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The CD-Lagrange scheme, a robust explicit time-integrator for impact dynamics : A new singular mass formulation, and an extension to deformable-deformable contact

Jean Di Stasio 1, 2, 3
2 SMC - Systèmes Mécaniques et Contacts
LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]
3 MIMESIS - Mécanique Multiéchelle pour les solides
LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]
Abstract : Tyres are complex structures to simulate. The materials are heterogeneous and incompressible with non-linear responses. The geometry goes to the millimetre scales for tread patterns. For a finite elements simulation a precise mesh is then required. The model has then a large number of degrees of freedom and non-linear material laws. In dynamics, the simulation becomes even more challenging especially with impacts. Nevertheless it is crucial in the tire design process because it brings a deeper comprehension of the tire and avoids test on real structures. The explicit time-integration make feasible the impact simulations. They handle easily the non-linearities with a very low computational cost for a time-step. Merged with a precise contact formulation, they form robust, accurate and efficient schemes for addressing impact simulations. This work aims to choose and improve an explicit scheme for non-linear dynamics with impacts. The first part is a benchmark for selecting a scheme and enhance its possibilities of improvement. The selected one is the CD-Lagrange: an explicit scheme based on central difference method, a contact enforcement by Lagrange multipliers, and a contact condition on velocity. Two mains improvements are identified and explored. Firstly, the energy conservation at impact would make the scheme symplectic for deformable bodies. Secondly the formulation must be enlarged to deformable–deformable contact. The second part aims then to achieve the conservation of energy by adapting the singular mass matrix to the CD-Lagrange. The formulation is firstly built in 1D, and shows a major improvement for the energy balance. Then two possible extensions are explored for the 3D cases. The third part presents the CD-Lagrange scheme with a mortar formulation for deformable-deformable contact. It handles with stability and accuracy large sliding and friction. An acceleration technique is proposed for solving the contact problem, without any loss of accuracy.
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https://tel.archives-ouvertes.fr/tel-03368135
Contributor : Abes Star :  Contact
Submitted on : Wednesday, October 6, 2021 - 3:45:45 PM
Last modification on : Friday, October 8, 2021 - 3:27:22 AM

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  • HAL Id : tel-03368135, version 1

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Jean Di Stasio. The CD-Lagrange scheme, a robust explicit time-integrator for impact dynamics : A new singular mass formulation, and an extension to deformable-deformable contact. Mechanics [physics.med-ph]. Université de Lyon, 2021. English. ⟨NNT : 2021LYSEI029⟩. ⟨tel-03368135⟩

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