An approach is proposed to accelerate multiscale simulations of heterogeneous quasi-brittle materials exhibiting an anisotropic damage response. The present technique uses unsupervised machine learning classification based on k-means clustering to select integration points in the macro mesh within an FE2 strategy to track redundant micro nonlinear problems and to avoid unnecessary Representative Volume Element (RVE) calculations. More specifically, a classification vector including strains and internal damage variables is defined for each macro integration point. The macro internal damage variables are constructed using harmonic analysis of damage. At each step of the macro iterations, the integrations points are grouped into clusters and only one nonlinear problem is solved for each cluster. As a result, the computations are accelerated within an FE2 scheme by reducing the total number of RVE problems to be solved. The developed algorithm includes a macro regularization and an arc-length technique to capture macro snap-back due to the softening. Applications are proposed to simulate the response of different heterogeneous quasi-brittle materials with strong anisotropic responses. speed-up factors of the order of 12 to 15 can be achieved without the need to build a database, and without reduced-order modeling approximations at the micro level. Estimates of structural strength can be obtained with Speed-up factors between 45 and 85.

中文翻译：

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用于加速 FE[公式省略] 多尺度裂缝模拟的无监督机器学习分类


提出了一种方法来加速表现出各向异性损伤响应的异质准脆性材料的多尺度仿真。该技术使用基于 k-means 聚类的无监督机器学习分类，在 FE2 策略中选择宏网格中的积分点，以跟踪冗余的微观非线性问题并避免不必要的代表性体积单元 （RVE） 计算。更具体地说，为每个宏积分点定义了一个分类向量，包括应变和内部损伤变量。宏观内部损伤变量是使用损伤的谐波分析构建的。在宏迭代的每个步骤中，积分点被分组到集群中，并且每个集群只求解一个非线性问题。因此，通过减少要解决的 RVE 问题总数，在 FE2 方案中加速计算。开发的算法包括宏正则化和弧长技术，用于捕获由于软化引起的宏回弹。提出了模拟具有强各向异性响应的不同非均质准脆性材料的响应的应用。无需构建数据库即可实现 12 到 15 次的加速因子，也无需在微观层面进行降阶建模近似。结构强度的估计值可以在 45 到 85 之间的加速因子中获得。