Damage Phase-Field Model for Fractional Derivative-Based Viscoelastic Materials

This work presents a thermodynamically consistent damage phase-field model incorporating fractional derivatives for characterization of viscoelastic materials. The proposed framework addresses the complexities of hereditary behavior, finite strains, and thermal influences in materials modeled by a serial rheological arrangement based on a very consistent and general formulation. Mixed finite element approximations are used to solve the obtained differential equations. Numerical 3D simulations demonstrate the model's ability to represent a wide range of damage behaviors in both small and large strain regimes, highlighting its potential for studying failure mechanisms in viscoelastic media. Additionally, a Python-based implementation built on open-source libraries is provided to facilitate further use and development.