Physical interpretation of asymptotic expansion homogenization method for the thermomechanical problem

For the thermomechanical problem of periodical composite structures, mathematical formulation of asymptotic expansion homogenization (AEH) method up to any expansion is derived. This is done by constructing a full decoupling form for expansion terms of each order. The weighted residual method is utilized to convert the mathematical formulations into matrix forms for convenient use in the standard finite element method. Elastic and thermal characteristic displacements are compared to elastic and thermal quasi displacements, respectively. Then, the self-balancing property of the quasi load corresponding to quasi displacements, dimensional analysis method, and geometric intuitiveness method of the quasi load are utilized to reveal the physical interpretations of elastic and thermal characteristic displacements and expansion terms of each order. The necessity of the second-order expansion term for the micro analysis of periodical composite structures is emphasized. Numerical results validate the formulations and physical interpretation of AEH for the thermomechanical problem and lay the foundation for its application.