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Manipulating and tuning dynamic characteristics of soft electro-active materials: Modelling, simulations and experiments

Periodic Reporting for period 1 - DYN-SEAM (Manipulating and tuning dynamic characteristics of soft electro-active materials: Modelling, simulations and experiments)

Reporting period: 2020-08-01 to 2022-07-31

Owing to their unique electromechanical coupling properties, soft electro-active materials (SEAMs) have attracted considerable academic and industrial interest, which is reflected by the following three breakthroughs: (1) A general theoretical framework (nonlinear electro-elasticity theory), able to describe their high nonlinearity and notable electromechanical coupling; (2) Superior rapid response and large deformation under electric stimuli, making SEAMs ideal candidates for broad applications as transducers, actuators, sensors, energy harvesters, biomedical devices and flexible electronics; (3) Significant changes of SEAM dynamic characteristics induced by biasing fields (pre-stretch, internal pressure and electric stimuli), with potential prospects in tuneable resonators and oscillators, waveguides, phononic crystals (PCs) and metamaterials.

Intrinsically, the analysis of SEAMs is a geometrically/physically nonlinear and multi-physics coupling problem. Its analytical and even numerical resolutions are very challenging tasks, especially when studying dynamic characteristics. Most of up-to-date works have made contributions to the analysis of their nonlinear static response and quasi-static instabilities. However, a systematic understanding on their linearized and nonlinear dynamic behaviours remains largely elusive and many challenges have yet to be solved before their tremendous potential can be fully harvested in the industry.

In this context, the inter-disciplinary DYN-SEAM project aimed at conducting an in-depth and comprehensive study of the effects of key factors (biasing fields, inhomogeneity, fluid-solid interaction, periodic structures) on the linearized and nonlinear dynamic characteristics of SEAMs and explaining the underlying physical and mechanical mechanisms. It integrated new theoretical modelling with computational codes and simulations tools. Eventually it attempted to provide an important guidance for promising industrial and medical applications in ultrasonic nondestructive testing, ultrasound elastography, and design of actuators, tuneable resonators, and smart soft wave devices.
The main results of the DYN-SEAM project are new mathematical models with advanced theoretical methods and computational codes that effectively predicted the effects of some key factors on the dynamic behaviours of SEAMs and their structures. Specifically, we:
• Developed the Spectral Element Method to study tuneable topological PC plates for transverse waves. We presented the voltage-controlled topological transition process and topological phase diagram, showing the axial force and electric voltage are effective methods to actively control topological interface states in the SEA PC plate waveguide operating at a low frequency.
• Established the State-Space Method (SSM) in Cartesian coordinates combined with the Hankel transform technique to study linearized axisymmetric vibrations of multi-layered SEA circular plates interacting with fluids. We illustrated electrostatically tuneable vibration frequency and mode shapes, revealing various interesting phenomena, such as the intricate competition mechanism between biasing fields and fluid-induced added mass effect, and the material inhomogeneity effect.
• Developed the SSM in cylindrical coordinates to study voltage-controlled non-axisymmetric vibrations in SEA tubes. We demonstrated the effects of biasing fields and material constitutive models on the vibration characteristics. Our established solution system based on the SSM is universal for soft smart materials with different multi-field couplings.
• Reviewed the latest advances in the study of linearized and nonlinear vibration and wave behaviours of SEA structures under biasing fields, which provided a timely and informative guide for future studies on the dynamic topics of SEA structures.

Furthermore, we also implemented:
• The bifurcation equations based on Stroh formulations into Mathematica codes to present bifurcation diagrams to predict the onset of wrinkles in an SEA film bonded to a hyperelastic substrate.
• Unified formulations of full geometrically nonlinear plate/shell theories into customized refined FE codes in Fortran to simulate the large-deflection, post-buckling, and snap-through nonlinear responses for composite shells as well as anisotropic flat panels.

I completed 5 scientific journal papers: two published in the Int J Mech Sci (including one review paper), one accepted in Int J Solids Struct, one accepted in Int J Non-Linear Mech, and one currently under review in J Non-Newton Fluid Mech. All are high impact factor journals in Applied Mathematics, Engineering and Physics communities. Besides, I am completing another 3 articles related to the project, intended to the best Mechanics, Engineering and Physics journals. I set up a profile on ResearchGate, arXiv and Google Scholar, and also created my personal website to deposit and promote our scientific outputs.

Cooperating with other experts, I jointly organised online meetings: (1) a mini-symposium entitled “Computational Acoustics and Elastodynamics in Solids/Materials and Structures” at ICCM2020-2021; (2) a Topic Session entitled “Nonlinear Problems in Aerospace Structures” at IMECE2022.

I disseminated and communicated our results at several international conferences and workshops:
• 22/02/2021: Tuneable dynamic characteristics of soft electro-active materials. Virtual Conference of AIDAA Educational Series and Academy (Invited talk), Rome, Italy;
• 29/07/2021: Analysis of dynamic behaviours of smart materials and structures. 2021 Aerospace and Mechanics Young Scholars Forum, Hangzhou, China;
• 04/07/2022 – 08/07/2022: Tuneable topological Interface states in soft (dielectric) phononic crystals. 11th European Solid Mechanics Conference (In-person invited talk), Galway, Ireland.
By proposing verifiable predictions and promoting interdisciplinary and international exchanges, our research advanced understanding of dynamic behaviours of SEAMs and their structures and pushed novel conceptual ideas for the design of soft intelligent devices in material/life science and engineering. Specifically,
• Our systematic research on dynamic behaviours of SEA structures promoted technological advances in ultrasonic NDT to characterize SEAMs and their working states, novel intelligent materials for self-sensing, control and adjusting, and advanced wave devices for focusing and vibration/noise control. These are all aligned with the Key Enabling Technology ‘Advanced Materials’ and prefigure broad applications in advanced acoustic materials, smart medical devices, etc., boosting competitiveness for Europe’s position in this global market.
• By focusing on medical applications, our research helps many medical companies and research centres to characterize nonlinear behaviours of biological tissues interacting with fluids using ultrasound elastography, because of its practical importance in diagnostics and healthcare applications. Our outputs also impact R&D in flexible smart biomedical devices based on SEAMs (such as artificial muscles and flexible intelligent wearable devices monitoring basic physiological parameters).
• In terms of sustainable and renewable energy, our R&I results are beneficial for developing new energy systems based on SEAMs, with high efficiency and environmental protection to harvest ocean and wind energy.
Buckling and post-buckling of composite elastic flat panels/shells subjected to mechanical loadings
Electrostatically tunable non-axisymmetric vibrations of soft electro-active tubes
Vibrations and waves in soft dielectric elastomer structures (A review)
Voltage-controlled topological interface states for bending waves in SEA phononic crystal plates
Wrinkling of a soft dielectric film bonded to a hyperelastic substrate
Axisymmetric vibrations of multi-layered electroactive circular plates in contact with fluids