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.