Micromechanical modeling of 3D grid-reinforced composite structures and nanocomposites

A micromechanical model for 3D composite structures with an embedded regular grid of generally orthotropic reinforcements is developed and applied to various anisotropic structures to calculate effective elastic properties. The model is based on application of the multiscale asymptotic homogenization technique, and it allows application to composite materials of various scales, including 3D grid-reinforced nanostructures. The model provides flexibility in the design of such structures with desirable properties by changing material and/or geometric parameters. It is illustrated by means of several examples of practical importance including single walled carbon nanotubes, 3D grid-reinforced nanocomposite materials, and 3D grid-reinforced orthotropic composite structures with different arrangements of generally orthotropic reinforcements. The explicit formulae for Young's and Shear moduli of single walled carbon nanotubes are derived in terms of the pertinent material and geometric characteristics. It is noted that the reinforcements can be in the form of covalent bonds such as the ones that exist between carbon atoms in carbon nanotubes or other nanostructures.