A unified phase field model for continuous damage and chemically driven healing in self-healing composites

Abstract

Self-healing composites hold transformative potential for engineering structures by enabling autonomous damage repair, thereby substantially enhancing the damage tolerance and extending service life. This study develops a unified continuum phase-field model to systematically characterize the intrinsic healing mechanisms in such composites. The model fundamentally incorporates the diffusion of healing agents driven by chemical energy and integrates both damage evolution and healing recovery within a variational framework base on free energy minimization. A phase-field variable captures the diffusive damage state, while an independent healing field variable quantifies the restoration of mechanical properties. Finally, the damage and healing status of the material are uniformly described by using the effective damage degree variable. Governing equations are derived rigorously via the free energy minimization variational principle, ensuring thermodynamic consistency. A key advancement is the incorporation of stress-state regulation on healing, which accurately captures compressive-stress accelerated crack closure and tensile-stress inhibited healing behavior. For numerical implementation, customized user subroutines are developed in Abaqus, establishing a fully coupled solution scheme for healing dynamics, damage phase field, and displacement field. The model is validated through numerical simulations of healing performance in tapered double cantilever beams, and by reproducing the complete damage-healing trajectory in nacreous composites, including crack initiation, propagation, and subsequent healing. The results demonstrate that the model effectively captures crack growth and healing behaviors in composites with complex architectures, consequently providing a robust theoretical basis to guide the design and optimization of self-healing composites.