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arXiv · 2201.04002

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

Thaís C. da Costa Haveroth·Geovane A. Haveroth·Marco L. Bittencourt·José L. Boldrini
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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.

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Thaís C. da Costa Haveroth, Geovane A. Haveroth, Marco L. Bittencourt, José L. Boldrini. 2022-01-11. A Damage Phase-Field Model for Fractional Viscoelastic Materials in Finite Strain. https://arxiv.org/abs/2201.04002

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