Stochastic multiscale modeling of graphene reinforced composites

The present paper proposes a stochastic finite element based methodology in multiple scales for modeling composite materials reinforced with graphene nano-particles. As graphene platelets exhibit a shell-type structural behavior, the problem of finding an equivalent shell element (ESE) that can be used as an effective surrogate to the corresponding detailed molecular mechanics models of the graphene, is addressed. A methodology is proposed for the calculation of the effective properties of such ESE. It is shown that the shell finite element models of graphene that implement the derived ESE, can accurately represent both the membrane and the plate behavior of the graphene, regardless of its size. The graphene-ESE is embedded into a 3D solid element representation of a polymer matrix and a finite element model of a representative volume of the composite is constructed this way. The interfacial load transferring mechanism is addressed with the definition of cohesive zone between the ESE and the three dimensional matrix. The cohesive behavior inside this zone is modeled with a traction-separation law between the two surfaces, which can also follow a predefined damage model. To this purpose, cohesive finite elements have been successfully applied for capturing delamination and debonding phenomena. Finally, random wrinkled geometries of graphene particles, compatible to some power spectral density function are generated with the spectral representation method and the effect of random wrinkling of single layered graphenes on the overall behavior of the nanocomposite has been investigated in a stochastic finite element analysis context. Numerical results are presented demonstrating the applicability and effectiveness of the proposed approach.