Physically Based Machine Learning for the Multi-Objective Optimal Design of Partially Recycled Materials: The Case Study of Rubber Resources in the Automotive industry

This study presents a novel micromechanical-optimization framework that extends the traditional Halpin-Tsai model beyond mechanical properties to incorporate cost and environmental impact indicators, enabling quantitative sustainability assessment of recycled-additive mixtures. The extended multi-phase formulation provides a physically interpretable link between the intrinsic characteristics of recycled matrices, reinforcing additives, and life-cycle and market metrics, while remaining analytically tractable. Coupled with a physics-informed multi-objective optimization algorithm, the framework identifies optimal additive strategies that recover target properties of recycled materials under economic and regulatory constraints. A case study on end-of-life tire rubber demonstrates the model's predictive capability and flexibility for practical calibration. The proposed approach offers a transparent and scalable tool for circular material design and decision-making, with potential applicability to other recycled material systems enhanced with functional additives, such as compatibilizers in recycled polymers, alloying elements in metal scrap, or mineral/polymeric admixtures in construction waste.