scholarly journals A Loaded beam in full frictionless contact with a couple stress elastic half-plane: effects of non-standard contact conditions

2021 ◽  
pp. 111175
Author(s):  
E. Radi
Keyword(s):  
Half Plane ◽  
Couple Stress ◽  
Contact Conditions ◽  
Frictionless Contact ◽  
Standard Contact

Two-Dimensional Frictionless Contact of a Coated Half-Plane Based on Couple Stress Theory

2018 ◽  
Vol 10 (05) ◽  
pp. 1850049 ◽  
Author(s):  
Hongxiaia Song ◽  
Liaoliang Ke ◽  
Yuesheng Wang ◽  
Jie Yang ◽  
Han Jiang
Keyword(s):  
Contact Problem ◽  
Half Plane ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Strong Dependence ◽  
Stress Theory ◽  
Frictionless Contact ◽  
Size Dependent ◽  
Contact Width ◽  
Material Length

Based on the couple stress theory, the size-dependent frictionless contact problem between a rigid punch and a homogeneous coated half-plane is investigated in this paper. This theory describes the size effect that emerges from the material microstructures by introducing the characteristic material length. With the aid of the Fourier transform method, the size-dependent contact problem of the rigid flat, cylindrical, parabolic and wedge punches is reduced to a Cauchy singular integral equation of the first kind. Subsequently, it is transformed into algebraic ones and solved numerically by using Gauss–Chebyshev integration formulas. Numerical results for the normal and in-plane contact stresses, contact width and indentation depth are given. The effect of the length scale parameters on the contact stress and indentation is predicted by the couple stress elasticity, which shows a strong dependence on the characteristic material length.

Frictionless Contact on Elastic Half Plane with Influence of Surface and Couple Stresses

2020 ◽  
Vol 897 ◽  
pp. 73-77
Author(s):  
Toan Minh Le ◽  
Tinh Quoc Bui ◽  
Jintara Lawongkerd ◽  
Suchart Limkatanyu ◽  
Jaroon Rungamornrat
Keyword(s):  
Contact Pressure ◽  
Half Plane ◽  
Numerical Study ◽  
Surface Elasticity ◽  
Fundamental Solutions ◽  
Internal Length ◽  
Frictionless Contact ◽  
Couple Stresses ◽  
Linear Elastic ◽  
Contact Width

In this paper, a frictionless contact of a rigid flat-ended indentor on a linear elastic half plane is investigated by taking the influence of surface and couple stresses into account. The surface elasticity and couple stress theories are utilized to form a mathematical model. The Green’s function method together with the equilibrium condition of the indentor is employed to formulate the key equations governing the contact pressure. A collocation technique and a set of available fundamental solutions of a half plane under the surface loading are adopted to determine the unknown contact pressure. Results from a numerical study reveal that the presence of both surface and couple stresses significantly alters the distribution of the contact pressure from that predicted by the classical linear elasticity, and the size-dependent characteristics of predicted solutions are obviously observed when the contact width is comparable to the internal length scales of the surface and bulk materials.

Multiply Loaded Rigid Punch on a Stressed Orthotopic Half-Plane via a Thin Elastic Layer

1992 ◽  
Vol 59 (2S) ◽  
pp. S115-S122 ◽  
Author(s):  
Hans L. Bjarnehed
Keyword(s):  
Half Plane ◽  
Elastic Layer ◽  
Singular Integral Equations ◽  
Free Edge ◽  
Shear Stresses ◽  
Rigid Punch ◽  
Fem Model ◽  
Frictionless Contact ◽  
Thin Elastic Layer ◽  
Elastic Cushion

A uniaxially stressed orthotropic half-plane indented on the free edge by a multiply loaded rigid punch via a thin elastic layer is considered. The layer is formulated as a generalized Winkler cushion including also shear stresses and strains. Governing singular integral equations are stated for the unknown interface stresses between the cushion and the half-plane. Two kinds of friction conditions between the cushion and half-plane are treated, viz. completely adhesive and frictionless contact. An analytical solution for contact with a rigid cushion and a numerical solution with an elastic cushion are presented. Also, a comparison with a corresponding FEM model is performed. For frictionless contact, some analytical results concerning optimum design of the elastic cushion are given.

The Strength of Some Non-Hertzian Plane Contacts

1986 ◽  
Vol 108 (4) ◽  
pp. 655-658 ◽  
Author(s):  
A. Sackfield ◽  
D. A. Hills
Keyword(s):  
Stress Field ◽  
Half Plane ◽  
Chebyshev Polynomials ◽  
Sliding Contact ◽  
Elastic Contact ◽  
Contact Conditions ◽  
Large Load ◽  
Practical Implications

The problem of plane elastic contact between a symmetrical indentor and a half-plane is addressed. The form of the contacting profile of the indentor is represented in terms of Chebyshev polynomials, and the resulting stress-field is deduced, for both static and sliding contact. It is shown that by making the profile somewhat flatter than a cylinder a large load may be sustained without yielding. Practical implications of the result, including profiles needed to attain optimal contact conditions, are discussed.

scholarly journals Large deformation contact mechanics of long rectangular membranes. I. Adhesionless contact

2013 ◽  
Vol 469 (2160) ◽  
pp. 20130424 ◽  
Author(s):  
Abhishek Srivastava ◽  
Chung-Yuen Hui
Keyword(s):  
Finite Strain ◽  
Large Deformations ◽  
Contact Region ◽  
Elastic Membrane ◽  
Maximum Pressure ◽  
Rigid Substrate ◽  
Contact Conditions ◽  
Frictionless Contact ◽  
Closed Form Solutions ◽  
Finite Strain Theory

In part I of this work, we study adhesionless contact of a long rectangular elastic membrane with a rigid substrate. Our model is based on finite strain theory and is valid for arbitrarily large deformations. Both frictionless and no-slip contact conditions are considered. Exact closed form solutions are obtained for frictionless contact. For small contact, the differences between these two contact conditions are small. However, significant differences occur for large contacts. For example, frictionless contact predicts a maximum pressure (and contact region) beyond which there is no solution; while the no-slip model places no restriction on both quantities. The effect of adhesion will be considered in part II of this work.

scholarly journals Dispersion of generalized Rayleigh waves in the half-plane covered with pre-stretched two layers under complete contact

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 247-253
Author(s):  
Muslum Ozisik
Keyword(s):  
Wave Propagation ◽  
Rayleigh Wave ◽  
Half Plane ◽  
Single Layer ◽  
Theory Of Elasticity ◽  
Phase Zone ◽  
Contact Conditions ◽  
Linearized Theory Of Elasticity ◽  
Linearized Theory ◽  
Complete Contact

In this paper the dispersion of the generalized Rayleigh wave propagation in the non-prestressed half-plane covered with pre-stretched two layers under complete contact conditions is investigated by 3-D linearized theory of elasticity. The layers and the half-plane are assumed that elastic, homogeneous, isotropic, and the complete contact conditions are existed. The inter phase zone between the upper layer and half-plane is modeled by this second layer. The purpose of the investigation is the determination on the effect of the existence of the second layer to the considered generalized Rayleigh wave propagation velocity. For this purpose, firstly the same materials were selected for both layers and the results obtained in previous studies for a single layer in the literature were verified, the accuracy of the modeling was shown, and then the effect of the second layer on the considered problem was shown by selecting the different materials and applying different initial pre-stresses. Consequently, the present study can be considered as the investigation of the existence of the inter phase zone which is characteristic one for the composite materials to the dispersion of the generalized Rayleigh wave propagation. Numerical results obtained and discussed.

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