A nonlinear 3D constitutive theory is implemented to describe the hysteresis exhibited by carbon nanotube nanocomposites due to the shear stick-slip between the carbon nanotubes and the polymer chains of the hosting matrix. The meso-scale theory is a combination of the Eshelby equivalent inclusion theory, the Mori-Tanaka homogenization method, and the introduction of inhomogeneous inclusions with inelastic eigenstrains besides the standard elastic eigenstrains. The shear stick-slip is accounted for as an incremental hysteretic eigenstrain whose evolution is regulated by the von Mises function of the deviatoric part of the interfacial stress discontinuity. The 3D material model is implemented in explicit dynamic form in a finite element platform called Fenics which makes use of a time integration scheme based on the Extended Average Mean Value Theorem and a special form of the Impulse-Momentum Law. The code written in Python and C++ has a layer structure and is fully optimized for fast computations. The code is embedded in a genetic-type optimization algorithm (Differential Evolutionary) to optimize the damping capacity exhibited by carbon nanotube nanocomposites made of thermosetting and thermoplastic polymers.
Formica, G., Milicchio, F., & Lacarbonara, W. (2016). A computational platform for carbon nanotube nanocomposites optimization. In 4th International Conference on Nanomechanics and Nanocomposites.