Symmetrical frictionless indentation over a uniformly expanding contact region—I. Basic analysis

Brock, L. M.

doi:10.1016/0020-7225(76)90088-4

Cited by 21 publications

(24 citation statements)

References 5 publications

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“…Typical of such problems are those that exhibit no self-similarity, or include super-Rayleigh/subseismic contact-zone velocities and frictional effects. Nevertheless, considerable progress has been made in elastodynamic contact problems during the last two decades (Bedding and Willis [5,6], Willis [7,8], Brock 1,[9][10][11][12][13][14] and Cherepanov [15]). …”

Section: Introductionmentioning

confidence: 99%

“…The constant indentor speed in the wedge case, or the constant indentor acceleration in the parabolic case, in conjunction with dimensional considerations lead us to anticipate a self-similar solution in which certain fields (particle velocities or accelerations in the elastic medium) are homogeneous and the contact region expands at uniform velocity ~ (see e.g. Brock [9,12]). Notice also in the wedge case that it is the velocity ~ which determines the dynamic character of the problem (depending upon the magnitude of ~ in respect to the elastic-wave velocities), not the punch velocity V, which will generally be much lower than ~, since small strain considerations demand that the inclination of the wedge face (re -20)/2 << 1 (where 0 is the half-wedge angle).…”

Section: Introductionmentioning

confidence: 99%

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Dynamic frictional indentation of an elastic half-plane by a rigid punch

Brock

Georgiadis

1994

J Elasticity

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Dynamic rigid indentation of a linearly elastic half-plane in the presence of Coulomb friction is studied in this paper. A rigid punch, which is either wedge-or parabolic-shaped, is rapidly driven into the deformable body so that stress waves are generated. The contact region is assumed to extend at a constant sub-Rayleigh speed (this situation can be achieved by conveniently specifying the kinetic and geometric characteristics of indentor), whereas, due to symmetry, friction acts in opposing directions on opposite sides of the indentor. As the present exact analysis shows, this sign reversal of the tangential traction along the half-plane surface creates an extra stress-singularity at the changeover point of the boundary conditions (due to symmetry, this point here coincides with the point where the indentor apex makes contact with the half-plane surface). The study exploits the problem's self-similarity by utilizing homogeneous-function techniques previously used by L.M. Brock, along with the Riemann-Hilbert problem analysis. Representative numerical results are given for the wedge indentation case.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic frictional indentation of an elastic half-plane by a rigid punch

Brock

Georgiadis

1994

J Elasticity

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“…Brock has largely contributed to this field by establishing some very effective procedures in applying the Busemann-Chaplygin technique. He has also solved numerous elastodynamic contact problems [20][21][22][23] by the same methods.…”

Section: Introductionmentioning

confidence: 99%

An integral equation approach to self-similar plane-elastodynamic crack problems

Georgiadis¹

1991

J Elasticity

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Akstraet. The elastodynamic problem of an expanding crack under homogeneous polynomialform loading was reduced to the solution of a Cauchy singular integral equation. In this manner the solution of the original problem can be obtained by using well-known numerical treatments available for Cauchy SIEs. The procedure was accomplished by means of the Busemann-Chaplygin similarity technique and complex variable methods. The analysis has been restricted to the subsonic case.

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“…Perhaps a more cogent argument is that the sub-Rayleigh solution, which has been independently obtained and discussed by numerous authors [20,[24][25][26][27][28][29], also contains a disturbance of the same form in the vertical velocity v~(x, O, t) at the Rayleigh points, which of course are now outside the contact area. However, as we have shown in Section 4.3.1, the disturbance does not affect the satisfaction of the contact boundary conditions and hence if it is deemed to be unacceptable, it must be equally unacceptable when it occurs outside the contact region.…”

Section: Inadmissible Singularitiesmentioning

confidence: 99%

“…The half-plane is assumed to be at rest and stress-free at time t = 0. Many authors [20,[24][25][26][27][28][29] have considered this problem in the sub-Rayleigh regime, a < ca, for which the inequalities demand that the traction be bounded at Ixl --at and lead to a unique solution. However, as in Section 2.4, it is found that the bounded solution violates the inequalities if ca < a < ci, but that infinitely many singular solutions can be found which satisfy them.…”

Section: Uy(xot)> Vt-lxltan(~-~-);lxl>atmentioning

confidence: 99%