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

TL;DR

This paper introduces an improved energy conservation method for hyperelastodynamic contact problems using a novel normal compliance law, ensuring energy preservation and dissipation properties, validated through numerical experiments.

Contribution

It proposes an Improved Normal Compliance (INC) law based on Moreau--Yosida regularization that conserves energy and handles frictional impacts effectively.

Findings

The INC method conserves energy in frictionless impacts.

It manages dissipation during frictional contact.

Numerical experiments demonstrate improved efficiency and energy conservation.

Abstract

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 $\alpha$-regularization to approximate the unilateral contact law. Then, based on the work of Hauret--LeTallec \cite{hauret2006energy}, 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.