Semi-analytical method for computing effective thermoelastic properties of periodic composite materials with ellipsoidal inclusions

The effective properties of thermoelastic composite materials with ellipsoidal inclusions are determined. Inclusions are embedded in a homogeneous matrix, forming a three-dimensional periodic structure. Constituents are assumed to be isotropic materials. The effective properties are evaluated using a semi-analytical approach. In this method, the governing equations of the local problems over a unit cell are obtained via asymptotic homogenization and solved using the finite element method. In the proposed methodology, the local problems within the periodic cell are transformed into boundary value problems defined over one-eighth of the unit cell. This reduction is achieved by implementing the symmetry properties of the unit cell and the involved fields, assuming the periodicity of the microstructure and that the material properties are modeled as even functions with respect to the local coordinate system centered at the unit cell. Then, the effective elastic coefficients ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi mathvariant="bold-italic">C</mml:mi> </mml:mrow> <mml:mi mathvariant="bold-italic">¯</mml:mi> </mml:mover> </mml:mrow> </mml:math> ), thermal expansion coefficients ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi mathvariant="bold-italic">α</mml:mi> </mml:mrow> <mml:mi mathvariant="bold-italic">¯</mml:mi> </mml:mover> </mml:mrow> </mml:math> ), and thermal conductivity ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi mathvariant="bold-italic">κ</mml:mi> </mml:mrow> <mml:mi mathvariant="bold-italic">¯</mml:mi> </mml:mover> </mml:mrow> </mml:math> ) are obtained. Furthermore, a COMSOL Multiphysics program is implemented to compute these effective coefficients.