a b s t r a c tEstablishing structure-property relationships for nanoparticle/polymer composites is a fundamental task for a reliable design of such new systems. A micromechanical analytical model is proposed in the present work, in order to address the problem of stiffness and yield stress prediction in the case of nanocomposites consisting of silica nanoparticles embedded in a polymer matrix. It takes into account an interphase corresponding to a perturbed region of the polymer matrix around the nanoparticles. Its modulus is continuously graded from that of the silica nanoparticle to that of the polymer matrix. Considering the thickness of the third phase as a characteristic length scale, the influence of particle size on the overall nanocomposite behaviour is examined. The key role of the interphase on both the overall stiffness and yield stress is studied and the model output is compared to experimental data of various silica spherical nanoparticle/polymer composites extracted from the literature. The model is also used to examine the influence of interphase features on the overall nanocomposite behaviour. A finite element analysis is then achieved and the numerical results are validated using the analytical predictions. Local stress and strain distributions are analysed in order to understand the phenomena occurring at the nano-scale.

To provide a better understanding of the relationship between nanostructure and overall material stiffness in the case of polymer/clay nanocomposites, both analytical and finite element modeling were considered. A micromechanical analytical approach based on a multiscale framework is presented in which special attention is devoted to the constrained region around reinforcements. The thickness of the constrained region is seen as a characteristic length scale and the effect of particle size is explicitly introduced in the model. Moreover, the constrained region presents graded properties. The hierarchical morphology of intercalated silicate stacks is also explicitly introduced in the micromechanical model from an equivalent stiffness method in which the silicate stacks are replaced by homogeneous particles with constructed equivalent anisotropic stiffness. The orientational averaging process is used to derive the overall stiffness tensor of nanocomposite materials containing randomly oriented reinforcements. The respective influence of volume fraction, aspect ratio, size and orientation of the reinforcements, matrix properties, number of silicate layers per stack, and interlayer spacing on the overall nanocomposite stiffness is analyzed. The overall stiffness of polymer/clay nanocomposite systems is also evaluated by means of finite element simulations and the results compare favorably with model predictions. From an experimental point of view, relevant morphological and mechanical data were obtained on polyamide-6 nanocomposites prepared using a modified montmorillonite Cloisite 30B and an unmodified sodium montmorillonite Cloisite Na þ . The amount of constrained region around reinforcements was estimated using results issued from dynamic mechanical analyses and differential scanning calorimetry. Comparison to the model clearly underlines the contribution of the constrained region to the stiffness improvement.