Abstract
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.
Highlights
Interest in damage modeling for viscoelastic materials has increased greatly in recent years
We presented a general thermodynamically consistent phasefield model to describe damage in viscoelastic materials
Viscoelasticity is included in the model by using a suitable free-energy potential and a pseudo-potential of dissipation that lead to stress/strain constitutive relation in terms of fractional derivatives with finite strain and ensure the validity of the second principle of thermodynamics
Summary
Interest in damage modeling for viscoelastic materials has increased greatly in recent years. Phase-field models are an interesting concept to deal with material damage due to the ability to describe state changes in a continuum way In other words, they replace the sharp interface by a gradual, but fast, description of the state change induced by the crack propagation; they may couple thermal and deformation processes by taking into account the influence on stored energy of the material [78,91]. There are relations between sharp-crack models and phase field models; an example of an article considering such relations is [80], One important aspect to be considered is the thermodynamic consistency of the phase-field models In this regard, many authors have presented interesting contributions. Miehe et al [66] outlined a framework for phase-field
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