  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.
