Pull-off force prediction in viscoelastic adhesive Hertzian contact by physics augmented machine learning

Predicting the adhesive properties of viscoelastic Hertzian contacts is crucial for diverse engineering applications, including robotics, biomechanics, and advanced material design. This study introduces a novel physics-augmented machine learning (PA-ML) framework as a hybrid approach to study the maximum adherence force of a Hertzian indenter unloaded from a viscoelastic substrate, bridging the gap between analytical models and data-driven solutions. The PA-ML model is capable of rapidly predicting the pull-off force in an Hertzian profile unloaded from a broad band viscoelastic material, with varying Tabor parameter, preload and retraction rate. Compared to previous models, the PA-ML approach provides fast yet accurate predictions in a wide range of conditions, properly predicting the effective surface energy and the work-to-pull-off. The integration of the analytical model provides critical guidance to the PA-ML framework, supporting physically consistent predictions. We demonstrate that physics augmentation enhances predictive accuracy, reducing mean squared error (MSE) while increasing model interpretability. We provide data-driven and PA-ML models for real-time predictions of the adherence force in soft materials like silicons and elastomers opening to the possibility to integrate PA-ML into materials and interface design. The models are openly available on Zenodo and GitHub.