Numerical conformal mapping method based Voronoi cell finite element model for analyzing microstructures with irregular heterogeneities

Numerical conformal mapping (NCM) is an effective method for transforming arbitrary polygonal domains into a regular domain such as a unit circle. This paper incorporates NCM-based stress functions in the Voronoi cell finite element model (VCFEM) for modeling microstructures with irregular shaped heterogeneities. Additional stress function components using the multi-resolution wavelet bases are also introduced to enrich stress functions in regions of sharp corners. The resulting enhanced model, termed as NCM–VCFEM, is able to effectively analyze real micrographs of heterogeneous materials with irregular shapes that have considerable effects on the evolution of stresses, strains and local damage. To optimize the use of the expensive NCM–VCFEM elements for the entire microstructure, a method of identification of heterogeneities that cannot be approximated as ellipses is first developed. Subsequently, a tessellation process is devised to accommodate arbitrary shapes in the VCFEM mesh. Validation studies comparing the results of NCM–VCFEM simulations with other numerical and analytical results demonstrate the effectiveness of NCM–VCFEM.