Periodic Reporting for period 1 - NANOWAVE (Dynamics of nano-electromechanical waveguides: A computational multi-physics framework)
Periodo di rendicontazione: 2023-06-01 al 2025-10-31
Advances in nanotechnology have transformed the design of sensors, communication platforms, and energy devices, yet the mechanical and acoustic behaviour at the nanoscale remains one of the most complex challenges in modern physics and engineering. Conventional continuum models fail to capture nanoscale effects where nonlocal interactions, surface interactions, and lattice discreteness play significant roles. The NANOWAVE project responds to this scientific gap by developing an advanced computational framework for analysing the dynamic performance of nano-electromechanical waveguides (NEWs). These miniature structures, typically fabricated from graphene and carbon nanotubes, can guide, modulate, and filter energy and information at molecular dimensions, forming the foundation for next-generation technologies in sensing, signal processing, and nanoscale energy management.
Despite their vast potential, NEWs are difficult to study experimentally due to fabrication costs and measurement limitations. Furthermore, existing numerical models are unable to reproduce their size-dependent stiffness and dynamic responses. To address these barriers, NANOWAVE proposes a unified multi-physics approach that merges second strain gradient (SSG) elasticity theory—a higher-order continuum formulation that captures microstructural effects—with homogenisation theory, which condenses complex atomistic configurations into equivalent, computationally efficient models.
The overarching objective of the project is to create a numerical platform capable of accurately predicting the wave transmission characteristics of nanoscale systems. The project is structured around three specific aims:
1. Modelling simple unit cells: Establishing analytical and numerical models for single-layer graphene waveguides under mechanical and electrical excitation.
2. Modelling complex unit cells: Extending the analysis to multilayer and hybrid structures, including graphene–nanotube composites, while considering van der Waals interactions.
3. Dynamic analysis and simulation: Implementing the developed formulations and validating the predictions against literature.
4. Scientifically, NANOWAVE provides insight into nanoscale wave transmission, highlighting higher-order wave modes, stiffness hardening, and multi-modal coupling. Technologically, the framework serves as a design and optimisation tool for ultra-sensitive nanosensors and efficient energy-harvesting devices, directly supporting the EU’s strategic priorities in advanced materials, digitalisation, and green innovation.
Despite their vast potential, NEWs are difficult to study experimentally due to fabrication costs and measurement limitations. Furthermore, existing numerical models are unable to reproduce their size-dependent stiffness and dynamic responses. To address these barriers, NANOWAVE proposes a unified multi-physics approach that merges second strain gradient (SSG) elasticity theory—a higher-order continuum formulation that captures microstructural effects—with homogenisation theory, which condenses complex atomistic configurations into equivalent, computationally efficient models.
The overarching objective of the project is to create a numerical platform capable of accurately predicting the wave transmission characteristics of nanoscale systems. The project is structured around three specific aims:
1. Modelling simple unit cells: Establishing analytical and numerical models for single-layer graphene waveguides under mechanical and electrical excitation.
2. Modelling complex unit cells: Extending the analysis to multilayer and hybrid structures, including graphene–nanotube composites, while considering van der Waals interactions.
3. Dynamic analysis and simulation: Implementing the developed formulations and validating the predictions against literature.
4. Scientifically, NANOWAVE provides insight into nanoscale wave transmission, highlighting higher-order wave modes, stiffness hardening, and multi-modal coupling. Technologically, the framework serves as a design and optimisation tool for ultra-sensitive nanosensors and efficient energy-harvesting devices, directly supporting the EU’s strategic priorities in advanced materials, digitalisation, and green innovation.
The research was executed in three interlinked technical phases, integrating theoretical formulation, numerical implementation, and computational verification.
1. Modelling of Simple Unit Cells: This phase established a size-dependent model for monolayer graphene. Using SSG elasticity, the governing equations and boundary conditions were derived to incorporate higher-order gradients. The periodic structure approach enabled the evaluation of wave dispersion and resonance modes, revealing size-induced frequency shifts and stiffness enhancement. These results validated that classical models underestimate nanoscale rigidity and confirmed nonlinear observations from the researcher’s studies.
2. Modelling of Complex Unit Cells: In this stage, the framework was generalised to complex and heterogeneous materials, particularly nanotube systems. By applying homogenisation theory, the model reduced computational demands while retaining nanoscale fidelity. Effective mechanical parameters were derived for multiple configurations, and weak formulations were constructed to compute equivalent stiffness and inertia matrices. The homogenised system captured nonlocal interactions and interlayer coupling with high accuracy, reducing runtime while maintaining physical consistency.
3. Dynamic Analysis and Wave Propagation: The full model was implemented and produced an computational framework for wave simulation in NEWs. Through eigenvalue, frequency response, and energy-flow analyses, the project demonstrated multi-mode propagation, localised resonance, and directional wave beaming—phenomena that underpin next-generation nanomechanical filters and resonators. A comprehensive sensitivity analysis quantified the influence of nanoscale parameters on system performance, establishing practical guidelines for design optimisation.
Main Achievements:
1. Developed the first integrated computational framework combining higher-order elasticity and homogenisation for NEWs.
2. Accurately captured nonlinear, size-dependent phenomena in graphene and nanotube structures.
3. Reduced computation time while retaining nanometre-level predictive precision.
4. Discovered stiffness hardening, directional energy confinement, and multi-mode energy transport effects.
1. Modelling of Simple Unit Cells: This phase established a size-dependent model for monolayer graphene. Using SSG elasticity, the governing equations and boundary conditions were derived to incorporate higher-order gradients. The periodic structure approach enabled the evaluation of wave dispersion and resonance modes, revealing size-induced frequency shifts and stiffness enhancement. These results validated that classical models underestimate nanoscale rigidity and confirmed nonlinear observations from the researcher’s studies.
2. Modelling of Complex Unit Cells: In this stage, the framework was generalised to complex and heterogeneous materials, particularly nanotube systems. By applying homogenisation theory, the model reduced computational demands while retaining nanoscale fidelity. Effective mechanical parameters were derived for multiple configurations, and weak formulations were constructed to compute equivalent stiffness and inertia matrices. The homogenised system captured nonlocal interactions and interlayer coupling with high accuracy, reducing runtime while maintaining physical consistency.
3. Dynamic Analysis and Wave Propagation: The full model was implemented and produced an computational framework for wave simulation in NEWs. Through eigenvalue, frequency response, and energy-flow analyses, the project demonstrated multi-mode propagation, localised resonance, and directional wave beaming—phenomena that underpin next-generation nanomechanical filters and resonators. A comprehensive sensitivity analysis quantified the influence of nanoscale parameters on system performance, establishing practical guidelines for design optimisation.
Main Achievements:
1. Developed the first integrated computational framework combining higher-order elasticity and homogenisation for NEWs.
2. Accurately captured nonlinear, size-dependent phenomena in graphene and nanotube structures.
3. Reduced computation time while retaining nanometre-level predictive precision.
4. Discovered stiffness hardening, directional energy confinement, and multi-mode energy transport effects.
Prior to NANOWAVE, most NEMS modelling relied on simplified elasticity, neglecting size effects. The project introduced a paradigm shift by integrating higher-order elasticity with homogenisation, bridging atomic and continuum scales.
Scientific and Technical Advances:
1. Novel modelling paradigm: A generalised framework for heterogeneous nano-waveguides including interatomic forces and higher order strain gradient effects.
2. Integration of SSG and homogenisation: Combines physical fidelity with computational efficiency, offering a new standard for nanoscale simulations.
3. Discovery of new wave phenomena: Multi-mode propagation, localised resonance, and directional energy beaming, enabling controlled nanoscale energy transfer.
Potential Impacts:
1. Scientific: Establishes a foundation for nonlinear nanoscale wave mechanics and higher-order material theories.
2. Technological: Accelerates the development of high-sensitivity nanosensors and resonators for phonics, microelectronics, and biomedical applications.
3. Economic and Societal: Reduces dependence on costly experiments, fostering collaboration between academia and industry and strengthening Europe’s technological leadership.
Key Actions for Further Uptake:
1. Continued experimental validation in collaboration with nanofabrication laboratories.
2. Industrial partnerships and innovation funding for prototype development.
3. Interdisciplinary research linking mechanics, materials, and electronics.
Scientific and Technical Advances:
1. Novel modelling paradigm: A generalised framework for heterogeneous nano-waveguides including interatomic forces and higher order strain gradient effects.
2. Integration of SSG and homogenisation: Combines physical fidelity with computational efficiency, offering a new standard for nanoscale simulations.
3. Discovery of new wave phenomena: Multi-mode propagation, localised resonance, and directional energy beaming, enabling controlled nanoscale energy transfer.
Potential Impacts:
1. Scientific: Establishes a foundation for nonlinear nanoscale wave mechanics and higher-order material theories.
2. Technological: Accelerates the development of high-sensitivity nanosensors and resonators for phonics, microelectronics, and biomedical applications.
3. Economic and Societal: Reduces dependence on costly experiments, fostering collaboration between academia and industry and strengthening Europe’s technological leadership.
Key Actions for Further Uptake:
1. Continued experimental validation in collaboration with nanofabrication laboratories.
2. Industrial partnerships and innovation funding for prototype development.
3. Interdisciplinary research linking mechanics, materials, and electronics.