A computationally efficient gradient-enhanced healing model for soft biological tissues

Soft biological tissues, such as arterial tissue, have the ability to grow and remodel in response to damage. Computational method plays a critical role in understanding the underlying mechanisms of tissue damage and healing. However, the existing healing model often requires huge computation time and it is inconvenient to implement finite element simulation. In this paper, we propose a computationally efficient gradient-enhanced healing model that combines the advantages of the gradient-enhanced damage model, the homeostatic-driven turnover remodeling model, and the damage-induced growth model. In the proposed model, the evolution of healing-related parameters can be solved explicitly. Additionally, an adaptive time increment method is used to further reduce computation time. The proposed model can be easily implemented in Abaqus, requiring only a user subroutine UMAT. The effectiveness of proposed model is verified through a semi-analytical example, and the influence of the variables in the proposed model is investigated using uniaxial tension and open-hole plate tests. Finally, the long-term development of aneurysms is simulated to demonstrate the potential applications of the proposed model in real biomechanical problems.