Publication details for Dr Charles AugardeBordas, S.P.A., Natarajan, S., Kerfriden, P., Augarde, C.E. , Mahapatra, D.R., Rabczuk, T. & Dal Pont, S. (2011). On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM). International Journal for Numerical Methods in Engineering 86(4-5): 637-666.
- Publication type: Journal papers: academic
- ISSN/ISBN: 0029-5981, 1097-0207
- DOI: 10.1002/nme.3156
- View online: Online version
Author(s) from Durham
By using the strain smoothing technique proposed by Chen et al.  for meshless methods in the
context of the finite element method (FEM), Liu et al.  developed the Smoothed FEM (SFEM).
Although the SFEM is not yet well-understood mathematically, numerical experiments point to
potentially useful features of this particularly simple modification of the FEM: (1) relative insensitivity
to mesh distortion; (2) lack of isoparametric mapping; (3) avoidance of volumetric and shear locking;
(4) suppression of the need to compute the derivatives of the shape functions; (5) possible super-
convergence in the energy norm. To date, the SFEM has only been investigated for bilinear and
Wachspress approximations and limited to linear reproducing conditions.
The goal of this paper is to extend the strain smoothing to higher order elements and to investigate
numerically the convergence properties in which conditions strain smoothing is beneficial to accuracy
and convergence of enriched finite element approximations. We focus on three widely used enrichment
schemes, namely: (a) weak discontinuities; (b) strong discontinuities; (c) near-tip linear elastic fracture
The main conclusion is that strain smoothing in enriched approximation is only beneficial when the
enrichment functions are polynomial [cases (a) and (b)], but that non-polynomial enrichment of type
(c) lead to inferior methods compared to standard enriched FEM (e.g. XFEM).