Modeling the nanomechanical responses of biopolymer composites during the nanoindentation

• FE analysis was adapted to model nanoindentation of two-phase polymers composites.
• The applicability of the existing indentation based models was examined.
• A simple but effective model has been presented based on Clifford model.
• This new model could well describe the indentation responses of various composites.

Many empirical models have been proposed to study how the elastic moduli of the coated systems changes with the penetration. However, little work has been done for the inclusion/matrix composite materials. Clifford et al. proposed an alternative model to deal with this, but this model has more complicated fitting parameters. It appears that their model works better due to better fitting capability of their empirical mathematical equations. Therefore, we aim to examine if it is the case. Finite element analysis was adapted to model nanoindentation by a conical indenter with varied half-included angles, axially indenting a composite with a cylindrical polymer inclusion embedded in a semi-infinite polymer matrix. The simulated results are used to determine the modulus measured as a function of the indentation penetration. This study reveals that introducing a new parameter which combines the relative penetration depth and the ratio of Young's modulus between the inclusion and matrix in Clifford model is the key. Based on this, a simpler model has been proposed to describe the nanoindentation responses of inclusion/matrix composite materials, which works equally well but with less fitting parameters compared to Clifford model.