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Open research questions in Nonlocal and gradient elasticity in micro/nano structures

196 gap statements mined from Nonlocal and gradient elasticity in micro/nano structures papers in our 7.9M-paper local library, which holds 1,358 papers on the topic — drawn mostly from each paper's own stated research gap, future-work, challenge and limitation notes, and its abstract. The ones listed below are a selection still marked open; each names the study that raised it, with a DOI link where the paper has one.

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What the literature leaves open

  • The paper also mentions the need for a comprehensive investigation of the influence of size effects, slenderness, BCs, TPMS architectures, and distribution types on the mechanical response of FG-TPMS microbeams.

    Size-dependent analysis of functionally graded triply periodic minimal surface microbeams using a modified strain gradient theory-based quasi-3D displacement · 2026 · DOI

  • The gap is related to the lack of consideration of temperature influences on material properties. The study aims to address this gap by deriving equations of motion and analyzing geometrical properties.

    Mechanical characterization and thermomechanical free vibration of butterfly-shaped sandwich nanoplates with MEE face layers · 2026 · DOI

  • The study highlights the need to capture time-dependent viscoelastic phenomena in these nanostructures. The research gap includes the lack of a framework for designing and optimizing next-generation nanoscale systems.

    Dynamic behavior of graphene-origami-based meta-auxetic doublet nanobeam with memory-dependent effect · 2026 · DOI

  • The lack of a high-order shear deformation theory integrated with the modified couple stress theory for FG-TPMS microbeams. The need to consider size effects in the analysis of FG-TPMS microbeams. The requirement for a comprehensive study on the influence of size effects on the mechanical responses of FG-TPMS beams.

    A Gegenbauer shear deformation theory and a modified couple stress theory for size-effect analysis of functionally graded triply periodic minimal surface microbeams · 2026 · DOI

  • The paper does not explicitly state the research gap. However, it can be inferred that the study aims to investigate the thermoelastic vibration of FG multilayer hybrid nanocomposite microbeams, which is a relatively new area of research.

    Investigation on thermoelastic vibration of FG multilayer hybrid nanocomposite microbeam reinforced by CNTs and GPLs under nonlocal strain gradient elasticity and three-phase-lag generalized thermoelastic theory · 2026 · DOI

  • Prior models do not account for small-scale effects. There is a need for alternative models that capture the dynamic behavior and surface adsorption of microscale structures.

    Nonlinear thermo-vibration of sensitive double adsorber under coupling spring-driven resonance via nonlocal multiple scales-Galerkin approach · 2026 · DOI

  • The lack of a comprehensive analysis of shear wave behavior in porous cylindrical structures. The need for a better understanding of the influence of key parameters on shear wave propagation. The gap in prior work is the absence of a closed-form dispersion relation for shear wave propagation in such structures.

    Shear wave behavior in porous cylindrical layered composites using strain gradient theory · 2026 · DOI

  • The need to validate the proposed beam model against benchmark solutions and peer-reviewed computational data.

    Hygrothermal analysis of composite beams with graphene nanoplatelet reinforcements · 2026 · DOI

  • The lack of understanding of the fundamental microstructural interactions and stress redistribution phenomena in GNP-reinforced composite structures. The need for a systematic investigation of the mechanical behavior of FG-GNPRC systems. The limited knowledge on the influences of key parameters on the mechanical performance of such composite beams.

    Hygrothermal analysis of composite beams with graphene nanoplatelet reinforcements · 2026 · DOI

  • Nonlocal continuum mechanics has limitations in addressing the effects of nonlinear foundation, magnetic field, and thermal effects on the nanotube's dynamic behavior.

    An analytical investigation on nonlinear vibrations of timoshenko nanotubes conveying flow based on stress-driven nonlocal theory considering nonlinear foundation, magnetic field and thermal effects · 2026 · DOI

  • The non-linearity of contact problems requires an iterative procedure to find the true contact solution. The paper identifies the need for a reliable and optimal design approach to address the challenges of multilayered and FG materials.

    Indentation on multilayered and functionally graded anisotropic elastic plates · 2026 · DOI

  • There is a lack of research on the nonlinear in-plane time-dependent vibration of rotating integer and fractional-order viscoelastic micro-discs.

    Novel fractional-order strain gradient theory for pressure-induced radial vibration of shrink-fitted viscoelastic rotating micro-discs · 2026 · DOI

  • Experimental observations show that materials exhibit scale effects at lower length scales. The existing models do not incorporate both nonlocality and strain gradient effects for the laminated plate. There is a need to develop a combined nonlocal and strain gradient model for the bending analysis of laminated nanoplates.

    Nonlocal strain gradient model for bending analysis of laminated composite nanoplates using higher-order shear deformation effects · 2026 · DOI

  • The study highlights the need to incorporate the effects of the Knudsen number and surface characteristics in the analysis. The paper notes that existing nonlocal piezoelectric beam models do not account for electrically induced axial force modulation, spatially graded piezoelectric actuation, and nonlocal electromechanical coupling effects.

    Stochastic nonlocal vibrations in fractional thermo-piezoelectric fluid-conveying carbon nanotubes · 2026 · DOI

  • The gap in the existing research is the limitation of the Euler-Bernoulli theory in analyzing nanoscale structures. The paper identifies the need for a nonlocal elasticity theory that can accurately model the behavior of nanobeams. The study highlights the importance of considering surface effects and nonlocal boundary conditions in the analysis of nanobeams.

    Nonlocal elasticity-based analysis of surface-affected piezoelectric nanobeams under thermo-electro-magnetic fields · 2026 · DOI

  • The Galerkin solution can lose accuracy if too few terms are taken or for some complex boundary conditions. Numerical methods (Ritz, FEM, IGA) could be employed for highest accuracy. The study is limited to a specific type of plate and boundary conditions.

    Vibration characteristics of bio-inspired helicoidal CNT-reinforced functionally graded laminated nanoplates on orthotropic foundation · 2026 · DOI

  • Further research could investigate the effects of different material properties and geometric parameters on the vibrational frequencies of FG-AP-BiH-CNTsRLC plates. The development of more accurate and efficient numerical methods for analyzing the dynamic behavior of these plates could be explored.

    Vibration characteristics of bio-inspired helicoidal CNT-reinforced functionally graded laminated nanoplates on orthotropic foundation · 2026 · DOI

  • The need to satisfy the higher-order C2-continuity requirement. The challenge of accurately capturing the size-dependent effects on the vibration and buckling behaviors of microplates.

    A numerical approach based on the higher-order Bezier extraction and a new quasi-3D theory for analyzing porous functionally graded multi-patch microplates · 2026 · DOI

  • The analysis is limited to a specific type of beam, - The study only considers a few types of boundary conditions, - The results are based on a specific mathematical…

    Instability of the third-gradient beam · 2026 · DOI

  • Further analysis of the instability of higher-order beams, - Investigation of the effects of different boundary conditions on the instability of third-gradient beams, - Study of the instability of beams with more complex…

    Instability of the third-gradient beam · 2026 · DOI

  • Further study of the dynamic pull-in phenomenon, - Investigation of the influence of higher vibration modes, - Development of more accurate models for MEMS…

    On pull-in and stable vibration of a microplate due to symmetric electrostatic actuation · 2026 · DOI

  • The gap in the study of dynamic pull-in of microplates. The difficulty in analyzing mathematical models for MEMS and NEMS due to power and non-power nonlinearities.

    On pull-in and stable vibration of a microplate due to symmetric electrostatic actuation · 2026 · DOI

  • Further study on the effect of other parameters on the contact behavior, - Investigation of the contact behavior of other types of materials, - Study on the application of the developed contact-BFEM to other engineering…

    Indentation on multilayered and functionally graded anisotropic elastic plates · 2026 · DOI

  • Investigating the effects of different micro-dimension coefficients on the vibration of rotating discs. Developing more complex fractional-order constitutive models for viscoelastic materials. Analyzing the vibration of rotating discs with different types of nonlinear contact conditions.

    Novel fractional-order strain gradient theory for pressure-induced radial vibration of shrink-fitted viscoelastic rotating micro-discs · 2026 · DOI

  • Investigating the behavior of other types of nanobeams or materials, - Examining the effects of different boundary conditions, - Studying the behavior of nanobeams under different types of loading, - Developing more advanced theoretical frameworks…

    Nonlocal elasticity-based analysis of surface-affected piezoelectric nanobeams under thermo-electro-magnetic fields · 2026 · DOI

Most-cited papers in Nonlocal and gradient elasticity in micro/nano structures

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Open questions raised by papers listed on this page include: (1) The gap is related to the lack of consideration of temperature influences on material properties (“Mechanical characterization and thermomechanical free vibration of…”, 2026); (2) The research gap includes the lack of a framework for designing and optimizing next-generation nanoscale systems (“Dynamic behavior of graphene-origami-based meta-auxetic doublet nanobeam with…”, 2026); (3) The lack of a high-order shear deformation theory integrated with the modified couple stress theory for FG-TPMS microbeams (“A Gegenbauer shear deformation theory and a modified couple stress theory for…”, 2026); (4) There is a need for alternative models that capture the dynamic behavior and surface adsorption of microscale structures (“Nonlinear thermo-vibration of sensitive double adsorber under coupling…”, 2026); (5) The lack of a comprehensive analysis of shear wave behavior in porous cylindrical structures (“Shear wave behavior in porous cylindrical layered composites using strain…”, 2026). 196 gap statements have been mined from Nonlocal and gradient elasticity in micro/nano structures papers in our 7.9M-paper local library, which holds 1,358 papers on the topic; the gaps come from whichever of those papers state one. They are mostly the research gaps the authors state and the papers' abstracts, plus future-work, limitations and challenges passages. The ones listed below are a selection still marked open; each names the study that raised it, with a DOI link where the paper has one, so you can read the original claim in context.

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