On the super-Rayleigh/subseismic elastodynamic indentation problem

Georgiadis, H.G.; Barber, J. R.

doi:10.1007/bf00044967

Cited by 55 publications

(40 citation statements)

References 31 publications

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“…As noted above sliding contact solutions for speeds v R < v < v S violate Signorini conditions [Georgiadis and Barber 1993]. In particular, in the sliding die problem here (28a) for normal stress in C still holds for this speed range, and is still both bounded and continuous on zone boundary .…”

Section: Comment On Supercritical/subseismic Behaviormentioning

confidence: 60%

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Two cases of rapid contact on an elastic half-space: Sliding ellipsoidal die, rolling sphere

Brock

2012

J. Mech. Mater. Struct.

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In one case a rigid ellipsoidal die translates over the surface of a half-space. Because of friction, both compression and shear force are required. In the other, a rigid sphere rolls on the surface under a compressive force. Both motions occur along a straight path at constant subcritical speed. A dynamic steady state is treated, that is, the contact zone and its traction remain constant in the frame of the die or sphere. Exact solutions for contact zone traction are derived in analytic form, as well as formulas for the contact zone shape. Axial symmetry is not required in the solution process. Cartesian coordinates are used, but a system of quasipolar coordinates is introduced that allows problem reduction to singular integral equations similar in form to those found in 2D contact.

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Section: Comment On Supercritical/subseismic Behaviormentioning

confidence: 60%

“…The negative gives σ an integrable singularity as x → x + . Signorini conditions for contact [Georgiadis and Barber 1993] prohibit singular gradients at the contact zone boundary. Therefore (27) leads to…”

Section: Louis Milton Brockmentioning

confidence: 99%

Two cases of rapid contact on an elastic half-space: Sliding ellipsoidal die, rolling sphere

Brock

2012

J. Mech. Mater. Struct.

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“…In this context, Craggs and Roberts [1] studied the elastodynamic problem of a moving indentor and obtained physically acceptable solutions for sub-Rayleigh and supersonic sliding speeds. Subsequent work by Georgiadis and Barber [2] yielded an additional physically acceptable result for a particular speed in the transonic range and also discussed a paradox occurring in the super-Rayleigh / subseismic regime. Other efforts by Brock [3,4] dealt with the 2D sliding indentation of thermoelastic half-spaces in the presence of Coulomb friction.…”

Section: Introductionmentioning

confidence: 97%

“…Also, it is assumed that the surface of the elastic body outside the contact region is free from tractions and thermally insulated. Our analysis is restricted to the subRayleigh regime, so as to avoid non-uniqueness of the solution or violation of the condition of non-tensile normal stress along the contact area [2].…”

Section: Introductionmentioning

confidence: 99%

Rapid sliding motion of a rigid frictionless indentor with a flat base over a thermoelastic half-space

2012

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. (2012) 'Rapid sliding motion of a rigid frictionless indentor with a at base over a thermoelastic half-space.', Archive of applied mechanics., 82 (10). pp. 1481-1495. Further information on publisher's website:http://dx.doi.org/10.1007/s00419-012-0670-0Publisher's copyright statement:The nal publication is available at Springer via http://dx.doi.org/10.1007/s00419-012-0670-0Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Since there is an analogy between the steady-state theories of thermoelasticity and poroelasticity, the present results carry over to the latter case directly.

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“…The more basic models are generally quasistatic, assume Hertzian contact, and are isothermal. However, more recent studies consider, variously, thermoelastic contact and inertial effects [Hills and Barber 1986;Georgiadis and Barber 1993;Pauk and Yevtushenko 1997;Barber 1999;Jang 2000;Pauk and Zastrau 2002;Andersson et al 2005;Jang 2005]. In addition, studies of the mathematically-similar problem of the interface crack [Hills and Barber 1993; address issues that also arise in contact.…”

Section: Introductionmentioning

confidence: 99%

Rolling contact with slip on a thermoelastic half-space: comparison with perfect rolling contact

Brock

2008

J. Mech. Mater. Struct.

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A rigid cylinder rolls at constant speed on a thermoelastic half-space under a compressive load. Heat flow across the contact zone is neglected, and the zone has a central region of perfect contact and two edge regions of frictionless slip. A robust asymptotic inversion of the exact transform solution to a related unmixed boundary value problem allows the mixed-mixed problem of rolling contact to be solved analytically. The solution is compared with that for perfect rolling contact. Both show variations in contact zone size and temperature change with rolling speed and load. Distinctions exist however: slip zones preclude oscillatory solution behavior and are much smaller than zones of oscillation. Moreover, perfect rolling contact may exaggerate the difference between imposed and effective angular velocity due to surface deformation.

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On the super-Rayleigh/subseismic elastodynamic indentation problem

Cited by 55 publications

References 31 publications

Two cases of rapid contact on an elastic half-space: Sliding ellipsoidal die, rolling sphere

Two cases of rapid contact on an elastic half-space: Sliding ellipsoidal die, rolling sphere

Rapid sliding motion of a rigid frictionless indentor with a flat base over a thermoelastic half-space

Rolling contact with slip on a thermoelastic half-space: comparison with perfect rolling contact

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