From images to physics: Multiphysics modelling of random metallic meshes

Fractal and random conductive networks are increasingly exploited in transparent heaters and smart multifunctional structures due to their inherent scalability, robustness, and efficient transport properties, yet their intrinsic disorder poses major challenges for quantitative modelling. Here we introduce a computationally efficient, image-driven framework for the automated digitisation, reconstruction, and multi-physics analysis of random conductive meshes. High-resolution microscopy images are converted into graph-based network representations via skeletonization, branch tracking, and connectivity refinement, preserving local geometry while drastically reducing degrees of freedom. An analytical model is developed to predict sheet resistance directly from extracted network metrics, enabling rapid, non-destructive electrical characterisation. The digitised networks are further used to perform coupled electro-thermal and electro-thermo-mechanical finite-element simulations. Experimental validation using silver mesh heaters embedded in polymer laminates shows excellent agreement with predicted electrical resistance, temperature evolution, and stiffness modulation under electrical loading. The framework reduces analysis time and enables systematic assessment of structural features, such as dangling branches, on device performance. This approach provides a scalable route for predictive design and optimisation of fractal-based multifunctional electronic materials.