Differential geometry-based thermodynamics derivation of isotropic and anisotropic eikonal non-local gradient damage models using a micromorphic media framework
| Autor: | RIBEIRO NOGUEIRA, Breno, RASTIELLO, Giuseppe, Giry, Cédric, Gatuingt, Fabrice, Callari, Carlo |
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| Přispěvatelé: | Dipartimento di Bioscienze e Territorio (DiBT), Università degli Studi del Molise = University of Molise (UNIMOL), Laboratoire de Mécanique Paris-Saclay (LMPS), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Ecole Normale Supérieure Paris-Saclay (ENS Paris Saclay), DES-Service d’études mécaniques et thermiques (SEMT), CEA, Université Paris-Saclay, F-91191 Gif sur Yvette, France (CEA Saclay) |
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: |
thermodynamics
implicit gradient Eikonal non-local damage anisotropic/isotropic damage differential geometry [SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph] Eikonal non-local damage implicit gradient anisotropic/isotropic damage thermodynamics differential geometry |
| Popis: | The Eikonal non-local damage (ENL) approach models damage as a space-deforming phenomenon that affects the interaction distance between material points. As damage increases, interactions between points decrease, ultimately resulting in no interaction. In the integral version of such an approach, non-local interaction distances between material points are computed by solving a stationary Hamilton-Jacobi equation with a damage-dependent Riemannian metric. In the implicit gradient version of ENL models, the Riemannian metric figures in the Helmholtz equation to be solved for computing the non-local field controlling damage evolution. However, one of the main criticisms of such formulation is the lack of thermodynamics basis in its derivation. This paper presents a thermodynamics derivation of the Eikonal implicit gradient formulation based on differential geometry concepts to overcome this issue. A free-energy potential is defined considering the non-local strain as a morphological descriptor belonging to the abstract differentiable manifold (where the Riemannian metric is defined). Following a micromorphic media framework, the balance equations of the model are obtained. It is shown that the stress tensor and thermodynamic force associated with damage are the sum of standard and additional non-local contributions. It is also shown that the resulting energy dissipation is always positive, thus verifying the Clausium-Duhem inequality. After presenting all development considering second-order anisotropic continuum damage, the isotropic formulation is obtained as a particular case. Finally, a two-dimensional numerical implementation of an isotropic implicit Eikonal non-local gradient damage model is illustrated. Test cases are simulated to show the relocalization features of the considered formulation and its natural capability of naturally representing damage-to-fracture transition for high damage levels. |
| Databáze: | OpenAIRE |
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