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Normal Compliance Contact Models with Finite Interpenetration
Authors:Christof Eck  Jiří Jarušek  Jana Stará
Institution:1. Institute for Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, Stuttgart, 70569, Germany
2. Mathematical Institute, Academy of Sciences of the Czech Republic, ?itná 25, 115 67, Praha 1, Czech Republic
3. Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18600, Praha 8, Czech Republic
Abstract:We study contact problems with contact models of normal compliance type, where the compliance function tends to infinity for a given finite interpenetration. Such models are physically more realistic than standard normal compliance models, where the interpenetration is not restricted, because the interpenetration is typically justified by deformations of microscopic asperities of the surface; therefore it should not exceed a certain value that corresponds to a complete flattening of the asperities. The model can be interpreted as intermediate between the usual normal compliance models and the unilateral contact condition of Signorini type. For the static problem without friction, we prove the existence and uniqueness of solutions and establish the equivalence to an optimization problem. For the static problem with Coulomb friction, we show the existence of a solution. The analysis is based on an approximation of the problems by standard normal compliance models, the derivation of regularity results for these auxiliary problems in Sobolev spaces of fractional order by a special translation technique, and suitable limit procedures.
Keywords:
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