Nitsche Method for resolving boundary conditions on embedded interfaces using XFEM in Code Aster

TL;DR

This paper presents a Nitsche method combined with XFEM for accurately imposing boundary conditions on embedded interfaces, implemented in the open-source Code-Aster platform, enhancing modeling of interfaces without meshing cracks.

Contribution

It introduces a novel integration of Nitsche's method with XFEM for boundary conditions on embedded interfaces, implemented in Code-Aster, facilitating improved interface modeling.

Findings

Effective enforcement of boundary conditions on embedded interfaces.

Implementation in Code-Aster demonstrates practical applicability.

Enhanced accuracy in interface problems without meshing cracks.

Abstract

As X-FEM approximation does not need meshing of the crack, the method has garnered a lot of attention from industrial point of view. This thesis report summarises some of the concepts involved in Nitsche approach for resolving boundary conditions in embedded interfaces using XFEM. We consider here cases in which the jump of a field across the interface is given, as well as cases in which the primary field on the interface is given. We will first derive the basics of Nitsche method and then discretize it with X-FEM using shifted basis enrichment. We will then implement this on an open source platform, Code-Aster.