Advanced theoretical and numerical multiscale modeling of cohesion/adhesion interactions in continuum mechanics and its applications for filled nanocomposites

In this paper, a multiscale model of the continuous media is developed to describe a spectrum of cohesion and superficial phenomena within a unified continuum description, a set of constitutive equations for the gradient model of the interphase layer is derived and a corresponding consistent boundary value problem is formulated. An interphase layer model is used to develop tools for numerical simulations and for analyses of mechanical properties of nanoparticle-reinforced materials.