A node-based smoothed finite element method (NS-FEM) for upper bound solution to visco-elastoplastic analyses of solids using triangular and tetrahedral meshes

T. Nguyen-Thoi, H. C. Vu-Do, Timon Rabczuk, H. Nguyen-Xuan

Research output: Contribution to journalArticle

110 Citations (Scopus)


A node-based smoothed finite element method (NS-FEM) was recently proposed for the solid mechanics problems. In the NS-FEM, the system stiffness matrix is computed using the smoothed strains over the smoothing domains associated with nodes of element mesh. In this paper, the NS-FEM is further extended to more complicated visco-elastoplastic analyses of 2D and 3D solids using triangular and tetrahedral meshes, respectively. The material behavior includes perfect visco-elastoplasticity and visco-elastoplasticity with isotropic hardening and linear kinematic hardening. A dual formulation for the NS-FEM with displacements and stresses as the main variables is performed. The von-Mises yield function and the Prandtl-Reuss flow rule are used. In the numerical procedure, however, the stress variables are eliminated and the problem becomes only displacement-dependent. The numerical results show that the NS-FEM has higher computational cost than the FEM. However the NS-FEM is much more accurate than the FEM, and hence the NS-FEM is more efficient than the FEM. It is also observed from the numerical results that the NS-FEM possesses the upper bound property which is very meaningful for the visco-elastoplastic analyses which almost have not got the analytical solutions. This suggests that we can use two models, NS-FEM and FEM, to bound the solution, and can even estimate the global relative error of numerical solutions.

Original languageEnglish
Pages (from-to)3005-3027
Number of pages23
JournalComputer Methods in Applied Mechanics and Engineering
Issue number45-48
Publication statusPublished - 2010 Nov 15
Externally publishedYes



  • Finite element method (FEM)
  • Meshfree methods
  • Node-based smoothed finite element method (NS-FEM)
  • Numerical methods
  • Upper bound
  • Visco-elastoplastic analyses

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)

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