Contact mechanics for gradient materials

提出的研究项目的总体目标是开发、分析和实施一套新的高阶梯度材料的接触公式，为进一步应用于复杂材料的模拟铺平道路。因此，最近扩展到IGA背景下一般高阶区域分解问题的砂浆类型方法的概念将被重新表述并应用于第二和第三梯度材料的接触。此外，我们将证明与经典方法相比，所提出的方法的收敛性和准确性。这允许我们限制适用性，并强调根据材料配对和界面拓扑在特定情况下的必要性。

The overall goal of the proposed research project is to develop, analyze and implement a novel set of contact formulations for higher order gradient materials, paving the way for further applications in the simulation of complex materials. Therefore, the concept of Mortar type methods, recently extended to general higher order domain decomposition problems in the context of IGA, will be reformulated and applied to contact of second and third gradient materials. Moreover, we will demonstrate convergence and accuracy of the proposed methodology compared to classical approaches. This allows us to limit the applicability and emphasise the necessity in specific situations depending on the material pairing and the interface topology.