Nonlocal Elasticity in Graphene Structures

Graphene’s exceptional stiffness and near two-dimensional nature present unique challenges for classical continuum models, which often neglect interactions at the nanoscale. Nonlocal elasticity theory addresses this limitation by incorporating long-range forces between material points, thereby capturing size-dependent phenomena observed in graphene membranes and nanoplates. This approach modifies constitutive relations to include a characteristic length scale, enabling accurate predictions of vibration frequencies, buckling behaviour and dynamic response under varied mechanical and thermal loads. Nonlocal models also facilitate coupling between in-plane stresses and out-of-plane deformations, crucial for designing nanoelectromechanical systems, flexible electronics and advanced composite materials. By bridging atomistic simulations and continuum mechanics, nonlocal formulations yield efficient analytical and numerical tools, offering insight into the interplay of geometric imperfections, boundary conditions and environmental effects on the mechanical performance of single- and multi-layer graphene structures. Global interest in exploiting graphene’s mechanical versatility has spurred refinements in nonlocal theories, promising enhanced predictive capabilities for next-generation nanodevices and structural components.

Research from Nature Portfolio

No recent Nature Portfolio content available.

Research from all publishers

Recent studies have employed a nonlocal strain gradient model to investigate the nonlinear thermal and mechanical buckling of orthotropic annular and circular graphene nanoplates. By combining higher-order shear deformation theory with nonlocal continuum mechanics, researchers derived stability equations that account simultaneously for bending, shear effects and small-scale interactions. Numerical results reveal significant reductions in critical buckling loads when thermal and mechanical actions are coupled, and an analytical relation between thermal and mechanical buckling thresholds has been proposed, facilitating quick estimation of one behaviour from the other.

Another line of enquiry has examined uncertainty in the nonlocal parameter governing size-effects on the vibration of a simply supported single-layer graphene sheet. By treating the small-scale coefficient as a bounded random variable and applying interval analysis, investigators obtained upper and lower bounds for natural frequencies. This probabilistic approach demonstrates that minor uncertainty in nanoscale parameters can lead to pronounced variability in vibrational response, particularly for smaller sheets, underscoring the need for careful parameter characterisation in device design.

Nonlocal Elasticity in Graphene Structures publication trend

The graph below shows the total number of articles in nonlocal elasticity in graphene structures across all publications each year (not limited to Nature Index journals).

Technical terms

Nonlocal elasticity theory: Continuum mechanics framework that incorporates long-range interactions between material points, introducing a characteristic length scale to capture size-dependent phenomena.

Nonlocal parameter: Material constant quantifying the intensity of nonlocal interactions, governing the deviation from classical (local) elasticity predictions.

Higher-order shear deformation theory: Plate theory accounting for transverse shear deformation through the thickness without requiring shear correction factors, improving accuracy for thick or multilayered systems.

Buckling load: Critical mechanical or thermal load at which a structure transitions from a stable to an unstable equilibrium configuration.

References

1. Nonlinear Thermal/Mechanical Buckling of Orthotropic Annular/Circular Nanoplate with the Nonlocal Strain Gradient Model. Micromachines (2023).
2. Vibration of a simply supported graphene sheet with uncertain small scale parameter based on nonlocal theory. Mathematical Models in Engineering (2021).