Determining the Sub-Surface Stresses in a Graded-Elastic Solid Using Fourier Series Decomposition

2011 ◽  
Author(s):  
Stewart Chidlow ◽  
Mircea Teodorescu ◽  
Nick Vaughan
Keyword(s):  
Fourier Series ◽  
Shear Modulus ◽  
Solution Method ◽  
Analytic Solution ◽  
Elastic Solid ◽  
Local Deformation ◽  
Elastic Substrate ◽  
Micro Scale ◽  
Surface Stresses ◽  
Layered Solid

This paper describes a fully analytic solution method for the displacements and sub-surface stresses within a graded elastic layered solid. This method can be utilised to predict the local deformation of nano or micro-scale depositions under contacting conditions. The solid consists of two distinct layers which are considered to be perfectly bonded and comprise of a graded elastic coating whose shear modulus varies exponentially with the depth coordinate and an infinitely deep homogeneously elastic substrate. The solution given in this paper is generic and easily utilised to solve real problems as it requires only known physical characteristics of the solid under study and an applied surface pressure. As a result, this model is very cheap to use and can be easily integrated into tribological codes to predict local deflections.

A New Solution Method for the Contact Mechanics of Graded Coatings

2010 ◽  
Author(s):  
S. J. Chidlow ◽  
M. Teodorescu ◽  
N. D. Vaughan
Keyword(s):  
Fourier Transform ◽  
Fourier Series ◽  
Stress Function ◽  
Solution Method ◽  
Inverse Fourier Transform ◽  
Elastic Solid ◽  
Airy Stress Function ◽  
Graded Coatings ◽  
Contour Plots ◽  
Selection Of

This paper attempts to solve analytically for the stresses present in a graded elastic solid resulting from pressure applied to its surface by computing the Airy stress function. The horizontal dimensions of the solid are assumed finite and hence we form the solution of the stress function as a Fourier series rather than an inverse Fourier transform. Finally, a selection of contour plots is presented to exhibit the behavior of this new model.

Plane Deformations of an Inhomogeneity–Matrix System Incorporating a Compressible Liquid Inhomogeneity and Complete Gurtin–Murdoch Interface Model

2018 ◽  
Vol 85 (12) ◽  
Author(s):  
Ming Dai ◽  
Min Li ◽  
Peter Schiavone
Keyword(s):  
Analytic Solution ◽  
Elastic Solid ◽  
Compressible Liquid ◽  
External Loading ◽  
Interface Model ◽  
Interface Tension ◽  
Soft Solids ◽  
Remote Loading ◽  
Interface Elasticity ◽  
Plane Deformations

We consider the plane deformations of an infinite elastic solid containing an arbitrarily shaped compressible liquid inhomogeneity in the presence of uniform remote in-plane loading. The effects of residual interface tension and interface elasticity are incorporated into the model of deformation via the complete Gurtin–Murdoch (G–M) interface model. The corresponding boundary value problem is reformulated and analyzed in the complex plane. A concise analytical solution describing the entire stress field in the surrounding solid is found in the particular case involving a circular inhomogeneity. Numerical examples are presented to illustrate the analytic solution when the uniform remote loading takes the form of a uniaxial compression. It is shown that using the simplified G–M interface model instead of the complete version may lead to significant errors in predicting the external loading-induced stress concentration in gel-like soft solids containing submicro- (or smaller) liquid inhomogeneities.

The Elastic Coefficients of the Theory of Consolidation

1957 ◽  
Vol 24 (4) ◽  
pp. 594-601
Author(s):  
M. A. Biot ◽  
D. G. Willis
Keyword(s):  
Nonlinear Systems ◽  
Shear Modulus ◽  
Physical Interpretation ◽  
Compressible Fluid ◽  
Elastic Solid ◽  
Fluid Content ◽  
Alternate Forms ◽  
Elastic Coefficients ◽  
Methods Of Measurement

Abstract The theory of the deformation of a porous elastic solid containing a compressible fluid has been established by Biot. In this paper, methods of measurement are described for the determination of the elastic coefficients of the theory. The physical interpretation of the coefficients in various alternate forms is also discussed. Any combination of measurements which is sufficient to fix the properties of the system may be used to determine the coefficients. For an isotropic system, in which there are four coefficients, the four measurements of shear modulus, jacketed and unjacketed compressibility, and coefficient of fluid content, together with a measurement of porosity appear to be the most convenient. The porosity is not required if the variables and coefficients are expressed in the proper way. The coefficient of fluid content is a measure of the volume of fluid entering the pores of a solid sample during an unjacketed compressibility test. The stress-strain relations may be expressed in terms of the stresses and strains produced during the various measurements, to give four expressions relating the measured coefficients to the original coefficients of the consolidation theory. The same method is easily extended to cases of anisotropy. The theory is directly applicable to linear systems but also may be applied to incremental variations in nonlinear systems provided the stresses are defined properly.

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 Diffraction of Elastic Waves in Fluid-Layered Solid Interfaces by an Integral Formulation

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
J. E. Basaldúa-Sánchez ◽  
D. Samayoa-Ochoa ◽  
J. E. Rodríguez-Sánchez ◽  
A. Rodríguez-Castellanos ◽  
M. Carbajal-Romero
Keyword(s):  
Elastic Waves ◽  
Single Layer ◽  
Elastic Solid ◽  
Boundary Integral ◽  
Wave Number ◽  
Intermediate Step ◽  
Solid Models ◽  
Time Domains ◽  
Scattering Of Elastic Waves ◽  
Layered Solid

In the present communication, scattering of elastic waves in fluid-layered solid interfaces is studied. The indirect boundary element method is used to deal with this wave propagation phenomenon in 2D fluid-layered solid models. The source is represented by Hankel’s function of second kind and this is always applied in the fluid. Our method is an approximate boundary integral technique which is based upon an integral representation for scattered elastic waves using single-layer boundary sources. This approach is typically called indirect because the sources’ strengths are calculated as an intermediate step. In addition, this formulation is regarded as a realization of Huygens’ principle. The results are presented in frequency and time domains. Various aspects related to the different wave types that emerge from this kind of problems are emphasized. A near interface pulse generates changes in the pressure field and can be registered by receivers located in the fluid. In order to show the accuracy of our method, we validated the results with those obtained by the discrete wave number applied to a fluid-solid interface joining two half-spaces, one fluid and the other an elastic solid.

Surface waves in homogenous visco-elastic media of higher order under the influence of surface stresses

2013 ◽  
Vol 22 (5-6) ◽  
pp. 185-191 ◽  
Author(s):  
Munish Sethi ◽  
K.C. Gupta ◽  
Monika Rani ◽  
A. Vasudeva
Keyword(s):  
Surface Waves ◽  
Solid Medium ◽  
Elastic Solid ◽  
Higher Order ◽  
Love Waves ◽  
Elastic Media ◽  
Time Rate ◽  
Surface Stresses ◽  
Rayleigh And Love Waves

AbstractThe aim of the present paper is to investigate the surface waves in a homogeneous, isotropic, visco-elastic solid medium of nth order, including time rate of strain under the influence of surface stresses. The theory of generalized surface waves is developed to investigate particular cases of waves such as the Stoneley, Rayleigh, and Love waves. Corresponding equations have been obtained for different cases. These are reduced to classical results, when the effects of surface stresses and viscosity are ignored.

A Fast-Solving Semi-Analytical Solution Method for Contact Problems Involving Multi-Layered Inhomogeneously Elastic Solids

2012 ◽  
Author(s):  
Stewart Chidlow ◽  
Mircea Teodorescu
Keyword(s):  
Analytical Solution ◽  
Contact Pressure ◽  
Solution Method ◽  
Elastic Solid ◽  
Contact Problems ◽  
Accurate Estimation ◽  
Rigid Punch ◽  
Iterative Solver ◽  
Elastic Solids ◽  
Selection Of

This work is concerned with the derivation of an iterative solver which allows the accurate estimation of both the contact half-width and contact pressure when an inhomogeneouly elastic solid comprising a homogeneous coating and substrate joined by a graded layer is indented by a rigid punch. A selection of numerical results are then presented illustrating the accuracy of this model.

Comparison of the shear modulus of mature and immature rabbit lungs

1999 ◽  
Vol 87 (2) ◽  
pp. 711-714 ◽  
Author(s):  
Robert S. Tepper ◽  
Barry Wiggs ◽  
Susan J. Gunst ◽  
Peter D. Paré
Keyword(s):  
Shear Modulus ◽  
Bulk Modulus ◽  
Transpulmonary Pressure ◽  
Lung Parenchyma ◽  
Local Deformation ◽  
Mean Value ◽  
Airway Narrowing ◽  
Significant Difference ◽  
Muscle Shortening ◽  
Immature Lung

Maximal airway narrowing during bronchoconstriction is greater in immature than in mature rabbits. At a given transpulmonary pressure (Pl), the lung parenchyma surrounding the airway resists local deformation and provides a load that opposes airway smooth muscle shortening. We hypothesized that the force required to produce lung parenchymal deformation, quantified by the shear modulus, is lower in immature rabbit lungs. The shear modulus and the bulk modulus were measured in isolated mature ( n = 8; 6 mo) and immature ( n = 9; 3 wk) rabbit lungs at Pl of 2, 4, 6, 8, and 10 cmH2O. The bulk modulus increased with increasing Pl for mature and immature lungs; however, there was no significant difference between the groups. The shear modulus was lower for the immature than the mature lungs ( P < 0.025), progressively increasing with increasing Pl( P < 0.001) for both groups, and there was no difference between the slopes for shear modulus vs. Pl for the mature and the immature lungs. The mean value of the shear modulus for mature and immature rabbit lungs at Pl = 6 cmH2O was 4.5 vs. 3.8 cmH2O. We conclude that the shear modulus is less in immature than mature rabbit lungs. This small maturational difference in the shear modulus probably does not account for the greater airway narrowing in the immature lung, unless its effect is coupled with a relatively thicker and more compliant airway wall in the immature animal.

Research on Analytic Calculation Method of the Dynamic Response of Buried Pipelines under Indirect Ground Shock

2013 ◽  
Vol 477-478 ◽  
pp. 77-80 ◽  
Author(s):  
Guo Fu Xu ◽  
Zheng Dong Deng ◽  
Chong Ji ◽  
Jing Jing Jia
Keyword(s):  
Solution Method ◽  
Static Load ◽  
Analytic Solution ◽  
Engineering Application ◽  
Buried Pipeline ◽  
Buried Pipelines ◽  
Equivalent Static Load ◽  
Conventional Weapons ◽  
Ground Shock ◽  
Dynamic Damage

Buried pipelines are important lifeline engineering. During war conventional weapons blasting in the air would induce indirect ground shock, and the shock to the buried pipeline can lead to the paralyzed of urban economic and social function. And the numerical simulation of the dynamic damage of buried pipeline is complicated and time consuming, so this article using the equivalent static load method proposes analytic solution method of stress calculation of buried pipeline under ground shock. Through comparing the results calculated by analytic solution method and numerical solution, it shows that the analytical solution is feasible in engineering application.

Sign in / Sign up

Export Citation Format

Share Document