A coupled higher-order theory for functionally graded composites with partial homogenization

Abstract

In a recent series of papers, the authors have shown that the currently employed micromechanics approach applied to functionally graded materials, based on the concept of a representative volume element (RVE) assumed to exist at every point within the material, may produce erroneous results in the presence of macroscopically nonuniform material properties and large field variable gradients. As a result, a new higher-order theory for functionally graded materials has been developed that explicitly couples the microstructural and macrostructural effects, thereby providing both a rational methodology for analyzing the response of this new class of materials and a means for evaluating the uncoupled RVE-based micromechanics approach. Herein, the new theory is further generalized by combining it with a partial homogenization scheme applied along the nonfunctionally graded directions, while preserving the elements of micro-macrostructural coupling along the graded direction. As a practical consequence, composite plates functionally graded in the through-thickness direction and subjected to a thermal gradient along the same direction can now be analyzed in the presence of imposed average normal stresses in the nongraded inplane directions. Examples dealing with such composite plates are presented that illustrate the effect of partial homogenization on the internal stress fields and inplane moment resultants.