Multiscale modeling of bending behavior of nanotube reinforced polymer composite beams

In multiscale methods, two or more length scales are considered in formulation of the problem and solved simultaneously to obtain the global response based on local microstructure. These methods can be classified in two categories, namely concurrent and hierarchical. In concurrent multiscale methods, the solution domain is explicitly divided in to certain subdomains in which a proper modeling method is used. But in hierarchical multiscale methods, both scales exist implicitly everywhere in the solution domain. This method is suitable for studying general behavior of the material depending on its microstructure.In this paper, we present a hierarchical multiscale modeling scheme using nonlinear finite element formulation to study the global behavior of nanocomposites. We apply this technique to study the effective bending stiffness of carbon nanotube reinforced polymer nanocomposites. Also, the effective elastic modulus of nanocomposites are determined and compared with the results other similar studies. Varius nanocomposites with different CNT volume fractions are analyzed to study the effect of CNT volume fraction on the global behavior of nanocomposite.In every material point which the constitutive response is needed, a microscale boundary value problem is defined and solved, and then the overall constitutive response is calculated and returned back to the macroscale problem. The micro and macro scale relation is shown in Fig.