In the paper, we present an integrated data-driven modeling framework based on process modeling, material homogenization, mechanistic machine learning, and concurrent multiscale simulation. We are interested in the injection-molded short fiber reinforced composites, which have been identified as key material systems in automotive, aerospace, and electronics industries. The molding process induces spatially varying microstructures across various length scales, while the resulting strongly anisotropic and nonlinear material properties are still challenging to be captured by conventional modeling approaches. To prepare the linear elastic training data for our machine learning tasks, Representative Volume Elements (RVE) with different fiber orientations and volume fractions are generated through stochastic reconstruction. More importantly, we utilize the recently proposed Deep Material Network (DMN) to learn the hidden microscale morphologies from data. With essential physics embedded in its building blocks, this data-driven material model can be extrapolated to predict nonlinear material behaviors efficiently and accurately. Through the transfer learning of DMN, we create a unified process-guided material database that covers a full range of geometric descriptors for short fiber reinforced composites. Finally, this unified DMN database is implemented and coupled with macroscale finite element model to enable concurrent multiscale simulations. From our perspective, the proposed framework is also promising in many other emergent multiscale engineering systems, such as additive manufacturing and compressive molding.
An FE-DMN method for the multiscale analysis of thermomechanical composites
我们将FE-DMN方法扩展到复合材料的完全耦合热力学双尺度模拟。特别地，宏观有限元模型的每个高斯点配备有深层材料网络（DMN）。这样的DMN作为一个高保真度的代理模型的全场解决方案的微观尺度上的非弹性，非等温成分。基于Chatzigeorgiou等人的均质化框架[Int. J. Plast，第81卷，18- 39，2016]，我们通过结合双向热机械耦合将DMN的框架扩展到热机械复合材料，即，从宏观尺度到微观尺度的耦合，反之亦然，进入框架。我们提供的细节，我们的方法作为一个用户材料子程序（UMAT）的有效实施。我们在微观尺度上验证了我们的方法，并表明DMNs预测的有效应力，有效耗散和宏观绝对温度的变化具有很高的精度。经过验证，我们证明了我们的方法的能力，同时热机械双尺度模拟的宏观组件规模。
Multiscale Structural Reliability Analysis in high dimensions with Tensor Trains and Physics-Augmented Neural Networks
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of Sydney（悉尼大学）；The Oden Institute of Computational Science and Engineering, The University of Texas at Austin（德克萨斯大学奥斯汀分校奥登计算科学与工程研究所）
