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A model-adaptivity method for the solution of Lennard-Jones based adhesive contact problems

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Abstract

The surface micro-interaction model of Lennard-Jones (LJ) is used for adhesive contact problems (ACP). To address theoretical and numerical pitfalls of this model, a sequence of partitions of contact models is adaptively constructed to both extend and approximate the LJ model. It is formed by a combination of the LJ model with a sequence of shifted-Signorini (or, alternatively, -Linearized-LJ) models, indexed by a shift parameter field. For each model of this sequence, a weak formulation of the associated local ACP is developed. To track critical localized adhesive areas, a two-step strategy is developed: firstly, a macroscopic frictionless (as first approach) linear-elastic contact problem is solved once to detect contact separation zones. Secondly, at each shift-adaptive iteration, a micro-macro ACP is re-formulated and solved within the multiscale Arlequin framework, with significant reduction of computational costs. Comparison of our results with available analytical and numerical solutions shows the effectiveness of our global strategy.

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  1. Laboratoire Mécanique des Sols, Structures et Matériaux, UMR CNRS 8579, CentraleSupélec, 3 Rue Joliot Curie, 91190, Gif-sur-Yvette, France

    Hachmi Ben Dhia & Shuimiao Du

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  1. Hachmi Ben Dhia
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  2. Shuimiao Du
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Correspondence to Hachmi Ben Dhia.

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Ben Dhia, H., Du, S. A model-adaptivity method for the solution of Lennard-Jones based adhesive contact problems. Comput Mech 62, 1543–1562 (2018). https://doi.org/10.1007/s00466-018-1578-5

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