies intermediate distances between l b and l c   ( > l b ) where surface stress dominates. At distances larger than l c we retrieve the classical elasticity solution. The size of region 2 depends on κ = l c / l b and vanishes for small l c .

scholarly journals Coupled flow and deformation fields due to a line load on a poroelastic half space: effect of surface stress and surface bending

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190761 ◽  
Author(s):  
Zezhou Liu ◽  
Nikolaos Bouklas ◽  
Chung-Yuen Hui
Keyword(s):  
Half Space ◽  
Surface Stress ◽  
Polymer Network ◽  
Elastic Solid ◽  
Coupled Flow ◽  
Line Load ◽  
Small Surface ◽  
Surface Stresses ◽  
Line Force ◽  
Solvent Flow

In the past decade, many experiments have indicated that the surfaces of soft elastic solids can resist deformation by surface stresses. A common soft elastic solid is a hydrogel which consists of a polymer network swollen in water. Although experiments suggest that solvent flow in gels can be affected by surface stress, there is no theoretical analysis on this subject. Here we study the solvent flow near a line load acting on a linear poroelastic half space. The surface of this half space resists deformation by a constant, isotropic surface stress. It can also resist deformation by surface bending. The time-dependent displacement, stress and flow fields are determined using transform methods. Our solution indicates that the stress field underneath the line load is completely regularized by surface bending—it is bounded and continuous. For small surface bending stiffness, the line force is balanced by surface stresses; these forces form what is commonly known as ‘Neumann's triangle’. We show that surface stress reduces local pore pressure and inhibits solvent flow. We use our line load solution to simulate the relaxation of the peak which is formed by applying and then removing a line force on the poroelastic half space.

New methods of analyzing indentation experiments on very thin films

2010 ◽  
Vol 25 (4) ◽  
pp. 728-734 ◽  
Author(s):  
Han Li ◽  
Nicholas X. Randall ◽  
Joost J. Vlassak
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Elastic Modulus ◽  
Rigorous Solution ◽  
Elastic Substrate ◽  
Substrate Effects ◽  
New Methods ◽  
Elastic Mismatch

Indentation experiments on thin films are analyzed by using a rigorous solution to model elastic substrate effects. Two cases are discussed: elastic indentations where film and substrate are anisotropic and elastoplastic indentations where significant material pileup occurs. We demonstrate that the elastic modulus of a thin film can be accurately measured in both cases, even if there is significant elastic mismatch between film and substrate.

Elastohydrodynamic Lubrication Line Contact Based on Surface Elasticity Theory

2020 ◽  
Vol 87 (8) ◽  
Author(s):  
Jie Su ◽  
Hong-Xia Song ◽  
Liao-Liang Ke
Keyword(s):  
Elastic Modulus ◽  
Film Thickness ◽  
Elasticity Theory ◽  
Surface Stress ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Fluid Pressure ◽  
Elastohydrodynamic Lubrication ◽  
Line Contact ◽  
Residual Surface Stress

Abstract Using surface elasticity theory, this article first analyzes the surface effect on the elastohydrodynamic lubrication (EHL) line contact between an elastic half-plane and a rigid cylindrical punch. In this theory, the surface effect is characterized with two parameters: surface elastic modulus and residual surface stress. The density and viscosity of the lubricant, considered as Newtonian fluid, vary with the fluid pressure. A numerical iterative method is proposed to simultaneously deal with the flow rheology equation, Reynolds equation, load balance equation, and film thickness equation. Then, the fluid pressure and film thickness are numerically determined at the lubricant contact region. Influences of surface elastic modulus, residual surface stress, punch radius, resultant normal load, and entraining velocity on the lubricant film thickness and fluid pressure are discussed. It is found that the surface effect has remarkable influences on the micro-/nano-scale EHL contact of elastic materials.

Evolution of Tenacity in Mixed Mode Fracture – Volumetric Approach

2020 ◽  
Vol 22 (4) ◽  
pp. 931-938
Author(s):  
O. Zebri ◽  
H. El Minor ◽  
A. Bendarma
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Intensity Factors ◽  
Mixed Mode ◽  
Local Stress ◽  
Critical Stress Intensity Factor ◽  
Mixed Mode Fracture ◽  
Intensity Factors ◽  
Singular Stress

AbstractIn fracture mechanics most interest is focused on stress intensity factors, which describe the singular stress field ahead of a crack tip and govern fracture of a specimen when a critical stress intensity factor is reached. In this paper, stress intensity factors which represents fracture toughness of material, caused by a notch in a volumetric approach has been examined, taking into account the specific conditions of loading by examining various U-notched circular ring specimens, with various geometries and boundary conditions, under a mixed mode I+II. The bend specimens are computed by finite element method (FEM) and the local stress distribution was calculated by the Abaqus/CAE. The results are assessed to determine the evolution of the stress intensity factor of different notches and loading distances from the root of notch. This study shows that the tenacity is not intrinsic to the material for all different geometries notches.

A Parametric Investigation of Surface Initiated Rolling Contact Fatigue Using the Asperity Point Load Mechanism

2013 ◽  
Vol 577-578 ◽  
pp. 45-48
Author(s):  
Dave Hannes ◽  
B. Alfredsson
Keyword(s):  
Surface Roughness ◽  
Fatigue Life ◽  
Surface Stress ◽  
Crack Path ◽  
Rolling Contact Fatigue ◽  
Contact Fatigue ◽  
Local Stress ◽  
Point Load ◽  
Rolling Contact ◽  
Residual Surface Stress

Rolling contact fatigue (RCF) will eventually become an issue for machine elementsthat are repeatedly over-rolled with high contact loads and small relative sliding motion. Thedamage consists of cracks and craters in the contact surfaces. Asperities on the contact surfacesact as local stress raisers and provide tensile surface stresses which can explain both initiationand propagation of surface initiated RCF damage. A parametric study was performed to inves-tigate the contribution of surface roughness, friction and a residual surface stress to the RCFdamage process. The effects on initiation, crack path and fatigue life at both early and devel-oped damage were examined for a gear application. Both a one-parameter-at-a-time approachand a 2-level full factorial design were carried out. Surface roughness and local friction prop-erties were found to control crack initiation, whereas the simulated crack path was primarilyaffected by the residual surface stress, especially for developed damage. Reduced surface rough-ness, improved lubrication and a compressive residual surface stress all contributed to increasethe simulated fatigue life. The asperity point load model could predict effects on RCF that areobserved with experiments. The results further support the asperity point load mechanism asthe source behind surface initiated RCF.

scholarly journals The Green's Function BEM for Bimaterial Solids Applied to Edge Stress Concentration Problems

2007 ◽  
Vol 1 (2) ◽  
Author(s):  
M. Denda
Keyword(s):  
Stress Concentration ◽  
Green’S Function ◽  
Green's Function ◽  
Free Edge ◽  
Fundamental Solutions ◽  
Singular Stress ◽  
Thin Coatings ◽  
Edge Stress ◽  
Line Force ◽  
Isotropic Solids

A boundary element method (BEM) for bimaterial domains consisting of two isotropic solids bonded perfectly along the straight interface will be developed. We follow the physical interpretation of Somigliana’s identity to represent the displacement in the bimaterial domain by the continuous distributions of the line forces and dislocation dipoles over its boundary. The fundamental solutions used are the Green’s functions for the line force and the dislocation dipole that satisfy the traction and displacement continuity across the interface of two domains. There is no need to model the interface because the required continuity conditions there are automatically satisfied by the Green’s functions. The BEM will be applied to study the edge stress concentration of the bimaterial solids. We calculate the singular stress distribution at the free edge of the interface for various bimaterial configurations and loadings, in particular, for the domain consisting of thin coating over the substratum. Since the Green's function BEM does not require the boundary elements on the interface, it can handle the edge singularity on the interface accurately even for extremely thin coatings. The BEM developed here is not limited to the edge stress concentration problems and can be applied to a broad range of the bimaterial domain problems effectively.

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