Investigation of the Embedded Element Technique for Modelling Wavy CNT Composites

Abstract

This paper presents a comparison of different finite element approaches to modelling polymers reinforced with wavy, hollow fibres with the aim of predicting the effective elastic stiffness tensors of the composites. The waviness of the tubes is described by sinusoidal models with different amplitude-to-wavelength parameters. These volume elements are discretized by structured volume meshes onto which fibres in the form of independently meshed beam, shell or volume elements are superimposed. An embedded element technique is used to link the two sets of meshes. Reference solutions are obtained from conventional three-dimensional volume models of the same phase arrangements. Periodicity boundary conditions are applied in all cases and fibre volume fractions of up to a few percent are considered. The results indicate that embedded element techniques using shell elements for discretizing the fibres may provide an attractive combination of accuracy, computational cost and flexibility for modelling composites reinforced by arbitrarily, three-dimensionally curved nanotubes.