This paper addresses the problem of friction-free contact between two elastic bodies. We develop an augmented Lagrangian method that provides computational convenience by reformulating the contact problem as a nonlinear variational equality. To achieve this, we propose a Nitsche-based method incorporating a hybrid displacement variable defined on an interstitial layer. This approach enables complete decoupling of the contact domains, with interaction occurring exclusively through the interstitial layer. The layer is independently approximated, eliminating the need to handle intersections between unrelated meshes. Additionally, the method supports introducing an independent model on the interface, which we leverage to represent a membrane covering one of the bodies. We present the formulation of the method, establish stability and error estimates, and demonstrate its practical utility through illustrative numerical examples.

翻译：本文研究两个弹性体之间的无摩擦接触问题。我们发展了一种增广拉格朗日方法，通过将接触问题重构为非线性变分等式，从而提供计算上的便利。为此，我们提出了一种基于Nitsche的方法，该方法引入了一个定义在中间层上的杂交位移变量。这一方法实现了接触域的完全解耦，相互作用仅通过中间层发生。该层被独立近似，从而无需处理无关网格间的相交问题。此外，该方法支持在界面上引入独立模型，我们利用这一点来表示覆盖其中一个物体的薄膜。我们给出了该方法的公式表述，建立了稳定性与误差估计，并通过说明性的数值算例展示了其实用价值。