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Streszczenie:
This contribution presents the extensions of beam‐to‐beam and beam‐inside‐beam contact schemes of the same authors towards frictional interactions. Since the schemes are based on the beams' true surfaces (instead of surfaces implicitly deduced from the beams' centroid lines), the presented enhancements are not only able to account for frictional sliding in the beams' axial directions, but also in the circumferential directions. Both the frictional beam‐to‐beam approach as well as the frictional beam‐inside‐beam approach are applicable to shear‐deformable and shear‐undeformable beams, as well as to beams with both circular and elliptical cross‐sections (although the cross‐sections must be rigid). A penalty formulation is used to treat unilateral and frictional contact constraints. FE implementation details are discussed, where automatic differentiation techniques are used to derive the implementations. Simulations involving large sliding displacements and large deformations are presented for both beam‐to‐beam and beam‐inside‐beam schemes. All simulation results are compared to those of the frictionless schemes.

Słowa kluczowe:
beam contact, beam-to-beam contact, beam-inside-beam contact, friction, Coulomb's law

Streszczenie:
This contribution presents a rapid computational framework to mechanically simulate the insertion of a slender medical instrument in a tubular structure such as an artery, the cochlea or another slender instrument.

Słowa kluczowe:
surgical simulation, contact mechanics, beam-inside-beam, artery, cochlea

Streszczenie:
The key novelty of this contribution is a dedicated technique to efficiently determine the distance (gap) function between parallel or almost parallel beams with circular and elliptical cross-sections. The technique consists of parametrizing the surfaces of the two beams in contact, fixing a point on the centroid line of one of the beams and searching for a constrained minimum distance between the surfaces (two variants are investigated). The resulting unilateral (frictionless) contact condition is then enforced with the Penalty method, which introduces compliance to the, otherwise rigid, beams' cross-sections. Two contact integration schemes are considered: the conventional slave-master approach (which is biased as the contact virtual work is only integrated over the slave surface) and the so-called two-half-pass approach (which is unbiased as the contact virtual work is integrated over the two contacting surfaces). Details of the finite element formulation, which is suitably implemented using Automatic Differentiation techniques, are presented. A set of numerical experiments shows the overall performance of the framework and allows a quantitative comparison of the investigated variants.

Słowa kluczowe:
beams, contact, circular and elliptical cross-sections, rigid cross-sections, single-pass algorithm, two-half-pass algorithm