Evaluation of the higher-order theory for functionally graded materials via the finite-element method

A comparison is presented between the predictions of the finite-element analysis and a recently developed higher-order theory for functionally graded materials subjected to a through-thickness temperature gradient. In contrast to existing micromechanical theories that utilize classical (i.e. uncoupled) homogenization schemes to calculate micro-level and macro-level stress and displacement fields in materials with uniform or nonuniform fibre spacing (i.e. functionally graded materials), the new theory explicitly couples the microstructural details with the macrostructure of the composite. Previous thermo-elastic analysis has demonstrated that such coupling is necessary when: the temperature gradient is large with respect to the dimension of the reinforcement; the characteristic dimension of the reinforcement is large relative to the global dimensions of the composite and the number of reinforcing fibers or inclusions is small. In these circumstances, the standard micromechanical analyses based on the concept of the representative volume element used to determine average or effective properties of macroscopically homogeneous composites produce questionable results. The comparison between the results of the finite-element method and the higher-order theory presented herein establishes the theory's accuracy in predicting thermal and stress fields within composites with a finite number of fibers in the thickness direction subjected to a through-thickness thermal gradient. (C) 1997 Elsevier Science Limited.