scholarly journals Comparison of contact problem exact solutions for transversely isotropic half-space

2015 ◽  
Vol 15 (1) ◽  
pp. 23-28 ◽  
Author(s):  
Dmitriy Pogarskiy ◽  
David Davtyan
Keyword(s):  
Contact Problem ◽  
Exact Solutions ◽  
Half Space ◽  
Transversely Isotropic

Exact Analysis of Dynamic Sliding Indentation at any Constant Speed on an Orthotropic or Transversely Isotropic Half-Space

2002 ◽  
Vol 69 (3) ◽  
pp. 340-345 ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Plane Strain ◽  
Half Space ◽  
Contact Zone ◽  
Transversely Isotropic ◽  
Exact Formula ◽  
Constant Speed ◽  
Displacement Fields ◽  
Rigid Indentor

A plane-strain study of steady sliding by a smooth rigid indentor at any constant speed on a class of orthotropic or transversely isotropic half-spaces is performed. Exact solutions for the full displacement fields are constructed, and applied to the case of the generic parabolic indentor. The closed-form results obtained confirm previous observations that physically acceptable solutions arise for sliding speeds below the Rayleigh speed, for a single critical transonic speed, and for all supersonic speeds. Continuity of contact zone traction is lost for the latter two cases. Calculations for five representative materials indicate that contact zone width achieves minimum values at high, but not critical, subsonic sliding speeds. A key feature of the analysis is the factorization that gives, despite anisotropy, solution expressions that are rather simple in form. In particular, a compact function of the Rayleigh-type emerges that leads to a simple exact formula for the Rayleigh speed itself.

Solution of the Contact Problem of a Rigid Conical Frustum Indenting a Transversely Isotropic Elastic Half-Space

2013 ◽  
Vol 81 (4) ◽  
Author(s):  
X.-L. Gao ◽  
C. L. Mao
Keyword(s):  
Contact Problem ◽  
Closed Form ◽  
Half Space ◽  
Cone Angle ◽  
Closed Form Solution ◽  
Transversely Isotropic ◽  
Elastic Half Space ◽  
Form Solution ◽  
Potential Functions ◽  
Displacement Method

The contact problem of a rigid conical frustum indenting a transversely isotropic elastic half-space is analytically solved using a displacement method and a stress method, respectively. The displacement method makes use of two potential functions, while the stress method employs one potential function. In both the methods, Hankel's transforms are applied to construct potential functions, and the associated dual integral equations of Titchmarsh's type are analytically solved. The solution obtained using each method gives analytical expressions of the stress and displacement components on the surface of the half-space. These two sets of expressions are seen to be equivalent, thereby confirming the uniqueness of the elasticity solution. The newly derived solution is reduced to the closed-form solution for the contact problem of a conical punch indenting a transversely isotropic elastic half-space. In addition, the closed-form solution for the problem of a flat-end cylindrical indenter punching a transversely isotropic elastic half-space is obtained as a special case. To illustrate the new solution, numerical results are provided for different half-space materials and punch parameters and are compared to those based on the two specific solutions for the conical and cylindrical indentation problems. It is found that the indentation deformation increases with the decrease of the cone angle of the frustum indenter. Moreover, the largest deformation in the half-space is seen to be induced by a conical indenter, followed by a cylindrical indenter and then by a frustum indenter. In addition, the axial force–indentation depth relation is shown to be linear for the frustum indentation, which is similar to that exhibited by both the conical and cylindrical indentations—two limiting cases of the former.

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