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

Abstract

In this paper, an adaptive Voronoi cell finite element model is presented for analyzing micromechanical response of composites and porous materials. Both elastic and elastic–plastic materials are considered. Two error measures, 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 executed in two consecutive stages. In the first stage, displacement function adaptations on the element boundaries and matrix–inclusion/void interfaces are carried out to minimize the corresponding traction reciprocity errors. This is accomplished through a sequence of h-refinement and spectral p-enrichment strategy in an optimal displacement direction. Following this, an enrichment of matrix and inclusion stress functions or enr p-adaptation is conducted to reduce the error in kinematic relations. The complete process improves convergence characteristics of the VCFEM solution. Numerical analysis is conducted to examine the potential of the resulting VCFEM code in analyzing microstructures with different distributions, sizes and shapes of heterogeneities. The method is seen to perform very well for the wide variety of problems solved.