An Improved Normal Compliance Method for Dynamic Hyperelastic Problems with Energy Conservation Property

Mikaël Barboteu (1) , Francesco Bonaldi (1) , David Danan (2) , Soad El-hadri (3)

1 LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations
2 IRT SystemX
3 ENAC - Ecole Nationale de l'Aviation Civile

The purpose of this work is to present an improved energy conservation method for hyperelastodynamic contact problems based on specific normal compliance conditions. In order to determine this Improved Normal Compliance (INC) law, we use a Moreau-Yosida α-regularization to approximate the unilateral contact law. Then, based on the work of Hauret-LeTallec [1], we propose in the discrete framework a specific approach allowing to respect the energy conservation of the system in adequacy with the continuous case. This strategy (INC) is characterized by a conserving behavior for frictionless impacts and admissible dissipation for friction phenomena while limiting penetration. Then, we detail the numerical treatment within the framework of the semi-smooth Newton method and primal-dual active set strategy for the normal compliance conditions with friction. We finally provide some numerical experiments to bring into light the energy conservation and the efficiency of the INC method by comparing with different classical methods from the literature throught representative contact problems.

Mots clés: AMS Subject Classification : 74M15 74M20 74M10 74B20 74H15 74S30 49M15 90C53 70F40 70-08 70E55 35Q70 Hyperelasticity Unilateral Contact Normal Compliance Moreau-Yosida Regularization Coulomb Friction Dynamics Semi-Smooth Newton method Primal-Dual Active Set Numerical simulations; AMS Subject Classification : 74M15; 74M20; 74M10; 74B20; 74H15; 74S30; 49M15; 90C53; 70F40; 70-08; 70E55; 35Q70 Hyperelasticity; Unilateral Contact; Normal Compliance; Moreau-Yosida Regularization; Coulomb Friction; Dynamics; Semi-Smooth Newton method; Primal-Dual Active Set; Numerical simulations

Domaines: Analyse numérique [math.NA]; Mécanique [physics]

Mikaël Barboteu, Francesco Bonaldi, David Danan, Soad El-hadri. An Improved Normal Compliance Method for Dynamic Hyperelastic Problems with Energy Conservation Property. 2023. ⟨hal-03955591v1⟩