Thermomechanical modeling of functionally graded materials based on bimaterial fundamental solutions

The Green's function technique has been used to directly calculate the local fields of a functionally graded material (FGM) under thermomechanical loading, thus predicting its effective material properties. For a bi-phase FGM continuously switching the particle and matrix phases, the particle size and material gradation play a complex role in its effective material behavior. Using Eshelby's equivalent inclusion method, particles are simulated by a source of eigen-fields in a bounded bi-layered domain, while the boundary effects are evaluated by the boundary integrals of the fundamental solutions. Using the volume integral of Green's functions, over 10,000 particles are used to simulate an FGM under thermal and mechanical loading, respectively. The dual equivalent inclusion method is used to solve for the temperature and stress fields coupled with temperature loading. The averaged thermomechanical field distribution in the gradation direction is evaluated under different loading conditions. The effective stiffness, thermal expansion coefficient, and heat conductivity significantly change with the loading condition, particle size, and material gradation. The homogenization methods, which approximate an FGM as a continuously graded material with thermoelastic properties depending on the volume fraction only, cannot capture these micromechanical features of FGMs, while the present cross-scale approach with the inclusion-based boundary element method (iBEM) directly evaluates local fields and predicts effective material behaviors with high fidelity and efficiency.