Adhesive Contacts for Graded-Elastic Coatings Using Fourier Series Decomposition

2011 ◽  
Author(s):  
S. J. Chidlow ◽  
W. W. F. Chong ◽  
M. Teodorescu ◽  
N. D. Vaughan
Keyword(s):  
Fourier Series ◽  
Analytic Solution ◽  
Adhesive Contact ◽  
Solution Technique ◽  
Control Case ◽  
Principal Stresses ◽  
Pressure Distributions ◽  
Surface Deflection ◽  
Elastic Layers ◽  
Adhesive Contacts

We propose a semi-analytic solution technique to determine the subsurface stresses and local deflections resulting in an adhesive contact of graded elastic layers. Identical pressure distributions, typical for a Maugis parameter λ = 1, were applied to a range of graded elastic coatings. The principal stresses and surface deflection in both regions (graded elastic layer and substrate) are computed in terms of Fourier series. This control case has the advantage that the response of different coatings can be easily monitored and compared.

scholarly journals Manufactured solutions and the verification of three-dimensional Stokes ice-sheet models

2013 ◽  
Vol 7 (1) ◽  
pp. 19-29 ◽  
Author(s):  
W. Leng ◽  
L. Ju ◽  
M. Gunzburger ◽  
S. Price
Keyword(s):  
Computational Models ◽  
Analytic Solution ◽  
Initial Conditions ◽  
Model Simulation ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Solution Technique ◽  
Order Partial Differential Equation ◽  
Manufactured Solutions ◽  
Manufactured Solution

Abstract. The manufactured solution technique is used for the verification of computational models in many fields. In this paper, we construct manufactured solutions for the three-dimensional, isothermal, nonlinear Stokes model for flows in glaciers and ice sheets. The solution construction procedure starts with kinematic boundary conditions and is mainly based on the solution of a first-order partial differential equation for the ice velocity that satisfies the incompressibility condition. The manufactured solutions depend on the geometry of the ice sheet, basal sliding parameters, and ice softness. Initial conditions are taken from the periodic geometry of a standard problem of the ISMIP-HOM benchmark tests. The upper surface is altered through the manufactured solution procedure to generate an analytic solution for the time-dependent flow problem. We then use this manufactured solution to verify a parallel, high-order accurate, finite element Stokes ice-sheet model. Simulation results from the computational model show good convergence to the manufactured analytic solution.

Contact Stress State in Elastic Layers

2009 ◽  
Author(s):  
Sergiu Spinu ◽  
Emanuel Diaconescu
Keyword(s):  
Stress State ◽  
Quadratic Form ◽  
Elastic Layer ◽  
Numerical Approach ◽  
Pressure Distributions ◽  
Influence Coefficients ◽  
Discrete Counterpart ◽  
Layer Contact ◽  
Elastic Layers ◽  
Continuous Formulation

This paper presents the discrete counterpart of an existing continuous formulation for an elastic layer loaded symmetrically. The influence coefficients based numerical approach allows for computing contact stresses induced in the elastic layer by arbitrary shaped indenters. The newly developed code is validated against existing pressure distributions in layer contact for quadratic form punches.

scholarly journals Cortactin is necessary for E-cadherin–mediated contact formation and actin reorganization

2004 ◽  
Vol 164 (6) ◽  
pp. 899-910 ◽  
Author(s):  
Falak M. Helwani ◽  
Eva M. Kovacs ◽  
Andrew D. Paterson ◽  
Suzie Verma ◽  
Radiya G. Ali ◽  
...  
Keyword(s):  
Contact Zone ◽  
Adhesive Contact ◽  
Actin Dynamics ◽  
Contact Formation ◽  
Biochemical Interaction ◽  
Embryonic Life ◽  
Generating Capacity ◽  
Mediated Contact ◽  
Adhesive Contacts ◽  
Cell Cell

Classical cadherin adhesion molecules are key determinants of cell–cell recognition during development and in post-embryonic life. A decisive step in productive cadherin-based recognition is the conversion of nascent adhesions into stable zones of contact. It is increasingly clear that such contact zone extension entails active cooperation between cadherin adhesion and the force-generating capacity of the actin cytoskeleton. Cortactin has recently emerged as an important regulator of actin dynamics in several forms of cell motility. We now report that cortactin is recruited to cell–cell adhesive contacts in response to homophilic cadherin ligation. Notably, cortactin accumulates preferentially, with Arp2/3, at cell margins where adhesive contacts are being extended. Recruitment of cortactin is accompanied by a ligation-dependent biochemical interaction between cortactin and the cadherin adhesive complex. Inhibition of cortactin activity in cells blocked Arp2/3-dependent actin assembly at cadherin adhesive contacts, significantly reduced cadherin adhesive contact zone extension, and perturbed both cell morphology and junctional accumulation of cadherins in polarized epithelia. Together, our findings identify a necessary role for cortactin in the cadherin–actin cooperation that supports productive contact formation.

scholarly journals Boundary element method for nonadhesive and adhesive contacts of a coated elastic half-space

2019 ◽  
Vol 234 (1) ◽  
pp. 73-83 ◽  
Author(s):  
Qiang Li ◽  
Roman Pohrt ◽  
Iakov A Lyashenko ◽  
Valentin L Popov
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Half Space ◽  
Adhesive Contact ◽  
Elastic Half Space ◽  
Fourier Space ◽  
Numerical Tests ◽  
New Formulation ◽  
Adhesive Contacts ◽  
Element Method

We present a new formulation of the boundary element method for simulating the nonadhesive and adhesive contact between an indenter of arbitrary shape and an elastic half-space coated with an elastic layer of different material. We use the Fast Fourier Transform-based formulation of boundary element method, while the fundamental solution is determined directly in the Fourier space. Numerical tests are validated by comparison with available asymptotic analytical solutions for axisymmetric flat and spherical indenter shapes.

A Surface Vorticity Theory for Propeller Ducts and Turbofan Engine Cowls in Non-Axisymmetric Incompressible Flow

1978 ◽  
Vol 20 (4) ◽  
pp. 201-219 ◽  
Author(s):  
V. P. Hill
Keyword(s):  
Mathematical Model ◽  
Fourier Series ◽  
Axisymmetric Flow ◽  
Three Dimensional ◽  
Axisymmetric Body ◽  
Fredholm Integral Equations ◽  
Three Dimensional Flow ◽  
Turbofan Engine ◽  
Pressure Distributions ◽  
Theoretical Pressure

Starting from the basic Fredholm integral equations, a surface vorticity theory is developed for the prediction of annular aerofoil performance in three-dimensional flow. A mathematical model is proposed for the general case of the axisymmetric body in non-axisymmetric flow, using a Fourier series to represent circumferential variations in bound vorticity strength. Using the pure incidence case as an example, it is indicated how an economical solution of the flow may be arrived at by use of a digital computer. The theoretical pressure distributions obtained are compared with the results of wind-tunnel tests on an annular aerofoil model.

scholarly journals Influence of Tangential Displacement on the Adhesion Force between Gradient Materials

2020 ◽  
Vol 65 (3) ◽  
pp. 205
Author(s):  
I. A. Lyashenko ◽  
Z. M. Liashenko
Keyword(s):  
Normal Force ◽  
Adhesion Force ◽  
Tangential Force ◽  
Adhesive Contact ◽  
Critical Force ◽  
Tangential Displacement ◽  
Optimal Parameters ◽  
Gradient Materials ◽  
Force Components ◽  
Adhesive Contacts

The influence of a tangential displacement on the strength of the adhesive contacts between gradient materials with different gradings of their properties has been studied. Variants with a controlled force (fixed load) and a controlled displacement (fixed grips) are considered. A relationship between the normal and tangential critical force components at which the contact is destroyed is obtained. It is valid within the whole interval of the gradient parameters, where the detachment criterium is obeyed. The optimal parameters at which the adhesive contact strength is maximum are determined. A case of detachment under the action of only the tangential force, i.e. when the normal force equals zero, is analyzed separately.

scholarly journals A JKR-Like Solution for Viscoelastic Adhesive Contacts

2021 ◽  
Vol 7 ◽  
Author(s):  
Guido Violano ◽  
Antoine Chateauminois ◽  
Luciano Afferrante
Keyword(s):  
Closed Form ◽  
Numerical Models ◽  
Closed Form Solution ◽  
Numerical Data ◽  
Adhesive Contact ◽  
Form Solution ◽  
Contact Radius ◽  
Rigid Sphere ◽  
Soft Spheres ◽  
Adhesive Contacts

A closed-form solution for the adhesive contact of soft spheres of linear elastic material is available since 1971 thanks to the work of Johnson, Kendall, and Roberts (JKR). A similar solution for viscoelastic spheres is still missing, though semi-analytical and numerical models are available today. In this note, we propose a closed-form analytical solution, based on JKR theory, for the detachment of a rigid sphere from a viscoelastic substrate. The solution returns the applied load and contact penetration as functions of the contact radius and correctly captures the velocity-dependent nature of the viscoelastic pull-off. Moreover, a simple approach is provided to estimate the stick time, i.e., the delay between the time the sphere starts raising from the substrate and the time the contact radius starts reducing. A simple formula is also suggested for the viscoelastic pull-off force. Finally, a comparison with experimental and numerical data is shown.

Semi-Analytic Iterative Solution for the Adhesive Contact Between a Micro-Indenter and a Graded Elasticity Coating

2014 ◽  
Author(s):  
Stewart J. Chidlow ◽  
William W. F. Chong ◽  
Mircea Teodorescu
Keyword(s):  
Stress Field ◽  
Analytic Solution ◽  
Superposition Principle ◽  
Elastic Solid ◽  
Iterative Solution ◽  
Normal Pressure ◽  
Adhesive Contact ◽  
Collocation Methods ◽  
Subsurface Stress ◽  
The Fourier Transform

This paper proposes a hybrid (semi-analytic) solution for determining the contact footprint and subsurface stress field in a two-dimensional adhesive problem involving a multi-layered elastic solid loaded normally by a rigid indenter. The subsurface stress field is determined using a semi-analytic solution and the footprint using a fast converging iterative algorithm. The solid to be indented consists of a graded elasticity coating with exponential increase of decay of its shear modulus bonded on a homogeneously elastic substrate. By applying the Fourier Transform to the governing boundary value problem, we formulate expressions for the stresses and displacements induced by the application of line forces acting both normally and tangentially at the origin. The superposition principle is then used to generalize these expressions to the case of distributed normal pressure acting on the solid surface. A pair of coupled integral equations are further derived for the parabolic stamp problem which are easily solved using collocation methods.

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