In this paper, we demonstrate for the first time how the Integrated Finite Element Neural Network (I-FENN) framework, previously proposed by the authors, can efficiently simulate the entire loading history of non-local gradient damage propagation. To achieve this goal, we first adopt a Temporal Convolutional Network (TCN) as the neural network of choice to capture the history-dependent evolution of the non-local strain in a coarsely meshed domain. The quality of the network predictions governs the computational performance of I-FENN, and therefore we perform an extended investigation aimed at enhancing them. We explore a data-driven vs. physics-informed TCN setup to arrive at an optimum network training, evaluating the network based on a coherent set of relevant performance metrics. We address the crucial issue of training a physics-informed network with input data that span vastly different length scales by proposing a systematic way of input normalization and output un-normalization. We then integrate the trained TCN within the nonlinear iterative FEM solver and apply I-FENN to simulate the damage propagation analysis. I-FENN is always applied in mesh idealizations different from the one used for the TCN training, showcasing the framework's ability to be used at progressively refined mesh resolutions. We illustrate several cases that I-FENN completes the simulation using either a modified or a full Newton-Raphson scheme, and we showcase its computational savings compared to both the classical monolithic and staggered FEM solvers. We underline that we satisfy very strict convergence criteria for every increment across the entire simulation, providing clear evidence of the robustness and accuracy of I-FENN. All the code and data used in this work will be made publicly available upon publication of the article.

翻译：本文首次展示了作者先前提出的集成有限元神经网络（I-FENN）框架如何高效模拟非局部梯度损伤传播的完整加载历程。为实现此目标，我们首先采用时序卷积网络（TCN）作为神经网络模型，以捕获粗网格域中非局部应变的历史依赖演化过程。网络预测质量直接影响I-FENN的计算性能，因此我们开展了旨在提升预测性能的扩展研究。我们探究了数据驱动与物理信息约束两种TCN配置方案以优化网络训练，并基于一套连贯的相关性能指标对网络进行评价。针对采用跨越多尺度量级的输入数据训练物理信息网络的关键难题，我们提出了一种规范化的输入归一化与输出反归一化方法。随后将训练好的TCN集成到非线性迭代有限元求解器中，应用I-FENN模拟损伤传播分析。I-FENN始终在与TCN训练所用网格理想化不同的网格上应用，展示了该框架在渐进加密网格分辨率下的适用性。我们展示了I-FENN采用修正或全牛顿-拉夫逊方案完成仿真的多个案例，并证明了相较经典整体式和交错式有限元求解器的计算效率优势。需要强调的是，我们在整个仿真的每个增量步均满足非常严格的收敛准则，为I-FENN的鲁棒性和准确性提供了明确证据。本文使用的所有代码和数据将在论文发表后公开。