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

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.pdf