A geometrically inspired constitutive framework for damage and intrinsic self-healing of elastomers

Autonomic interfacial self-healing in elastomers enables their reprocessing and recycling, making them valuable for applications such as ballistic resistance, surface coatings, adhesives, and biomedical materials. This article prescribes a geometry-based damage-healing theory for autonomic healing in elastomers, built on a framework where damage induces an incompatibility in the Euclidean material manifold, transforming it into a Riemannian manifold. Healing restores the Euclidean state through a reversing damage variable or an evolving healing variable. The reversing damage variable models the rebonding mechanism while the healing variable accounts for healing by chain diffusion and entanglement. The model also predicts healing where rebonding is preceded by chain diffusion. The microforce balance governs the evolution of the damage and healing variables, capturing rate-dependent damage and intrinsic temperature-independent healing. The model is validated through numerical simulations, including one-dimensional and two-dimensional simulations, demonstrating accurate predictions of coupling between damage and healing and post-healing mechanical response. The model also predicts the recovery of fracture toughness with healing time in supramolecular elastomers, aligning with experimental data. With minimal parameters, the model is versatile and can easily be used for material design and structural analysis, surpassing existing models in simplicity and predictive capability.