arXiv subjects

Emanuel Willert

Publications and source records attributed to Emanuel Willert.

7 recordsLinked to original sources

arXiv2024

Stress and Displacement Fields in the Surface of an Elastic Half-Space under the Action of a Constant Shear Load over a Circular Contact Domain

Based on the superposition of incremental frictional surface tractions that, in the case of an incompressible elastic half-space, correspond to a rigid tangential translation of a circular contact domain, the stress and displacement fields in the surface are determined in closed analytic form for an elastic half-space under the action of a constant shear traction over a circular contact domain on the surface. The obtained exact solutions can serve as benchmarks for numerical models, or can be used for the deeper contact-mechanical analysis of adhesive sliding contacts of soft materials.

cond-mat.soft↗

arXiv2023

Elastic Stress Field beneath a Sticking Circular Contact under Tangential Load

Based on a potential theoretical approach, the subsurface stress field is calculated for an elastic-half space, which is subject to normal and uniaxial tangential surface tractions that - in the case of elastic decoupling - correspond to rigid normal and tangential translations of a circular surface domain. The stress fields are obtained explicitly and in closed form as the imaginary parts of compact complex-valued expressions. The stress state in the surface and on the central axis are considered in detail. As, within specific approximations that have been discussed at length in the literature, any tangential contact problem with friction can be understood as a certain incremental series of such rigid translations, the solutions presented here can serve as the basis of very fast superposition algorithms for the analysis of subsurface stress fields in general tangential contact problems with friction.

cond-mat.mtrl-sci↗

arXiv2021

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

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.

cond-mat.mtrl-sci↗

arXiv2021

Short note: Transformation between different solution methods for general axisymmetric tangential contact problems in Hertz-Mindlin approximation

The transition between two conceptionally different solution procedures for general axisymmetric tangential contact problems with arbitrary laoding histories under Hertz-Mindlin assumptions is demonstrated, namely Jäger's superposition solution and the method of dimensionality reduction. Both finite and ininite superpositions of Cattaneo-Mindlin basis functions are considered. It is shown how the weights in the superposition solution can be easily obtained from the displacements in the MDR model.

cond-mat.soft↗

arXiv2018

The Influence of Compressibility on the Restitution Coefficient for Viscoelastic Spheres in Low-Velocity Normal Impacts

The influence of compressibility on the coefficient of restitution in the normal impact of a rigid sphere onto a linear-viscoelastic compressible standard solid under quasi-static conditions is studied using a numerical solution procedure for the contact-impact problem based on the Method of Dimensionality Reduction. We find that the influence of compressible material behavior is most significant in parameter combinations with high energy dissipation in the bulk material during the impact. Thereby the restitution coefficient is usually underestimated, if the material is assumed to be incompressible. This misestimating can be very significant (relative errors of 100% and more are possible), even, if the actual Poisson ratio is very close to 0.5.

cond-mat.soft↗

arXiv2018

Indentation of concave power law profiles with arbitrary exponents

We study analytically and numerically the process of indentation of cylindrical rigid indenter with concave face in form of a power-law function. In the well-known case of a parabolic concave indenter, the contact starts at sharp edges of the indenter and spreads inwards with increasing indentation depth. For all profiles with the exponent larger than 2, the contact area first spreads from the boarder inwards, but then a contact is established in the center of the indenter. Finally, the outer ring spreads inwards and the central contact area outwards until the complete contact is achieved. The critical indentation depth for the full contact is calculated ones proceeding from the full contact and looking for the condition of vanishing pressure and also proceeding from incomplete contact (in this case numerically, using Boundary Element Method). The results of both approaches coincide.

cond-mat.soft↗

arXiv2018

Detachment of adhesive normal contact between a rigid circular flat punch and a viscoelastic half-space

We propose an approach to describe the propagation of a crack (or boundary of an adhesive contact) in a viscoelastic material which is only based on the consideration of the rheology of the material without the introduction of any additional dependency of the separation energy on the velocity of crack propagation. The suggested idea is illustrated with an example of kinetics of detachment of a flat-ended indenter from a viscoelastic medium. It is shown that under the given assumptions the crack propagation is accelerating until the critical configuration is reached and the contact detaches instantaneously. The suggested criterion can be basically applied to arbitrary shapes and arbitrary loading histories.

cond-mat.soft↗