Liya Gaynutdinova

Liya Gaynutdinova, Petr Havlásek, Ondřej Rokoš et al.

This paper introduces a deep learning approach for predicting time-dependent full-field damage in concrete. The study uses an auto-regressive U-Net model to predict the evolution of the scalar damage field in a unit cell given microstructural geometry and evolution of an imposed shrinkage profile. By sequentially using the predicted damage output as input for subsequent predictions, the model facilitates the continuous assessment of damage progression. Complementarily, a convolutional neural network (CNN) utilises the damage estimations to forecast key mechanical properties, including observed shrinkage and residual stiffness. The proposed dual-network architecture demonstrates high computational efficiency and robust predictive performance on the synthesised datasets. The approach reduces the computational load traditionally associated with full-field damage evaluations and is used to gain insights into the relationship between aggregate properties, such as shape, size, and distribution, and the effective shrinkage and reduction in stiffness. Ultimately, this can help to optimize concrete mix designs, leading to improved durability and reduced internal damage.

Liya Gaynutdinova, Martin Doškář, Ondřej Rokoš et al.

Physics-informed neural networks (PINNs) have shown promise in solving partial differential equations (PDEs) relevant to multiscale modeling, but they often fail when applied to materials with discontinuous coefficients, such as media with piecewise constant properties. This paper introduces a dual formulation for the PINN framework to improve the reliability of the homogenization of periodic thermo-conductive composites, for both strong and variational (weak) formulations. The dual approach facilitates the derivation of guaranteed upper and lower error bounds, enabling more robust detection of PINN failure. We compare standard PINNs applied to smoothed material approximations with variational PINNs (VPINNs) using both spectral and neural network-based test functions. Our results indicate that while strong-form PINNs may outperform VPINNs in controlled settings, they are sensitive to material discontinuities and may fail without clear diagnostics. In contrast, VPINNs accommodate piecewise constant material parameters directly but require careful selection of test functions to avoid instability. Dual formulation serves as a reliable indicator of convergence quality, and its integration into PINN frameworks enhances their applicability to homogenization problems in micromechanics.