Parametric variational principle based elastic-plastic analysis of heterogeneous materials with Voronoi finite element method

Abstract

The Voronoi cell finite element method (VCFEM) is adopted to overcome the limitations of the classic displacement based finite element method in the numerical simulation of heterogeneous materials. The parametric variational principle and quadratic programming method are developed for elastic-plastic Voronoi finite element analysis of two-dimensional problems. Finite element formulations are derived and a standard quadratic programming model is deduced from the elastic-plastic equations. Influence of microscopic heterogeneities on the overall mechanical response of heterogeneous materials is studied in detail. The overall properties of heterogeneous materials depend mostly on the size, shape and distribution of the material phases of the microstructure. Numerical examples are presented to demonstrate the validity and effectiveness of the method developed.

Extended multiscale finite element method for mechanical analysis of heterogeneous materials

“…Figs. 21,22,23,24 show the distributions of microscopic von-Mises stress obtained by the FEM-F and EMsFEM-P with respect to the mesh refinement. As can be seen from the figures, little difference between the two methods can be found even with the coarse grids M × N = 12 × 2, and the results obtained by the EMsEFM-P can converge to the reference values with increasing of the number of elements.…”

“…To circumvent these difficulties, some numerical homogenization methods are proposed and become increasing popular. These methods contain the asymptotic computational homogenization method [8][9][10][11][12][13][14][15][16][17], the multilevel finite element method (FE 2 ) [18,19], the heterogeneous multiscale method (HMM) [20,21], the Voronoi cell method [22,23] and the RVE (representative volume element) method [24][25][26][27] et al Notable among them are the asymptotic computational homogenization method which was firstly proposed by Babuska [28] and Benssousan et al [29] and has been extensively studied (see Refs. [8][9][10][11][12][13][14][15][16][17]).…”

A multiscale method for the numerical analysis of active response characterization of 3D nastic structures

“…On the other hand, many computational multiscale methods were proposed and became increasingly popular. These methods included the computational homogenization method (see [20,23] for reviews and discussions), the multilevel finite element method (FE 2 ) [24], the Voronoi cell method [25,26], the heterogeneous multiscale method (HMM) [27][28][29], and the generalized finite element method [30][31][32] as well as the multiscale finite element type methods which can be used to solve second-order elliptic boundary value scalar field problems with high oscillating coefficients [33][34][35], etc.…”