1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 Stochastic analysis of the interphase effects on the mechanical properties of clay/epoxy nanocomposites Ashkan Almasi a , Mohammad Silani b,∗ , Hossein Talebi c , Timon Rabczuk a a Institute of Structural Mechanics, Bauhaus-Universit¨at Weimar, Marienstr. 15, D-99423 Weimar, Germany b Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran 84156-83111 c Department of Civil and Environmental Engineering, University of New South Wales, Sydney, NSW 2031, Australia Abstract The polymeric clay nanocomposites are a new class of materials which recently have become the center of attention because of their superior mechanical and physical properties. Several stud- ies have been performed on the mechanical characterization of these nanocomposites; however most of those studies have neglected the effect of the interphase and interfacial region be- tween the clays and the matrix despite of its significance on the mechanical performance of the nanocomposites. Based on a hierarchical multiscale approach on the mesoscopic level, in this study we use the stochastic analysis and the computational homogenization method to analyse the effect of thickness and stiffness of the interphase region on the overall elastic properties of the clay/epoxy nanocomposites. The results show that considering interphase layer reduces the stiffness of clay/epoxy nanocomposites and this decrease becomes significant in higher clay contents. Then, the significance of the stiffness and thickness of the interphase layer on the elastic modulus of clay/epoxy nanocomposites are studied using a sensitivity analysis. Finally, the results of this study are validated with available experimental results. Keywords: Nanocomposites, Multiscaling modeling, Homogenization, Stochastic methods, Micromechanics 1. Introduction Polymeric clay nanocomposites are a new class of materials that have been the subject of extensive research recently, owing to their outstanding mechanical properties. These materials have great multifunctional thermo-mechanical properties such as low permeability and flame retardancy, which are the results of using high aspect ratio clays inside the polymeric matrix. The high aspect ratios make a huge amount of interfacial connections between clays and the matrix [1, 2, 3]. The interface is defined as the first few molecular layers close to the solid surface that are responsible for the adhesion between two materials. Far from the solid surface, the properties of polymer is same as the bulk polymer, while the properties of the polymer near to the interface differ from that of the bulk polymer due to the influence of the interface adhesion. This region is called interphase, see Fig. 1. Interfaces and interphases play a sig- nificant role in the global properties of the nanocomposites [4, 5, 6, 7]. The thickness of the interphase region is in the order of nanometers. Meanwhile this very small thickness makes the experimental investigations limited, expensive and in some cases impractical to make an * Telefax: +98-(0)31-33919011, E-mail:m silani@me.iut.ac.ir Preprint submitted to Composite Structures March 1, 2015 *Manuscript without line numbers Click here to view linked References