Multi-scale computational modelling of the mechanical behaviour of the chitosan biological polymer embedded with graphene and carbon nanotube

A multi-scale modelling approach is employed to investigate the elasto-plastic behaviour of the pure chitosan biological polymer, as well as its composite when it is embedded with a graphene sheet, and a carbon nanotube. The model directly incorporates inter-atomic potentials, describing the energetics of molecular clusters, into a continuum-based computation without any need for a parameter fitting. The coupling of the atomistic and continuum levels is achieved via the adoption of the Cauchy–Born rule which provides a suitable framework for investigating the mechanical behaviour of materials undergoing large deformations. All data on atomic bonding, bond angle, bond torsion, and nonbonding interactions relevant to the molecular clusters are incorporated into the constitutive continuum model. The continuum point within a finite element (FE) mesh is represented by an atomic cluster, referred to as a nanoscopic representative volume element (NRVE). We have introduced a parameter R that represents the ratio of the volume of finite element within which the NRVE is embedded to the volume of the NRVE. It is shown that the variation of R directly affects the results on the stress–strain behaviour of the composite, and that for R ∼ 1.0, our computed results on the elastic modulus of the simple and composite systems are fair in agreement with the experimental data.