Relaxing the compatibility condition in (extended) finite element methods: applications to fracture and nano-mechanics

Abstract

Recently, novel nite element methods were proposed from the coupling of stabilized conforming nodal integration with the standard nite element method [1]. An overarching theory has been devel- oped in the recent paper [2]. The main premise of this theory is the wish to achieve reliable results using lower order elements, i.e. simple meshes (triangles, tetrahedra). SFEM retains the accuracy and inherit the advantages of triangular and tetrahedral meshes to represent complex geometries and can bene t directly from any advance in automatic remeshing. Furthermore, smoothed FEMs are a lot less sensitive to locking (volumetric and shear) as well as mesh distortion (because Jacobians are not required since no isoparametric mapping is used. In this sense, SFEMs are a way to improve the quality of the results obtained by simplex elements, thereby signi cantly reducing the need for human-intervention in the generation of hexahedral meshes. http://csma2013.csma.fr/resumes/r_6ATKU0V3.pd