Adaptivity and convergence in the Voronoi cell finite element model for analyzing heterogeneous materials

In this paper, an adaptive Voronoi cell finite element model is presented f or analyzing micromechanical response of composites and porous materials. B oth elastic and elastic-plastic materials are considered. Two error measure s, viz. a traction reciprocity error and an error in the kinematic relation , are formulated as indicators of the quality of VCFEM solutions. Based on a posteriori evaluation of these error measures, element adaptation is exec uted in two consecutive stages. In the first stage, displacement function a daptations on the element boundaries and matrix inclusion/void interfaces a re carried out to minimize the corresponding traction reciprocity errors. T his is accomplished through a sequence of h-refinement and spectral p-enric hment strategy in an optimal displacement direction. Following this, an enr ichmcnt of matrix and inclusion stress Functions or (ent)p-adaptation is co nducted to reduce the error in kinematic relations. The complete process im proves convergence characteristics of the VCFEM solution. Numerical analysi s is conducted to examine the potential of the resulting VCFEM code in anal yzing microstructures with different distributions, sizes and shapes of het erogeneities. The method is seen to perform very well for the wide variety of problems solved. (C) 2000 Elsevier Science S.A. All rights reserved.