Multiscale modeling of carbon nanotube fibers. Interpretation of microscopic properties from tensile tests

Although individual carbon nanotubes (CNTs) possess extraordinary mechanical properties, the macroscopic axial stiffness of assembled fibers, obtained through spinning, falls significantly short of theoretical expectations due to suboptimal load transfer between CNTs. We develop a first-principles multiscale analytical model that explicitly accounts for interfacial shear compliance to predict the effective axial stiffness. Assuming the fiber is a 1D array of aligned CNTs merged in a shear-compliant matrix, we variationally derive closed-form solutions for the effective Young’s modulus. A key contribution is the identification of an internal length scale — determined by CNT geometry and stiffness, and interfacial properties — which controls stress transfer efficiency. We establish asymptotic bounds through limiting-case analysis and validate its closed-form expressions against both simulated and experimental data for various fiber architectures. The model allows to interpret effective fiber properties from full-field micromechanical simulations for systems with well-characterized inputs. When applied to experimental data, the model enables back-calculation of interfacial shear stiffness for aligned CNT fibers. It correctly captures the asymptotic approach to the rule-of-mixtures upper bound for long CNTs and the steep reduction in stiffness for short CNTs. This quantitative agreement confirms the model utility in extracting interfacial properties from macroscopic tests and enables reliable performance prediction and inverse design.