In this paper, the efficiency of a multiscale strategy based on a domain decomposition method (DDM) for model-order reduction of time-dependent frictional contact problems is presented. The proposed strategy relies on the LArge Time INcrement (LATIN) nonlinear solver combined with model reduction based on the Proper Generalized Decomposition (PGD). The LATIN presents a robust treatment of contact conditions, sharing similarities with augmented Lagrangian approaches, and naturally leads to a mixed DDM. In addition, the global space–time formulation of the method allows PGD-based model reduction to be used during computations, creating and enriching on-the-fly reduced bases per substructure to better track sliding fronts and propagative phenomena. The introduction of a multiscale strategy in the LATIN framework is consistent with the physics of contact problems, in which phenomena with different wavelengths interact: local solutions at contact interfaces presents high gradient effects with a short wavelength compared to the characteristic length of the structure. By taking advantage of this, the coarse scale problem of the strategy enables to capture efficiently the behavior of the problem at the structural level, focusing then on capturing the local contact variations at the contact interfaces. The most important features of the approach are shown comprehensively on a simple one-dimensional frictional contact problem. Then, its robustness and effectiveness are tested on a two-dimensional multibody frictional contact problem with more complex loadings. Guidelines are also given for choosing the parameters of the strategy, in particular those driving the construction of the reduced basis.

中文翻译：

---

多尺度域分解方法对摩擦接触问题模型降阶的好处


在本文中，提出了基于域分解方法（DDM）的多尺度策略的效率，用于减少与时间相关的摩擦接触问题的模型阶数。所提出的策略依赖于 LArge Time INcrement (LATIN) 非线性求解器与基于适当广义分解 (PGD) 的模型缩减相结合。 LATIN 提出了对接触条件的稳健处理，与增强拉格朗日方法有相似之处，自然会导致混合 DDM。此外，该方法的全局时空公式允许在计算过程中使用基于 PGD 的模型简化，创建和丰富每个子结构的动态简化基数，以更好地跟踪滑动前沿和传播现象。 LATIN 框架中引入的多尺度策略与接触问题的物理原理一致，其中不同波长的现象相互作用：与结构的特征长度相比，接触界面处的局部解呈现出短波长的高梯度效应。利用这一点，该策略的粗尺度问题能够有效地捕获结构层面问题的行为，然后重点捕获接触界面处的局部接触变化。该方法最重要的特征在简单的一维摩擦接触问题上得到了全面的展示。然后，在具有更复杂载荷的二维多体摩擦接触问题上测试了其鲁棒性和有效性。还给出了选择策略参数的指南，特别是那些驱动缩减基础构建的指南。