Nonlocal Elasticity in Carbon Nanotube Modeling

Nonlocal elasticity theory extends classical continuum mechanics by incorporating long-range interatomic interactions, enabling accurate prediction of size-dependent mechanical properties in carbon nanotubes (CNTs). In this framework, stress at a point is influenced by strain over an extended domain, capturing the stiffness reduction observed at the nanoscale. Modelling approaches typically employ shell theories or beam theories—such as Donnell, Sanders and Flügge shell models and Timoshenko or Euler–Bernoulli beam formulations—augmented by nonlocal constitutive relations. These models account for chirality, diameter and aspect-ratio effects, yielding refined estimates of natural frequencies, mode shapes and stability boundaries. Practical applications span high-resolution sensors, resonators and nanoelectromechanical systems, where precise dynamic response is critical. Integration of thermal, viscoelastic and foundation interactions has further advanced predictive capabilities, guiding the design of CNT-based composites and devices with tailored mechanical and electromechanical performance.

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Nonlocal Elasticity in Carbon Nanotube Modeling publication trend

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Technical terms

Nonlocal elasticity theory: A continuum mechanics approach that accounts for long-range interactions by relating stress at a point to strains over a finite neighbourhood, capturing size-dependent effects in nanoscale structures.

Shell theory: A mathematical model describing thin curved structures, applied to nanotubes via formulations such as Donnell, Sanders and Flügge to predict bending and vibration behaviour.

Timoshenko beam model: A beam theory incorporating shear deformation and rotary inertia, extended with nonlocal elasticity to evaluate dynamic response of nanoscale beams.

Chirality: The specific helical arrangement of carbon atoms in a nanotube lattice that determines its anisotropic mechanical and electronic properties.

References

1. A Comparison of Shell Theories for Vibration Analysis of Single-Walled Carbon Nanotubes Based on an Anisotropic Elastic Shell Model. Nanomaterials (2023).
2. Nonlinear Vibration of a Nanobeam on a Pasternak Elastic Foundation Based on Non-Local Euler-Bernoulli Beam Theory. Mathematical and Computational Applications (2016).
3. Nonlinear Vibration of a Nonlocal Nanobeam Resting on Fractional-Order Viscoelastic Pasternak Foundations. Fractal and Fractional (2018).
4. Nonlocal effect in carbon nanotube resonators: A comprehensive review. Advances in Mechanical Engineering (2017).
5. Free vibration of a single-walled carbon nanotube based on the nonlocal Timoshenko beam model. Journal of Mechanics (2021).
6. Thermo-Mechanical Vibration of Short Carbon Nanotubes Embedded in Pasternak Foundation Based on Nonlocal Elasticity Theory. Shock and Vibration (2013).