Non-linear Constitutive Model to Represent Damping Phenomenon in CNT-reinforced Composites

Abstract Purpose The use of carbon nanotubes as reinforcement fillers has been associated with improvements in the damping characteristics of composites. The occurrence of stick-slip motion, a phenomenon that leads to interfacial slippage depending on the loading conditions, is often regarded as the predominant reason for these effects. In this paper, a constitutive model is presented with the goal of incorporating the stick-slip mechanism into the stress-strain relationship of composites reinforced with carbon nanotubes, thereby enabling the vibration analysis of structural components. Methodology The model is built on a set of assumptions related to a representative volume element, regarding the characteristics of the individual components and the interactions between them. Its mathematical representation is achieved through algebraic piecewise functions. Free vibration analysis is applied to a discrete single degree-of-freedom system, assuming a rod finite element, and using Newmark’s method for integration over time. Results and Conclusion The resulting model establishes a non-linear, history-dependent, hysteretic constitutive relationship. Assuming a known harmonic response solution, the features of the model, particularly concerning the resulting loss factor, are evaluated. Furthermore, free vibration analysis of the rod element was conducted and discussed, enabling the assessment of the dissipative characteristics of the model on the transient response of the system.