A New Coupled X-Fem/ Level-Set Strategy To Solve Contact Problem

Abstract eng:
When bodies come into contact, the contact surface is a priori unknown. This necessitates the addition of inequality equations to the formulation which are themselves still a challenge to solve efficiently. Moreover, a good representation of the boundary of the contact area is crucial as it is the locus of concentrated stress and strain. We propose to transform the inequality problem into a sequence of equality problems with an unknown domain depending on the contact surface. This surface is represented by an iso-level-set. Furthermore, to model field derivative discontinuities around the contact area, such as the derivative of the displacement, an enrichment strategy is set through the extended finite-element method (XFEM) [1]. The shape of the contact surface is found iteratively by means of configurational mechanics [2]. This shape-optimisation problem is driven by a sensitivity analysis. The same strategy has previously been implemented by [3] to solve volumetric inequalities constrains. As a first step to more general problems, we have treated simple problems such as a one dimensional medium governed by the rope equation or a two dimensional membrane. A pressure force was applied to these media and their displacements constrained by an undeformable body. The interest of these methods was highlighted by showing their efficiency using a coarse mesh. In addition, we compared the properties of our method with those of more classical approaches to contact.

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