Thermo-inelastic analysis of functionally graded materials: Inapplicability of the classical micromechanics approach

The standard micromechanical approach used to analyse the response of functionally graded materials is to decouple the local and global effects by assuming the existence of a representative volume element (RVE) at every point within the composite. In this paper, a new higher order micromechanical theory for the inelastic response of functionally graded materials (HOTFGM), which couples the local and global effects, is used to assess the limits of applicability of the standard uncoupled approach. Comparison of local stresses in the fiber and matrix phases of composites with a finite number of uniformly and nonuniformly spaced fibers in the through-thickness direction subjected to uniform and nonuniform temperature fields, obtained with HOTFGM and the standard RVE-based approach, illustrates the inaccuracy of the standard analysis in the presence of temperature-dependent and inelastic behavior of the matrix phase.