Efficient Reformulation of the Thermal Higher-order Theory for Fgms with Locally Variable Conductivity

Functionally graded materials are characterized by spatially variable microstructures introduced to satisfy given performance requirements. The graded microstructure gives rise to continuously or discretely changing properties, complicating the analysis of these materials. The majority of the computational techniques use the so-called uncoupled approach which ignores the effect of microstructural gradation by employing specific spatial material property variations that are either assumed or obtained by local homogenization. In contrast, the higher-order theory for functionally graded materials is a coupled approach which takes the effect of microstructural gradation into consideration and does not ignore the local-global interaction of the spatially variable inclusion phase(s). Despite its demonstrated utility, however, the original formulation of the higher-order theory is computationally intensive. Herein, an efficient reformulation of the higher-order theory for thermal problems, based on the local/glo...