Stress Tensor and Gradient of Hydrostatic Pressure in the Half-Space Beneath Axisymmetric Bodies in Normal and Tangential Contact

Forsbach, Fabian

doi:10.3389/fmech.2020.00039

Cited by 9 publications

(8 citation statements)

References 18 publications

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“…Due to the enormous reduction in degrees of freedom and the associated savings in computation time when calculating contact forces, the method is particularly well suited for mapping contact interfaces within simulations of macrodynamic systems. In addition, it can be applied for advanced tribological investigations such as wear calculations or the onset of plastic deformation, as both the stresses within the contact area as well as inside the body can be recovered from the one-dimensional model [9,10].…”

Section: Introductionmentioning

confidence: 99%

An Analytical Model for Almost Conformal Spherical Contact Problems: Application to Total Hip Arthroplasty with UHMWPE Liner

Heß

Forsbach

2021

Applied Sciences

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Due to its high relevance for designing ball joints in mechanical engineering and (artificial) hip joints in biomechanics, the almost conformal elastic contact between a sphere and a spherical cup represents an important contact problem of current research. As no closed-form analytical solution to the problem has been found to date, full computational methods such as the finite element method are needed for analysis. However, they often require incredibly long, unacceptable calculation times, making parameter studies hardly practicable. For this reason, approximate analytical and semi-analytical models are applied, capable of predicting quantities of interest with sufficient accuracy. In the present work, a very simple model based on a radially directed Winkler foundation is presented, which provides (approximate) closed-form analytical solutions for both the pressure distribution and the dependencies between macroscopic contact quantities such as normal force and indentation depth. To ensure an optimal mapping of a specific contact problem, only the foundation modulus must be defined in a suitable way. As an example, the proposed model has been successfully adapted to adequately simulate the frictionless normal contact for hard-on-soft hip implants. For this purpose, the foundation modulus was approximated with the aid of a finite element analysis instead of adopting it from already well-established models, as the latter produce clearly erroneous results for large liner thicknesses and large Poisson’s ratios. By a comparison with extensive parameter studies of finite element simulations, it is demonstrated that the proposed model provides acceptable results for all commonly used hard-on-soft hip implants. On this basis, the influence of geometrical changes of the femoral head and the acetabular cup on the maximum pressure as well as the half-contact angle is discussed, and consequences on the wear behavior are deduced.

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Section: Introductionmentioning

confidence: 99%

An Analytical Model for Almost Conformal Spherical Contact Problems: Application to Total Hip Arthroplasty with UHMWPE Liner

Heß

Forsbach

2021

Applied Sciences

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“…This result has in slightly different form already been reported by Forsbach [12]. To get rid of the derivative of the known solution for the parabolic contact, we introduce the substitutions…”

Section: Normal Contactmentioning

confidence: 57%

“…On the other hand, it has recently been demonstrated ( [11], [12]), how the full stress state below the surface in axisymmetric tangential contact problems can be determined via the appropriate superposition of respective flat-punch solutions. This procedure is valid within the restrictions of the Hertz-Mindlin approximation, which comprises the assumptions of elastic similarity of the contact partners, local Amontons-Coulomb friction with a constant coefficient of fricion and negligence of the lateral surface displacements resulting from the tangential contact tractions.…”

Section: Introductionmentioning

confidence: 99%

Determination of the stress state beneath arbitrary axisymmetric tangential contacts in Hertz-Mindlin approximation based on the superposition of solutions for parabolic contact

Willert

2021

Preprint

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As an improvement to the recently proposed procedure for the determination of the stress state beneath axisymmetric tangential contacts in Hertz-Mindlin approximation via an appropriate superposition of solutions for the respective flat-punch problem, the determination via the superposition of solutions for parabolic contact is demonstrated. It has two advantages over the flat-punch formulation: the numerical implementation is slightly easier and more stable, due to the absence of stress singularities for the smooth parabolic profile. As a numerical example, the oscillating tangential contact between a rigid indenter with a profile in the form of a power-law (with exponent 4) and an elastic half-space is considered in detail.

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“…Firstly, the Abel-like transforms can be written as explicit convolutions and, therefore, accelerated by the fast Fourier transform (FFT) [49]. Moreover, once the normal and tangential contact problems in the Hertz-Mindlin approximation are solved, the complete stress state inside the materials can be obtained via simple 1D-integrals [50], which allows for the fatigue analysis. Hence, the suggested semi-analytical model can be a part of a more global model of fretting in axisymmetric contacts.…”

Section: Discussionmentioning

confidence: 99%

A Simple Semi-Analytic Contact Mechanical Model for Tangential and Torsional Fretting Wear of Axisymmetric Contacts

Willert

2021

Symmetry

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Fretting wear of axisymmetric contacts is considered within the framework of the Hertz–Mindlin approximation and the Archard law for the linear wear. If the characteristic time scale for the wear is much larger than the duration of a single fretting oscillation, the profile change due to wear during one fretting cycle can be neglected for the contact problem as a zero-order approximation. This allows to give an exact contact solution during each fretting cycle, depending on the current worn profile, and thus for the explicit statement of an ordinary integro-differential equation system for the time-evolution of the fretting profile, which can be easily solved numerically. The proposed method gives the same results as a known, contact mechanically more rigorous simulation procedure that also operates within the framework of the Hertz–Mindlin approximation, but works significantly faster than the latter one. Tangential and torsional fretting wear are considered in detail. A comparison of the numerical prediction for the evolution of the worn profile in partial slip torsional fretting of a rubber ball on abrasive paper shows good agreement with experimental results from the literature.

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Stress Tensor and Gradient of Hydrostatic Pressure in the Half-Space Beneath Axisymmetric Bodies in Normal and Tangential Contact

Cited by 9 publications

References 18 publications

An Analytical Model for Almost Conformal Spherical Contact Problems: Application to Total Hip Arthroplasty with UHMWPE Liner

An Analytical Model for Almost Conformal Spherical Contact Problems: Application to Total Hip Arthroplasty with UHMWPE Liner

Determination of the stress state beneath arbitrary axisymmetric tangential contacts in Hertz-Mindlin approximation based on the superposition of solutions for parabolic contact

A Simple Semi-Analytic Contact Mechanical Model for Tangential and Torsional Fretting Wear of Axisymmetric Contacts

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