We present a Data-Driven framework for multiscale mechanical analysis of materials. The proposed framework relies on the Data-Driven formulation in mechanics (Kirchdoerfer and Ortiz 2016), with the material data being directly extracted from lower-scale computations. Particular emphasis is placed on two key elements: the parametrization of material history, and the optimal sampling of the mechanical state space. We demonstrate an application of the framework in the prediction of the behavior of sand, a prototypical complex history-dependent material. In particular, the model is able to predict the material response under complex nonmonotonic loading paths, and compares well against plane strain and triaxial compression shear banding experiments.

我们提出了一种用于数据的多尺度机械分析的数据驱动框架。拟议的框架依赖于力学中的数据驱动公式（Kirchdoerfer和Ortiz 2016），材料数据直接从低级计算中提取。特别强调两个关键要素：材料历史的参数化和机械状态空间的最佳采样。我们展示了该框架在预测沙子行为方面的应用，该行为是典型的复杂历史依赖材料。特别是，该模型能够预测复杂的非单调加载路径下的材料响应，并且可以很好地与平面应变和三轴压缩剪切带实验进行比较。