Physics-informed neural networks for predicting homogenized effective properties of one-dimensional composites with imperfect interface

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Abstract
The increasing demand for materials with enhanced functionalities has driven the development of multiscale methodologies capable of predicting their effective properties from their heterogeneous microstructure and the interfacial interactions. In this work, we develop a coupled multiscale framework combining the two-scale asymptotic homogenization method with physics-informed neural networks to predict the effective behavior of one-dimensional periodic composites with imperfect interface. Physics-informed neural networks solve the local cell problems arising from the asymptotic homogenization method, and the resulting local fields are subsequently used to compute the homogenized coefficients and reconstruct the formal asymptotic approximation. To capture field discontinuities induced by the imperfect interface, a dual-network architecture with suitable optimization strategies is employed. The one-dimensional configuration serves as a reference framework for systematic numerical validation of the asymptotic homogenization method–physics-informed neural networks methodology through direct comparison with the analytical homogenization solution. Numerical experiments consider different interface parameters κ from 1 to 1 0 7 , stiffness contrasts E 1 ∕ E 2 from 1 to 100, with additional calculations up to 1000, and volume fractions V 1 from 0.1 to 0.9. The predicted effective Young’s modulus shows close agreement with the analytical solution, with relative errors ranging from 6 . 21 × 1 0 − 12 to 3 . 55 × 1 0 − 6 , while reconstructed displacement fields for ε = 0 . 01 − 0 . 5 reproduce the analytical solution with root-mean-square errors between 1 . 50 × 1 0 − 11 and 5 . 1 × 1 0 − 7 . Convergence histories show accurate solutions for all tested configurations, while higher stiffness contrasts increase the sensitivity of the physics-informed neural network accuracy to the combined material and interface parameters. These results demonstrate that the proposed methodology provides an accurate computational framework for predicting the effective behavior of one-dimensional composites with an imperfect interface.
Funding Information
  • SECIHTI (CF-2023-G-792)

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