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-elemen t analysis and a recently developed higher-order theory for functional ly graded materials subjected to a through-thickness temperature gradi ent. In contrast to existing micromechanical theories that utilize cla ssical (i.e. uncoupled) homogenization schemes to calculate micro-leve l and macro-level stress and displacement fields in materials with uni form or nonuniform fibre spacing (i.e. functionally graded materials), the new theory explicitly couples the microstructural details with th e macrostructure of the composite. Previous thermo-elastic analysis ha s demonstrated that such coupling is necessary when: the temperature g radient is large with respect to the dimension of the reinforcement; t he characteristic dimension of the reinforcement is large relative to the global dimensions of the composite and the number of reinforcing f ibers or inclusions is small. In these circumstances, the standard mic romechanical analyses based on the concept of the representative volum e element used to determine average or effective properties of macrosc opically homogeneous composites produce questionable results. The comp arison between the results of the finite-element method and the higher -order theory presented herein establishes the theory's accuracy in pr edicting thermal and stress fields within composites with a finite num ber of fibers in the thickness direction subjected to a through-thickn ess thermal gradient. (C) 1997 Elsevier Science Limited.