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.
Stress-driven solution to rate-independent elasto-plasticity with damage at small strains and its computer implementation
Mathematical Institute, Charles University（查理大学数学研究所）；Institute of Thermomechanics, Czech Acad. Sci.（捷克科学院热力学研究所）；Institute of Information Theory and Autom., Czech Acad. Sci.（捷克科学院信息论与自动化研究所）；Institute of Information Theory and Automation, Czech Acad. Sci.（捷克科学院信息论与自动化研究所）；Institute of Mathematics and Biomathematics, Faculty of Science, University of South Bohemia（南波希米亚大学理学院数学与生物数学研究所）
Perfect plasticity with damage and healing at small strains, its modelling, analysis, and computer implementation
Mathematical Institute, Charles University（查尔斯大学数学研究所）；Institute of Thermomechanics, Czech Acad. Sci.（捷克科学院热力学研究所）；Institute of Information Theory and Automation, Czech Academy of Sciences（捷克科学院信息与自动化研究所）；Institute of Mathematics and Biomathematics, Faculty of Science, University of South Bohemia（南波希米亚大学理学院数学与生物数学研究所）
A Finite Element Implementation of a Ductile Damage Model for Small Strains
Gottfried Wilhelm Leibniz University Hannover（汉诺威莱布尼茨大学）；Faculty of Civil Engineering and Geodetic Science（土木与大地测量科学学院）；Institute of Mechanics and Computational Mechanics（力学与计算力学研究所）
An isogemetric analysis formulation for the dynamics of geometrically exact viscoelastic beams and beam systems with arbitrarily curved initial geometry
