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：这项工作的目的是根据具体的正常合规条件,提出一种更好的节能方法,用于处理超光层动力接触问题; 为了确定这一改进常态合规(INC)法,我们使用一个“Moreau-Yosida $\ alpha$”的常规化法,以近似单方面接触法; 然后,根据Hauret-LeTallec\cite{hauret2006年能源}的工作,我们在离散框架内提出一种具体方法,使系统节能与持续情况相适应; 这一战略(INC)的特点是保护不受摩擦影响的行为,允许摩擦现象消散,同时限制渗透; 然后,我们详细说明半摩擦牛顿法和对正常合规条件和摩擦的初步积极战略框架内的数字处理; 我们最后通过比较文献中不同的经典方法,通过具有代表性的接触问题,提供一些数字实验,以了解节能和INC方法的效率。