Programmable dynamics of locally multistable metamaterials

Project Information

ProgLMMsDyn

Grant agreement ID: 101026226

DOI

10.3030/101026226

Project closed

EC signature date 9 March 2021

Start date 6 April 2021

End date 5 April 2023

Funded under

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Total cost

€ 191 149,44

EU contribution

€ 191 149,44

Coordinated by

EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH
Switzerland

Periodic Reporting for period 1 - ProgLMMsDyn (Programmable dynamics of locally multistable metamaterials)

Reporting period: 2021-04-06 to 2023-04-05

Summary of the context and overall objectives of the project

This project focuses on modelling and analysis of reconfigurable metamaterials, consisting of unit-cells with several stable states, thus capable of stability maintaining complex deformations.

The primary focus of this project is a novel reconfigurable 1D array with great potential for haptic interfaces capable of conveying static and dynamic tactile sensations, while providing the general theoretical basis for a myriad of applications in both 2D and 3D. The key objective was developing the ability to produce desired dynamic reconfigurations following transitional wave fronts, originated from excitation in a minimal number of actuation points. Through proper design and actuation guided by our modelling and analysis, the system facilitates complex patterning using simple and cost-effective actuation methods.

When the investigated system holds a certain periodic stable state, it demonstrates a phononic behavior characterizing it by complex free wave propagation properties, which can be altered by reconfiguration. Controlled transmission of acoustic signals achievable by reversible reconfiguration is promising for applications such as encryption or sensing of mechanical signals, as well as vibration isolation. Consequently, an additional objective involved modelling the configuration-dependent acoustic wave propagation properties, providing a design tool for desired behavior in terms of acoustic wave manipulation.

We further introduced an additional class of reconfigurable metamaterials that augment truss structures with multistability. In these structures, certain members are modelled as multistable elements inspired by drinking straws, whose basic unit-cells possess two uniaxial and two bent stable states. This class of metamaterials offers a rich variety of complex multiaxial stable equilibria and can be reconfigured quasistatically, making it well-suited for shape morphing and deployable structures. The primary objective concerning multistable trusses was leveraging their extensive design space to achieve desired properties, such as energy absorption and predetermined reconfiguration patterns.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

The work on the main system started with analytical modelling utilizing a constraint-based approach, enabling description with more EOMs (equations of motion) than DOFs (degrees of freedom), employing kinematic constraints. Based on a leading order approximation, the system's constraints were simplified, resulting in a reduced set of EOMs, which were further homogenized using a long-wave approximation. The simplified discrete formulation as well as the homogenized equation were used for simplified numerical analyses as well as for deriving analytical solitary solutions. The analyses of the system revealed the capability to reconfigure the entire system or parts of it, following transitional waves that propagate from a minimal number of actuation points. By generating various transitional fronts, the array could be reconfigured into a wide range of stable states, including complex configurations that were not achievable in previous systems. The static and dynamic behaviors shown theoretically were demonstrated utilizing an experimental rig designed and manufactured in the lab. These behaviors include the multistability of the unit-cells and their energy transmission.

To analyze the configuration-dependent acoustic wave propagation within the system, we employed a generalized Bloch wave analysis considering an arbitrary periodicity. This analysis allowed us to compute the different waveforms that can be transmitted at different frequencies and identify frequency ranges where free wave propagation is prohibited. Additionally, we examined the influence of the system's parameters on its acoustic properties. This analysis can be utilized for designing arrays capable of providing different desired wave transmission or isolation characteristics, through reversible reconfigurations.

Next, to enable incorporating multistable straws as members in truss metamaterials, we first introduced an FE (finite element) scheme describing the elastic behavior of a single straw, considering dictated relative motion between its edges. This formulation allows simulating the mechanics of a single straw with uniform or spatially varying geometrical and physical parameters. The formulation of a single straw was then extended to describe any arbitrary straw-based planar truss metamaterial, considering dictated motion of selected nodes. Utilizing a numerical scheme based on this formulation, we investigated the effect of the spatially varying parameters of the straws as well as their arrangement, on the snapping pattern and energy absorption capabilities of different structures they form. To validate the theoretical model, an experimental rig capable of applying multiaxial loadings to various straw-based truss metamaterials was set up.

The methods and results developed in this project will be disseminated through presentations at three international conferences, and three journal papers which are currently in preparation.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The outcomes and methodologies derived from this project hold both scientific and industrial significance. First, both systems investigated here involve structures composed of unit-cells with multiple DOFs and stable equilibria. As a result, this project contributes to the understanding and control of reconfigurable metamaterials with higher complexity compared to the current state-of-the-art. Additionally, both configurations introduce constraint-based modelling to the field of reconfigurable metamaterials. While this approach presents computational challenges due to the large number of DOFs and potential constraint drift leading to inaccuracies, it offers significant flexibility in modelling highly complex systems.

The topology of the main system studied in this project allows minimally actuated changes of states that were previously unachievable, with the example of transitional wave-based reconfigurations that switch between non-uniform states. Furthermore, we demonstrated that the suggested system provides a wide range of configuration-dependent acoustic wave transmission and isolation characteristics. These properties can be fine-tuned through reversible reconfigurations alone. The precise control of both large amplitude reconfigurations and small amplitude acoustic wave propagation is crucial for applications such as haptic interfaces, encryption, and sensing of mechanical signals.

Finally, synergizing between the concept of high order multistability and the field of truss metamaterials represents a significant advancement in the research of reconfigurable metamaterials, as it enables implementing structures with an unprecedent number of complex stable states. Moreover, the developed FE formulation allows for exploration of a broad design space encompassing the arrangements of the straws as well as their internal parameters. This design space facilitates the optimization of straw-based truss metamaterials for diverse functionalities, including shock absorption and minimally actuated quasi-static reconfigurations.

Cover figure - Straw-based truss metamaterials

Cover figure - Main system