A semi-continuum finite element approach to evaluate the Young’s modulus of single-walled carbon nanotube reinforced composites

This paper describes a micromechanical finite element approach for the estimation of the effective Young’s modulus of single-walled carbon nanotube reinforced composites. These composite materials consist of aligned carbon nanotubes that are uniformly distributed within the matrix. Based on micromechanical theory, the Young’s modulus of the nanocomposite is estimated by considering a representative cylindrical volume element. Within the representative volume element, the reinforcement is modeled according to its atomistic microstructure while the matrix is modeled as a continuum medium. Spring-based finite elements are employed to simulate the discrete geometric structure and behavior of each single-walled carbon nanotube. The load transfer conditions between the carbon nanotubes and the matrix are modeled using joint elements of changeable stiffness that connect the two materials, simulating the interfacial region. The proposed model has been tested numerically and yields reasonable results for variable stiffness values of the joint elements. The effect of the interface on the performance of the composite is investigated for various volume fractions. The numerical results are compared with experimental and analytical predictions.