弹性固体的机器学习加速FE $^2$均匀化算法
A machine learning accelerated FE$^2$ homogenization algorithm for elastic solids
摘要：
用于多尺度建模的FE $^2$均匀化算法在宏观尺度和微观尺度（由代表性体积元素表示）之间迭代，直到在宏观尺度加载的每个增量处实现收敛。两个尺度之间的信息交换发生在宏观有限元离散的高斯点处。微尺度的问题也解决了使用有限元的飞行，从而使算法计算复杂的微结构昂贵。我们调用机器学习建立的RVE边值问题的输入输出因果关系，使用神经网络框架。这将RVE呈现为黑盒，其从宏尺度获得信息作为输入，并将信息返回到宏尺度作为输出，从而消除了在RVE级别对动态有限元求解的需要。该框架具有显著加速FE $^2$算法的潜力。
英文摘要：
The FE$^2$ homogenization algorithm for multiscale modeling iterates between the macroscale and the microscale (represented by a representative volume element) till convergence is achieved at every increment of macroscale loading. The information exchange between the two scales occurs at the gauss points of the macroscale finite element discretization. The microscale problem is also solved using finite elements on-the-fly thus rendering the algorithm computationally expensive for complex microstructures. We invoke machine learning to establish the input-output causality of the RVE boundary value problem using a neural network framework. This renders the RVE as a blackbox which gets the information from the macroscale as an input and gives information back to the macroscale as output, thereby eliminating the need for on-the-fly finite element solves at the RVE level. This framework has the potential to significantly accelerate the FE$^2$ algorithm.
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