Numerical methods of solving contact problem for finite linearly and nonlinearly elastic bodies

This paper presents a study on smooth elastic contact between two semi-infinite elastic bodies, one of which has a wavy surface, for the case when there are an incompressible liquid, not wetting the surfaces of the bodies, at the central region of each interface gap and a gas under constant pressure at the edges of each gap. Due to the surface tension of the liquid, a pressure drop occurs in the liquid and the gas, which is described by the Laplace formula. The formulated contact problem is reduced to a singular integral equation (SIE) with the Hilbert kernel, which is transformed into a SIE with the Cauchy kernel for a derivative of a height of the gaps. A system of transcendental equations for a width of each gap and a width of the gap region filled with the liquid is obtained from the condition of boundedness of the contact stresses at the gap ends and the condition of liquid amount conservation. It is solved numerically, and the dependences of the width and shape of the gaps, the width of the gap regions filled with the liquid and the contact approach of the bodies on the applied load and the surface tension of the liquid are analyzed.

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Using Nonlinear Contact Mechanics in Process of Tool Edge Movement on Deformable Body to Analysis of Cutting and Sliding Burnishing Processes

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.474.339 ◽

2014 ◽

Vol 474 ◽

pp. 339-344 ◽

Cited By ~ 4

Author(s):

Jaroslaw Chodor ◽

Leon Kukielka

Keyword(s):

Numerical Simulation ◽

Mathematical Model ◽

Surface Layer ◽

Numerical Methods ◽

Contact Problem ◽

Deformable Body ◽

Comprehensive Analysis ◽

Tool Edge ◽

Nonlinear Contact ◽

Performance Conditions

Properties of the surface layer after cutting or sliding burnishing depend mainly on type of process and its performance conditions. For its comprehensive analysis is necessary to develop an adequate mathematical model and numerical methods of solving it. A common feature of both processes is moving the tool edge on elastic/visco-plastic workpiece. However, these processes are different i.e. the chip formation or chipless forming, therefore, different properties of surface layer depend mainly on: the geometry of the tool edge and its workpiece relative and depth of process. Therefore, this article is about the application of an incremental modelling and numerical solution of the contact problem between movable rigid and elastic/visco-plastic bodies developed in [ to the numerical simulation of physical process of moving a rigid tool on the workpiece.

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The Quasilinear Wave Equation for Antiplane Shearing of Nonlinearly Elastic Bodies

Journal of Computational Physics ◽

10.1006/jcph.2001.6783 ◽

2001 ◽

Vol 171 (1) ◽

pp. 201-226 ◽

Cited By ~ 1

Author(s):

Dawn A. Lott ◽

Stuart S. Antman ◽

William G. Szymczak

Keyword(s):

Wave Equation ◽

Quasilinear Wave Equation ◽

Elastic Bodies ◽

Nonlinearly Elastic

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Quasistatic normal-compliance contact problem of visco-elastic bodies with Coulomb friction implemented by QP and SGBEM

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2016.10.010 ◽

2017 ◽

Vol 315 ◽

pp. 249-272 ◽

Cited By ~ 5

Author(s):

Roman Vodička ◽

Vladislav Mantič ◽

Tomáš Roubíček

Keyword(s):

Contact Problem ◽

Coulomb Friction ◽

Normal Compliance ◽

Elastic Bodies

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The Contact Problem Studied by Pseudocaustics Formed at the Vicinity of the Contact Zone

Journal of Engineering Materials and Technology ◽

10.1115/1.3225703 ◽

1984 ◽

Vol 106 (3) ◽

pp. 211-215 ◽

Cited By ~ 2

Author(s):

P. S. Theocaris ◽

C. A. Stassinakis

Keyword(s):

Contact Problem ◽

Contact Zone ◽

Contact Area ◽

The Other ◽

Tangential Stresses ◽

Elastic Bodies ◽

First Case ◽

Reflected Light ◽

Spline Polynomial ◽

Distribution Of Stresses

The method of caustics is applied to formulate the normal and tangential stresses developed in the contact zone of two elastic bodies, and also for one elastic and the other plastic. The stresses are represented by a cubic spline polynomial, its coefficients calculated by pseudocaustics from reflected light around the contact zone. The method is applied to determine the stresses along the boundary of a half-plane and the stresses along the contact area of two disks. The deviation of calculated stresses from the applied ones, in the first case was small, while in the second case it was found that the normal distribution of stresses was similar to a Hertzian distribution. This experimental method can be used to accurately obtain contact stresses.

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