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A nano-composite material can be defined as a composite material where at least one of its constituents' sizes is at the nanoscale. Furthermore, even for a small volume fraction of reinforcements, nanocomposites offer better material physical properties than the classical composites [1]. These good properties can be explained by the increasing of the interface inclusion/matrix ratio. This phenomenon is called size effect, as this ratio increases with a decrease of the size of the reinforcements. Such nanocomposites particularity can be exploited to design smart materials which is an explored way for the development of lightweight structures integrating a maximum of functions. With the increase of the use of nanocomposites, numerical and analytical tools are necessary to understand and predict their multi-physical behaviors.
The nanocomposite models have to take account the size effect. In the case of elastic materials, the interface can be considered as a thin elastic layer joining the matrix and inclusions. Using asymptotic development in these thin regions [2], a stress-strain relationship of the matrix-inclusion interface can be introduced. Thanks to the generalized Young-Laplace equation that governs the matrix-inclusion interface equilibrium, the size effect can be introduced in micromechanical models.
Focusing on homogenization, the analytical solutions of the effective material parameters require simple inclusions geometry (spherical, cylindrical) and are often limited to elastic behaviors. To overcome such constraints, numerical approaches have been proposed in the literature to handle more complex inclusions geometries and non-linear behaviors. To the best of our knowledge, only few studies have been carried out in the scope of thermo-elastic materials with imperfect interfaces. In this work, the finite element method using interface elements [3,4] is considered without extra degrees of freedom to study the imperfect coherent interface influence on the effective moduli for a thermo-elastic material. For the numerical analysis, a convergence study is performed for multiple homogenization schemes with different boundary conditions.
