The recently reconstructed higher-order theory for functionally graded materials is further
enhanced by incorporating arbitrary quadrilateral subcell analysis capability through a
parametric formulation. This capability significantly improves the efficiency of modeling
continuous inclusions with arbitrarily-shaped cross sections of a graded material's
microstructure previously approximated using discretization based on rectangular subcells,
as well as modeling of structural components with curved boundaries. Part I of this paper …

In Part I of this communication, the finite-volume theory for functionally graded materials was
further extended to enable efficient analysis of structural components with curved
boundaries, as well as efficient modeling of continuous inclusions with arbitrarily-shaped
cross sections of a graded material's microstructure, previously approximated using
discretizations by rectangular subcells. This was accomplished through a parametric
formulation based on mapping of a reference square subcell onto a quadrilateral subcell …