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.

翻译：本文旨在提出一种基于特定正则化接触条件的超弹动力学接触问题改进能量守恒方法。为确定这种改进正则化接触（INC）定律，我们采用Moreau-Yosida $\alpha$-正则化来逼近单边接触定律。随后基于Hauret-LeTallec \cite{hauret2006energy}的研究，在离散框架下提出一种与连续情况相匹配的特定策略，以保持系统的能量守恒性。该策略（INC）的特点在于：对无摩擦冲击具有守恒特性，对摩擦现象具有可接受的耗散行为，同时限制穿透深度。接着，我们详细阐述了在摩擦条件下基于半光滑牛顿法和原始-对偶积极集策略的正则化接触数值处理方法。最后通过代表性接触问题的数值实验，与文献中多种经典方法进行比较，验证了INC方法的能量守恒特性及计算效率。