  This paper proposes a thermodynamically consistent phase-field damage model
for viscoelastic materials. 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.
