A Damage Phase-Field Model for Fractional Viscoelastic Materials in Finite Strain

TL;DR

This paper introduces a thermodynamically consistent phase-field damage model for fractional viscoelastic materials under finite strain, capturing damage evolution and stress response with fractional derivatives and numerical validation.

Contribution

It presents a novel damage model coupling stress and damage evolution using fractional derivatives, with a new degradation function and numerical implementation for viscoelastic materials.

Findings

Model accurately fits experimental damage data.

Captures damage behavior under small and finite strains.

Provides a framework for non-isothermal extensions.

Abstract

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.