Micromechanics-based thermoelastic model for functionally graded particulate materials with particle interactions

H. M. Yin, G. H. Paulino, W. G. Buttlar, L. Z. Sun

Research output: Contribution to journalArticlepeer-review


Thermoelastic behavior of functionally graded particulate materials is investigated with a micromechanical approach. Based on a special representative volume element constructed to represent the graded microstructure of a macroscopic material point, the relation between the averaged strains of the particle and matrix phases is derived with pair-wise particle interactions, and a set of governing equations for the thermoelastic behavior of functionally graded materials is presented. The effective coefficient of thermal expansion at a material point is solved through the overall averaged strain of two phases induced by temperature change under the stress-free condition, and is shown to exhibit a weak anisotropy due to the particle interactions within the graded microstructure. When the material gradient is eliminated, the proposed model predicts the effective coefficient of thermal expansion for uniform composites as expected. If the particle interactions are disregarded, the proposed model recovers the Kerner model. The proposed semi-analytical scheme is consistent and general, and can handle any thermal loading variation. As examples, the thermal stress distributions of graded thermal barrier coatings are solved for two types of thermal loading: uniform temperature change and steady-state heat conduction in the gradation direction.

Original languageEnglish (US)
Pages (from-to)132-160
Number of pages29
JournalJournal of the Mechanics and Physics of Solids
Issue number1
StatePublished - Jan 2007
Externally publishedYes


  • Constitutive behavior
  • Functionally graded materials
  • Microstructures
  • Particulate reinforced material
  • Thermal stress

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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