A tribological model for geometrically structured anisotropic surfaces in a covariant form

Michaloudis, Georgios; Konyukhov, Alexander; Gebbeken, Norbert

doi:10.1002/nme.6356

Cited by 1 publication

(2 citation statements)

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“…The stiffness matrix

K

in the case of contact with friction consists of normal

K_{N}

and tangential parts

K_{T}

, which are derived from the discretization and corresponding transformations of the contact integral, respectively, from the normal and tangential parts of the contact integral, see more about their derivations in References 22 and 23:

K = K_{N} + K_{T} .

…”

Section: Overview Of the Ctsb Contact Algorithmmentioning

confidence: 99%

“…Remark The updated scheme in Equation (62) is correct for all cases of unidirectional loading (i.e., without the reverse loading). For more general case the initial sliding point with coordinates

ξ_{0}^{i}

should be updated within the return‐mapping scheme for the ”sliding” case also, see more details in Reference 22. This procedure, however, for the forthcoming examples, including only unidirectional loading, is not necessary.…”

Section: Overview Of the Ctsb Contact Algorithmmentioning

confidence: 99%

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New benchmark problems for verification of the curve‐to‐surface contact algorithm based on the generalized Euler–Eytelwein problem

Konyukhov

Shala

2021

Numerical Meth Engineering

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Development of the numerical contact algorithms for finite element method usually concerns convergence, mesh dependency, etc. Verification of the numerical contact algorithm usually includes only a few cases due to a limited number of available analytic solutions (e.g., the Hertz solution for cylindrical surfaces). The solution of the generalized Euler-Eytelwein, or the belt friction problem is a stand alone task, recently formulated for a rope laying in sliding equilibrium on an arbitrary surface, opens up to a new set of benchmark problems for the verification of rope/beam to surface/solid contact algorithms. Not only a pulling forces ratio T T 0 , but also the position of a curve on a arbitrary rigid surface withstanding the motion in dragging direction should be verified. Particular situations possessing a closed form solution for ropes and rigid surfaces are analyzed. The verification study is performed employing the specially developed Solid-Beam finite element with both linear and C1-continuous approximations together with the Curve-to-Solid Beam (CTSB) contact algorithm and exemplary employing commercial finite element software. A crucial problem of "contact locking" in contact elements showing stiff behavior despite the good convergence is identified. This problem is resolved within the developed CTSB contact element.

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“…The stiffness matrix