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.

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.

scholarly journals On Hydromechanical Interaction during Propagation of Localized Damage in Rocks

Minerals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 162
Author(s):  
A.A. Jameei ◽  
S. Pietruszczak
Keyword(s):  
Numerical Study ◽  
Fluid Pressure ◽  
Implicit Time ◽  
Integration Scheme ◽  
Internal Length ◽  
Element Analysis ◽  
Equivalent Permeability ◽  
Mechanical Coupling ◽  
Splitting Test ◽  
Localized Damage

This paper provides a mathematical description of hydromechanical coupling associated with propagation of localized damage. The framework incorporates an embedded discontinuity approach and addresses the assessment of both hydraulic and mechanical properties in the region intercepted by a fracture. Within this approach, an internal length scale parameter is explicitly employed in the definition of equivalent permeability as well as the tangential stiffness operators. The effect of the progressive evolution of damage on the hydro-mechanical coupling is examined and an evolution law is derived governing the variation of equivalent permeability with the continuing deformation. The framework is verified by a numerical study involving 3D simulation of an axial splitting test carried out on a saturated sample under displacement and fluid pressure-controlled conditions. The finite element analysis incorporates the Polynomial-Pressure-Projection (PPP) stabilization technique and a fully implicit time integration scheme.

Poroelastodynamic fundamental solutions of transversely isotropic half-plane

2019 ◽  
Vol 106 ◽  
pp. 52-67 ◽  
Author(s):  
Suraparb Keawsawasvong ◽  
Teerapong Senjuntichai
Keyword(s):  
Half Plane ◽  
Transversely Isotropic ◽  
Fundamental Solutions

scholarly journals Growth estimates in linear elasticity with a sublinear body force without definiteness conditions on the elasticities

1984 ◽  
Vol 27 (2) ◽  
pp. 223-228 ◽  
Author(s):  
Franca Franchi
Keyword(s):  
Wave Equation ◽  
Body Force ◽  
Displacement Vector ◽  
Fundamental Solutions ◽  
Existence Results ◽  
The Body ◽  
Heat Diffusion ◽  
Initial Value ◽  
Linear Elastic ◽  
Linear Elastic Body

In this paper, we study the boundary-initial value problem for a linear elastic body ina bounded domain, when the body force depends on the displacement vector u in asublinear way.Recently, much attention has been given to nonlinear body forces not only to studythe fundamental solutions of the equations governing linear elastodynamics, see e.g.Kecs [3], but also to derive global non existence results in abstract problems with directapplications to nonlinear heat diffusion or to the nonlinear wave equation, see e.g. Ball[1], Levine and Payne [10].

Numerical Study of a Plate with a Pre-Cracked Circular Notch

2014 ◽  
Vol 627 ◽  
pp. 101-104 ◽  
Author(s):  
Francesco Caputo ◽  
A. de Luca ◽  
Giuseppe Lamanna ◽  
Alessandro Soprano
Keyword(s):  
Fracture Mechanics ◽  
Plastic Zone ◽  
Numerical Study ◽  
Plastic Zone Size ◽  
Mode I ◽  
Zone Size ◽  
Linear Elastic ◽  
Elastic Fracture ◽  
Notch Edge ◽  
Circular Notch

In the recent years, the study of the behaviour of damaged structures has been focused on cracked components in presence of an extensive material yielding at the crack tip; under this condition, linear elastic fracture mechanics theory (LEFM) is not able to describe the real plastic zone shape and size. Within this work, an extensive numerical analysis, based on elastic plastic fracture mechanics theory (EPFM), of the plastic zone size at the tip of a Mode I pre-crack at the notch edge in a plate is presented.

Effects of Surface Elasticity on Scattering of P Waves by an Elastic Half-Plane with a Nanosized Semi-Cylindrical Inclusion

2013 ◽  
Vol 303-306 ◽  
pp. 2661-2666
Author(s):  
Zhi Ying Ou ◽  
Cheng Liu ◽  
Xiao Wei Liu
Keyword(s):  
Surface Energy ◽  
Half Plane ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Cylindrical Inclusion ◽  
P Waves ◽  
Wave Function Expansion Method ◽  
Plane P Waves ◽  
Incident Waves

The scattering of plane P waves by a nanosized semi-cylindrical inclusion embedded in an elastic half-plan has been studied in this paper. To account for the surface effect at nanoscale, the surface elasticity is also adopted. When the boundary condition at the straight edge of the half-plane is traction free, the analytical solutions of stress fields of the half plan with semi-cylindrical inclusion are expressed by employing a wave function expansion method. The results show that surface energy has a significant effect on the scattering of plane P waves as the radius of the semi-cylindrical inclusion shrinks to nanoscale. For incident waves with different frequencies, radius of semi-cylindrical inclusion, the effects of surface energy on the dynamic stress concentration near the semi-cylindrical inclusion are discussed in detail.

Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat

2002 ◽  
Vol 69 (5) ◽  
pp. 657-662 ◽  
Author(s):  
L. Kogut ◽  
I. Etsion
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Contact Pressure ◽  
Contact Zone ◽  
Contact Area ◽  
Large Range ◽  
Element Model ◽  
Contact Interface ◽  
Frictionless Contact ◽  
Elastic Plastic

An elastic-plastic finite element model for the frictionless contact of a deformable sphere pressed by a rigid flat is presented. The evolution of the elastic-plastic contact with increasing interference is analyzed revealing three distinct stages that range from fully elastic through elastic-plastic to fully plastic contact interface. The model provides dimensionless expressions for the contact load, contact area, and mean contact pressure, covering a large range of interference values from yielding inception to fully plastic regime of the spherical contact zone. Comparison with previous elastic-plastic models that were based on some arbitrary assumptions is made showing large differences.

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