Determination of the effective thermal conductivity of composites under the influence of an imperfect interface using a variational asymptotic-based method

Abstract

This paper provides a detailed examination of the anisotropic thermal conductivity of a two-phase layered composite material with an imperfect interface. The development of a closed-form solution focuses on using the variational asymptotic method (VAM). Highlighting the one-dimensional periodicity of the unit cell, the study includes reduced thermal conduction at the imperfect interface between the two layers of a laminate. In addition to the VAM approach, the research introduces the finite element method (FEM) for the one-dimensional periodicity of the unit cell, for the reduced thermal conduction at the imperfect interface. Validation of both the derived VAM-based closed-form analytical solutions and the FEM solutions, under identical imperfect interface conditions, has been conducted by comparing the results with those present in the literature. The results show satisfactory agreement. Furthermore, the VAM-based analytical solution is extended to unidirectional composites with similar imperfect interface conditions, predicting effective thermal conductivity. These predictions are validated against various literature models, showing significant agreement, especially with lower-bound models. As a practical application, the closed-form solution derived from VAM is used to investigate the influence of an imperfect interface on thermal conduction with changes in volume fraction, providing valuable insights for practical applications.