Multiscale systems of plasticity in a data-driven perspective

该项目旨在进一步开发和进一步分析数据驱动方案，以解决时间依赖问题。特别地，在第一个资助期内提出的方案将应用于塑性的双尺度均匀化问题。我们希望将此设置中的方案与FE$^2$-方法进行比较，并沿着以下路线进行开发；一个长远的目标是制定一个数据驱动的FE ^2方法。我们在这个项目中新增了离群值分析：为了更好地理解具有离群值的数据集的方案行为，我们研究了单个离群值的松弛数据集的分析问题。进一步的研究方向包括速率相关系统和可能的应变梯度塑性。

The project aims at the further development and further analysis of a data-driven scheme for a time dependent problem. In particular, the scheme which was suggested in the first funding period is to be applied to two-scale homogenization problems in plasticity. We want to compare the scheme in this setting with FE$^2$-methods and develop it along these lines; one far-set goal is to formulate a data driven FE$^2$-method. We newly include outlier analysis in this project: With the aim of understanding better the behavior of the scheme for a data set with an outlier, we investigate the analytical problem of relaxed data sets for a single outlier. Further research directions include rate-dependent systems and, possibly, strain gradient plasticity.