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Re: XFEM with second order hexahedral and tetrahedral elements

From: yves . renard
Subject: Re: XFEM with second order hexahedral and tetrahedral elements
Date: Mon, 5 Jun 2023 20:43:46 +0200 (CEST)

Dear Vikram,

There is a priori no problem using the Xfem with quadratic elements in Getfem, for both hexahedral or tetrahedral elements. The enrichement with the Heaviside like function corresponds to cut-elements and is optimal in both situations. I suppose that the limitation in ABAQUS is simply due to the fact that it has not been implemented for hexahedral elements (the only trick is the decomposition of cut elements for integration purpose which is different in the two cases). 

Concerning now the enrichment with singular functions at the crack tip/ front, it depends on how the transition is made between the enriched zone and th non-enriched zone. If nothing special is done (occurence of wath is called by some authors of blended elements), the partition of unity used will accomodate to approach a cut-off function, so that the fact to use quadratic elements can lead to  a better convergence (quadratic convergence). If the singular function for the enrichement are multiplied by a regular cut-off function whose support is inside the enriched zone, there is no need of a quadratic partition of unity (because what is to be approximated is more or less a constant in that case).

Best regards,


De: "Bhamidipati, Vikram" <>
À: "getfem-users" <>
Envoyé: Samedi 3 Juin 2023 00:31:28
Objet: XFEM with second order hexahedral and tetrahedral elements

Dear Getfem-users,



I am asking this question here since there are developers here who also wrote some important papers on using XFEM for fracture mechanics applications. My question is concerning using second order (quadratic) tetrahedral and hexahedral elements with XFEM. Can the partition of unity be chosen as linear Lagrange shape functions for the enrichment terms along with a fixed area asymptotic enrichment and expect a second order convergence? Or should the partition of unity be second order as well? Also is there any difference in how XFEM applies to quadratic hexahedral elements vs quadratic tetrahedral elements? I ask this because it seems like Abaqus software does not seem to support XFEM for quadratic hex elements but does support quadratic tet elements. Does anyone know why? Does this have anything to do with level set computation for 3D? For Getfem is XFEM supported for both hex and tet quadratic elements?


Thank you,








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Vikram Bhamidipati, PhD

Senior Research Engineer,

Computational Materials Integrity

Southwest Research Institute



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