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<p>This work presents a thermodynamically consistent damage phase-field model incorporating fractional derivatives for the characterization of viscoelastic materials. The proposed framework addresses the complexities of hereditary behavior, finite strains, and thermal influences in materials modeled by a series rheological arrangement based on a consistent and general formulation. Mixed finite element approximations are used to solve the obtained differential equations. Numerical 3D simulations demonstrate the model’s ability to represent a wide range of damage behaviors in both small and large strain regimes, highlighting its potential for studying failure mechanisms in viscoelastic media. Additionally, a Python-based implementation built on open-source libraries is provided to facilitate further use and development.</p>

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Finite-strain damage phase-field model for fractional viscoelastic materials in a series rheological arrangement

  • 期刊论文

  • 发表日期：

    2026年2月2日

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  • Geovane Augusto Haveroth,
  • Thais Clara da Costa Haveroth,
  • Marco Lúcio Bittencourt,
  • José Luiz Boldrini

摘要

This work presents a thermodynamically consistent damage phase-field model incorporating fractional derivatives for the characterization of viscoelastic materials. The proposed framework addresses the complexities of hereditary behavior, finite strains, and thermal influences in materials modeled by a series rheological arrangement based on a consistent and general formulation. Mixed finite element approximations are used to solve the obtained differential equations. Numerical 3D simulations demonstrate the model’s ability to represent a wide range of damage behaviors in both small and large strain regimes, highlighting its potential for studying failure mechanisms in viscoelastic media. Additionally, a Python-based implementation built on open-source libraries is provided to facilitate further use and development.