Nonlocal Strain Gradient Elasticity in Functionally Graded Structures

Functionally graded structures integrate materials with spatially varying properties to achieve tailored mechanical responses. At the nanoscale, traditional continuum mechanics fails to capture size-dependent effects that emerge due to internal microstructures and surface phenomena. Nonlocal strain gradient elasticity is a refined theoretical framework that incorporates both long-range interactions and strain gradient effects, thereby accounting for material heterogeneity and microstructure influences simultaneously. By including characteristic length scales, this theory predicts stiffness augmentation, altered natural frequencies and enhanced stability thresholds in functionally graded beams, plates and shells. These predictions have profound implications for the design of advanced sensors, energy harvesters and load-bearing components, where the interplay between graded material distribution and size-dependent mechanics can be tuned to optimise performance. Recent advances have extended the framework to multimaterial laminates, porous cores and piezoelectric nanodevices, revealing opportunities to control buckling behaviour, vibration modes and electromechanical coupling through strategic gradation profiles and boundary conditions.

Research from Nature Portfolio

No recent Nature Portfolio content available.

Research from all publishers

Recent work has demonstrated that incorporating nonlocal strain gradient theory into the modelling of porous functionally graded sandwich piezoelectric nanobeams under axial compression yields a more accurate prediction of dynamic and static responses. By employing Hamilton’s principle and a Galerkin approximation, researchers have elucidated how variations in porosity distribution, nonlocal and gradient parameters influence natural frequencies, buckling loads and the root mean square voltage output. Flexoelectric coupling has been shown to significantly amplify electromechanical conversion, particularly in the post-buckling regime, suggesting design strategies for high-efficiency nano-energy harvesters.

In parallel, an analytical treatment of thermal buckling in graded porous nanobeams using a symplectic formulation has highlighted the role of surface elasticity effects based on Gurtin–Murdoch theory. Mapping the buckling problem to a Hamiltonian eigenvalue system, the study reveals that surface stresses raise the critical thermal load and buckling temperature. The analysis further identifies optimal porosity coefficients and distribution profiles to enhance thermal stability, offering guidelines for thermally robust nanoscale structural elements.

Nonlocal Strain Gradient Elasticity in Functionally Graded Structures publication trend

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

Technical terms

Functionally graded materials: Materials whose composition and properties vary continuously along one or more dimensions to achieve tailored performance.

Nonlocal elasticity: A continuum theory that accounts for long-range interactions by relating stress at a point to strains within its spatial neighbourhood.

Strain gradient elasticity: A refinement of continuum mechanics that includes the influence of strain gradients, introducing intrinsic length scales to capture microstructural effects.

Flexoelectricity: Electromechanical coupling phenomenon whereby a strain gradient induces electric polarisation, significant at nanoscale dimensions.

Surface elasticity: Modification of material stiffness at the surface layer due to atomic-scale effects, described by surface energy theories.

References

1. Nonlinear Analyses of Porous Functionally Graded Sandwich Piezoelectric Nano-Energy Harvesters under Compressive Axial Loading. Applied Sciences (2021).
2. Symplectic method for the influence of surface effect on thermal buckling of graded porous nanobeams. Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University (2024).