Surrogate-based multiscale analysis of experiments on thermoplastic composites under off-axis loading

In this paper, we present a surrogate-based multiscale approach to model constant strain-rate and creep experiments on unidirectional thermoplastic composites under off-axis loading. In previous contributions, these experiments were modeled through a single-scale micromechanical simulation under the assumption of macroscopic homogeneity. Although efficient and accurate in many scenarios, simulations with low-off axis angles showed significant discrepancies with the experiments. It was hypothesized that the mismatch was caused by macroscopic inhomogeneity, which would require a multiscale approach to capture it. However, full-field multiscale simulations remain computationally prohibitive. To address this issue, we replace the micromodel with a Physically Recurrent Neural Network (PRNN), a surrogate model that combines data-driven components with embedded constitutive models to capture history-dependent behavior naturally. The explainability of the latent space of this network is also explored in a transfer learning strategy that requires no re-training. With the surrogate-based simulations, we confirm the hypothesis raised on the inhomogeneity of the macroscopic strain field and gain insights into the influence of adjustment of the experimental setup with oblique end-tabs. Results from the surrogate-based multiscale approach show better agreement with experiments than the single-scale micromechanical approach over a wide range of settings, although with limited accuracy on the creep experiments, where macroscopic test effects were implicitly taken into account in the material properties calibration.

A Microstructure-based Graph Neural Network for Accelerating Multiscale Simulations

Simulating the mechanical response of advanced materials can be done more accurately using concurrent multiscale models than with single-scale simulations. However, the computational costs stand in the way of the practical application of this approach. The costs originate from microscale Finite Element (FE) models that must be solved at every macroscopic integration point. A plethora of surrogate modeling strategies attempt to alleviate this cost by learning to predict macroscopic stresses from macroscopic strains, completely replacing the microscale models. In this work, we introduce an alternative surrogate modeling strategy that allows for keeping the multiscale nature of the problem, allowing it to be used interchangeably with an FE solver for any time step. Our surrogate provides all microscopic quantities, which are then homogenized to obtain macroscopic quantities of interest. We achieve this for an elasto-plastic material by predicting full-field microscopic strains using a graph neural network (GNN) while retaining the microscopic constitutive material model to obtain the stresses. This hybrid data-physics graph-based approach avoids the high dimensionality originating from predicting full-field responses while allowing non-locality to arise. By training the GNN on a variety of meshes, it learns to generalize to unseen meshes, allowing a single model to be used for a range of microstructures. The embedded microscopic constitutive model in the GNN implicitly tracks history-dependent variables and leads to improved accuracy. We demonstrate for several challenging scenarios that the surrogate can predict complex macroscopic stress-strain paths. As the computation time of our method scales favorably with the number of elements in the microstructure compared to the FE method, our method can significantly accelerate FE2 simulations.