A novel surrogate model to approximate microscopic behaviour and accelerate concurrent multiscale finite element simulations is proposed. The study serves as a proof of concept, focusing exclusively on 2D, geometric non-linear lattice materials. Despite numerous successful implementations of surrogate modelling techniques in literature, challenges remain, mainly with the black-box nature of most of these models, suffering from lack of interpretability. To tackle these issues, this study reintroduces physics into the model through the use of beam theory in so-called Beam Neural Networks. These networks are tested against a benchmark feed-forward neural network in both interpolation and extrapolation. Although the findings do not satisfy the requirements for practical application, they do indicate that the introduction of beam theory to the model has improved the model's extrapolation ability, suggesting that the proposal has improved robustness and interpretability of the model. Given further optimization, there is promise of Beam Neural Networks to become an useful tool to accelerate concurrent multiscale modelling in the future.

The growing use of composite materials in engineering applications accelerated the demand for computational methods, such as multiscale modeling, to accurately predict their behavior. Combining different materials with target mechanical properties helps achieve optimal structural performance. Nevertheless, the complex nature of composite materials poses several challenges. Current multiscale methods, such as the $\text{FE}^2$ method, are hindered by a computational bottleneck, limiting their widespread industrial adoption. Most of the existing surrogate modeling techniques that address this bottleneck are limited to predicting homogeneous materials or require an extensive dataset. The application of surrogate models in the fracture mechanics field is largely unexplored, where the existing models are highly convoluted.

The goal of this thesis is to apply surrogate modeling to predict cohesive damage in the fracture mechanics field. It focuses on one of the existing techniques using Physically Recurrent Neural Networks (PRNN). The core idea behind PRNNs is to implement the exact material models from the micromodel into the material layer of the network. The PRNN, which incorporates an elastoplastic model in what is referred to as bulk material points has resulted in exceptional performance when predicting elastoplastic behavior in composite materials. The primary objective of this thesis is to extend the existing PRNN to predict the effect of debonding at the fiber-matrix interface while capturing path-dependent behavior and minimizing the size of the training dataset with excellent extrapolation ability.

The fundamental capabilities of the existing PRNN with bulk material points only are evaluated in the microscale cohesive damage framework, particularly when interface elements are implemented at the fiber-matrix interface of the micromodel. This initial step reveals the limitations of the existing architecture and it becomes apparent that all types of nonlinearities present in the micromodel must also be implemented in the network.

This thesis extends the PRNN by incorporating a Cohesive Zone Model (CZM) within the existing material layer. This new architecture introduces cohesive integration points with the CZM along with the bulk integration points. Through model selection, various configurations of bulk and cohesive points are explored, along with different training dataset types and sizes, to maximize predictive accuracy and extrapolation capabilities. It is observed that training with non-monotonic data is required for the network to learn both types of nonlinearities. The limitations of the network's prediction are noted, which are due to the fact that its architecture does not represent the stress homogenization step of the multiscale method. This realization highlights the importance of the layout of the PRNN.

Further study investigates new PRNN architectures to improve the physical representation of the micromodel. The networks are trained on a single curve to select the optimal architecture. The most promising option is discussed in detail, in which the history parameter of the cohesive points is input to the bulk points. The network is proven to provide accurate prediction on a small training dataset when tested on the training dataset. Constraints of the PRNN are discussed and further improvements are recommended to extend the modified PRNN to a larger dataset.

This research contributes to the field of surrogate modeling for composite materials by investigating the predictive capabilities of the PRNNs and exploring new architectures. The results provide a promising outlook for accurately predicting the complex behavior of composite materials, specifically in the context of cohesive microscale damage considering debonding at the fiber-matrix interface. The proposed PRNN has the potential to increase computational efficiency of multiscale modeling in engineering applications.