We consider a one-dimensional fracture problem modelled using either the phase-field or lip-field approach. In both cases, we optimise the incremental potential with respect to the displacement and damage fields and the nodal coordinates of the mesh. This is thus a variational mesh study. We observe that, as the damage reaches its maximum value, the optimisation drives the most damaged element to zero size as the damage reaches its maximum value. This peculiar element provides a precise displacement jump representation as the bar breaks. The overall solution is also shown to be much more accurate than the fixed mesh solution. This work forms part of an exploration into the capabilities of extreme meshes in computational mechanics (X-Mesh).
Nous considérons un problème unidimensionnel de rupture modélisé à l’aide de l’approche phase-field ou lip-field. Dans les deux cas, nous optimisons le potentiel incrémental par rapport aux champs de déplacement et d’endommagement ainsi qu’aux coordonnées nodales du maillage. Il s’agit donc d’une étude variationnelle du maillage. Nous observons que, lorsque l’endommagement atteint sa valeur maximale, l’optimisation réduit à zéro la taille de l’élément le plus endommagé. Cet élément particulier permet une représentation précise du saut de déplacement lorsque la barre se rompt. La solution globale s’avère également beaucoup plus précise qu’avec un maillage fixe. Ce travail s’inscrit dans une exploration des capacités des maillages extrêmes en mécanique numérique (X-Mesh).
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Mots-clés : Phase-field, lip-field, fissure franche, X-Mesh
Nicolas Moës 1; Benoît Lé 2; Nicolas Chevaugeon 3; Jean-François Remacle 4
CC-BY 4.0
@article{CRMECA_2025__353_G1_1027_0,
author = {Nicolas Mo\"es and Beno{\^\i}t L\'e and Nicolas Chevaugeon and Jean-Fran\c{c}ois Remacle},
title = {Phase-field and lip-field approaches for fracture with extreme mesh deformation {(X-Mesh):} a one-dimensional study},
journal = {Comptes Rendus. M\'ecanique},
pages = {1027--1051},
year = {2025},
publisher = {Acad\'emie des sciences, Paris},
volume = {353},
doi = {10.5802/crmeca.318},
language = {en},
}
TY - JOUR AU - Nicolas Moës AU - Benoît Lé AU - Nicolas Chevaugeon AU - Jean-François Remacle TI - Phase-field and lip-field approaches for fracture with extreme mesh deformation (X-Mesh): a one-dimensional study JO - Comptes Rendus. Mécanique PY - 2025 SP - 1027 EP - 1051 VL - 353 PB - Académie des sciences, Paris DO - 10.5802/crmeca.318 LA - en ID - CRMECA_2025__353_G1_1027_0 ER -
%0 Journal Article %A Nicolas Moës %A Benoît Lé %A Nicolas Chevaugeon %A Jean-François Remacle %T Phase-field and lip-field approaches for fracture with extreme mesh deformation (X-Mesh): a one-dimensional study %J Comptes Rendus. Mécanique %D 2025 %P 1027-1051 %V 353 %I Académie des sciences, Paris %R 10.5802/crmeca.318 %G en %F CRMECA_2025__353_G1_1027_0
Nicolas Moës; Benoît Lé; Nicolas Chevaugeon; Jean-François Remacle. Phase-field and lip-field approaches for fracture with extreme mesh deformation (X-Mesh): a one-dimensional study. Comptes Rendus. Mécanique, Volume 353 (2025), pp. 1027-1051. doi: 10.5802/crmeca.318
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