A damage phase-field model for fractional viscoelastic materials in finite strain

This paper proposes a thermodynamically consistent phase-field damage model for viscoelastic materials following the strategy developed by Boldrini et al. (Methods Appl Mech Eng 312:395–427, 2016). Suitable free-energy and pseudo-potentials of dissipation are developed to build a model leading to a stress-strain relation, under the assumption of finite strain, in terms of fractional derivatives. A novel degradation function, which properly couples stress response and damage evolution for viscoelastic materials, is proposed. We obtain a set of differential equations that accounts for the evolution of motion, damage, and temperature. In the present work, for simplicity, this model is numerically solved for isothermal cases by using a semi-implicit/explicit scheme. Several numerical tests, including fitting with experimental data, show that the developed model accounts appropriately for damage in viscoelastic materials for small and finite strains. Non-isothermal numerical simulations will be considered in future works.