Penetration of a rigid indentor into a laminar obstacle

1993 ◽  
Vol 28 (6) ◽  
pp. 534-538
Author(s):  
E. N. Volodina
Keyword(s):  

2002 ◽  
Vol 69 (3) ◽  
pp. 340-345 ◽  
Author(s):  
L. M. Brock

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.



1983 ◽  
Vol 34 (3) ◽  
pp. 370-386 ◽  
Author(s):  
G. C. W. Sabin ◽  
P. N. Kaloni




1984 ◽  
Vol 51 (2) ◽  
pp. 289-293 ◽  
Author(s):  
J. R. Walton

In a previous paper, the title problem was solved for a homogeneous power-law linearly viscoelastic half-plane. Such material has a constant Poisson’s ratio and a shear modulus with a power-law dependence on time. In this paper, the shear modulus is assumed also to have a power-law dependence on depth from the half-plane boundary. As in the earlier paper, only a quasi-static analysis is presented, that is, the enertial terms in the equations of motion are not retained and the indentor is assumed to slide with constant speed. The resulting boundary value problem is reduced to a generalized Abel integral equation. A simple closed-form solution is obtained from which all relevant physical parameters are easily computed.



1978 ◽  
Vol 45 (1) ◽  
pp. 111-113 ◽  
Author(s):  
A. Nachman ◽  
J. R. Walton

The problem of the sliding of a rigid asperity over a power law viscoelastic layer is examined in the realistic limit of infinite (dimensionless) layer thickness. For a contact interval of unit length, asymptotic expansions for the normal traction over the interval together with several other physically relevant quantities (e.g., the friction coefficient) are developed in terms of an appropriate asymptotic sequence of powers of the (dimensionless) layer thickness.



2000 ◽  
Vol 68 (4) ◽  
pp. 589-595 ◽  
Author(s):  
D. L. Chertok ◽  
J. M. Golden ◽  
G. A. C. Graham

The problem of a smooth rigid indentor under variable loading moving across a viscoelastic half-space in one direction with variable speed is considered. The motion is assumed to be frictionless and the standard linear model is adopted to describe the viscoelastic material response. An integral equation is derived and a numerical algorithm for its solution subject to appropriate subsidiary conditions is constructed. The contact interval length, pressure, and coefficient of hysteretic friction are presented and the results discussed.



1983 ◽  
Vol 19 (10) ◽  
pp. 1555-1578 ◽  
Author(s):  
George Z. Voyiadjis ◽  
N. Ellis Buckner
Keyword(s):  




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