Periodic Reporting for period 4 - Extr3Me (Extreme Mechanics of Metamaterials: From ideal to realistic conditions)
Berichtszeitraum: 2024-07-01 bis 2024-12-31
Mechanical metamaterials exhibit a plethora of extreme mechanical functionalities, such as shape-changing or programmable stiffness. For their design, a purely geometrical framework was used.
However, before the start of the project, they had been mostly considered in idealised scenarios, with homogeneous loading, without defects and in the case where energy is conserved. However, in real world applications, these idealised scenarios don't hold, the loading is never homogeneous, there are defects and energy is not conserved. Therefore the purely geometrical framework falls short.
In Extr3Me, we set out to unveil the extreme mechanics of metamaterials in this realistic setting. We have followed three routes: the role of (i) non-homogeneous loading, (ii) disorder and (iii) breaking of energy conservation.
We have therefore started to establish a much needed conceptual framework, with new experimental, numerical and theoretical tools to capture the extreme mechanics of metamaterials. This is important to establish metamaterials as a viable technology in energy absorption, wave guiding and soft robotic applications.
The main conclusions we have drawn are that in the case of inhomogeneous loading, the deformations of metamaterials can be captured by new continuum theories that based on higher order gradients (Nat. Comm. 2022, Nature 2023) and concepts of topology (PNAS 2020, PNAS 2024a) that have beautiful mathematical implications (e.g. using conformal maps, Moebius strips, and topology).
In the case of torsional loading (Adv Science 2021, Nat Commun 2024b), the preferential deformations of metamaterials in specific directions enable unconventional responses under shear, such as a negative Poynting effect and a delayed torsional buckling. All these results were only possible because of the new framework of compliant mechanisms that we used. These studies have allowed up to expand it.
The main conclusions we have drawn from studying the effect of disorder (PNAS 2024b) is that unconventional properties such as auxeticity permeate into the physics of disordered materials, such as friction and yield. Auxeticity allows to tune these otherwise immutable properties. Hence auxetic granular metamaterials could be used in many scenarios where granular media need to flow in confined spaces.
The main conclusion we have drawn from studying the effect of dissipation (PNAS 2021, Soft Matter 2022, Adv Mater 2023, Nature 2024b, Nature Comm 2024a, JMPS 2025) is that buckling tends to amplify dissipative phenomena such as viscoelasticity and plasticity. At the same time, before the onset of buckling, metamaterials have a large structural integrity. This means that metamaterials can combine usually impossible properties: high stiffness and high dissipation (Adv. Mater. 2023, Nature 2024b, JMPS 2025, patent pending). In addition, this buckling enable tunable dissipation and can be used to create materials with multifunctional responses and life-like responses (PNAS 2021, Nat. Commun. 2024). Additionally, we have discovered that energy injection allows to create novel types of waves that are unidirectionally amplified and create nonlinear patterns and waves (PNAS 2020, Nature 2024a, Nature 2025).
The overall conclusion is that by embracing deviations from the traditional purely geometrical framework, this ERC allowed us to open a whole new world. This touches upon beautiful theoretical developments, and also enables the development of new technologies in energy damping applications (we secured two ERC-PoC along those lines) and soft robotic applications.
However, before the start of the project, they had been mostly considered in idealised scenarios, with homogeneous loading, without defects and in the case where energy is conserved. However, in real world applications, these idealised scenarios don't hold, the loading is never homogeneous, there are defects and energy is not conserved. Therefore the purely geometrical framework falls short.
In Extr3Me, we set out to unveil the extreme mechanics of metamaterials in this realistic setting. We have followed three routes: the role of (i) non-homogeneous loading, (ii) disorder and (iii) breaking of energy conservation.
We have therefore started to establish a much needed conceptual framework, with new experimental, numerical and theoretical tools to capture the extreme mechanics of metamaterials. This is important to establish metamaterials as a viable technology in energy absorption, wave guiding and soft robotic applications.
The main conclusions we have drawn are that in the case of inhomogeneous loading, the deformations of metamaterials can be captured by new continuum theories that based on higher order gradients (Nat. Comm. 2022, Nature 2023) and concepts of topology (PNAS 2020, PNAS 2024a) that have beautiful mathematical implications (e.g. using conformal maps, Moebius strips, and topology).
In the case of torsional loading (Adv Science 2021, Nat Commun 2024b), the preferential deformations of metamaterials in specific directions enable unconventional responses under shear, such as a negative Poynting effect and a delayed torsional buckling. All these results were only possible because of the new framework of compliant mechanisms that we used. These studies have allowed up to expand it.
The main conclusions we have drawn from studying the effect of disorder (PNAS 2024b) is that unconventional properties such as auxeticity permeate into the physics of disordered materials, such as friction and yield. Auxeticity allows to tune these otherwise immutable properties. Hence auxetic granular metamaterials could be used in many scenarios where granular media need to flow in confined spaces.
The main conclusion we have drawn from studying the effect of dissipation (PNAS 2021, Soft Matter 2022, Adv Mater 2023, Nature 2024b, Nature Comm 2024a, JMPS 2025) is that buckling tends to amplify dissipative phenomena such as viscoelasticity and plasticity. At the same time, before the onset of buckling, metamaterials have a large structural integrity. This means that metamaterials can combine usually impossible properties: high stiffness and high dissipation (Adv. Mater. 2023, Nature 2024b, JMPS 2025, patent pending). In addition, this buckling enable tunable dissipation and can be used to create materials with multifunctional responses and life-like responses (PNAS 2021, Nat. Commun. 2024). Additionally, we have discovered that energy injection allows to create novel types of waves that are unidirectionally amplified and create nonlinear patterns and waves (PNAS 2020, Nature 2024a, Nature 2025).
The overall conclusion is that by embracing deviations from the traditional purely geometrical framework, this ERC allowed us to open a whole new world. This touches upon beautiful theoretical developments, and also enables the development of new technologies in energy damping applications (we secured two ERC-PoC along those lines) and soft robotic applications.
So far, we have undertaken the following steps:
1. We have tackled the role of inhomogeneous loading, in particular, we have shown that metamaterials can be used to manipulate the Poynting effect (dilation in response to torsion), rectify fluid flows and we have introduced a novel theory using conformal maps to predict their response. We have also devised a new paradigm for metamaterials that can deform in more than one way and can be controlled by textured boundaries. We also have explored the role of geometrically frustrated materials, shown beautiful connections with the mathematics of Moebius strips and used it for mechanical computing.
2. We have introduced a new class of metamaterials: granular metamaterials that are made from particle with an unconventional tunable property, in our case they have a negative Poisson's ratio. We have seen that these granular metamaterials have a tenable elasticity and rheology and flow more easily and absorb more energy when they are confined.
3. We have also addressed the role of out-of-equilibrium effects such as dissipation and activity. We have shown that dissipation can be used to create metamaterials that exhibit distinct shape-changes when they are compressed slow or fast. More broadly, we have explored the potential of metamaterial for controlling highly dissipative processes such as friction and fracture. The latest was applied to the case of chocolate and the tenability of metamaterials was leveraged to to tune moughtfeel. On active metamaterials, we have demonstrated experimentally for the first time the interplay between topological edge modes and the non-Hermitian skin effect in active metamaterials, as well as unidirectional solitons and patterns.
In conclusion, the Extr3Me has led to 30 peer-reviewed publications in scientific journals, plus 7 still under review. These papers have been published in top journals such as Nature (5x), PNAS (4x), Nature Communications (3x), Nature Physics (2x), Physical Review Letters (3x), Science (1x), etc... and have lead to 50+ (invited) presentations at international conferences and seminars as well as broad societal reach (e.g. our work on edible metamaterials was read by more than 25Million people and has led to public lecture in the Science museum of Amsterdam NEMO).
1. We have tackled the role of inhomogeneous loading, in particular, we have shown that metamaterials can be used to manipulate the Poynting effect (dilation in response to torsion), rectify fluid flows and we have introduced a novel theory using conformal maps to predict their response. We have also devised a new paradigm for metamaterials that can deform in more than one way and can be controlled by textured boundaries. We also have explored the role of geometrically frustrated materials, shown beautiful connections with the mathematics of Moebius strips and used it for mechanical computing.
2. We have introduced a new class of metamaterials: granular metamaterials that are made from particle with an unconventional tunable property, in our case they have a negative Poisson's ratio. We have seen that these granular metamaterials have a tenable elasticity and rheology and flow more easily and absorb more energy when they are confined.
3. We have also addressed the role of out-of-equilibrium effects such as dissipation and activity. We have shown that dissipation can be used to create metamaterials that exhibit distinct shape-changes when they are compressed slow or fast. More broadly, we have explored the potential of metamaterial for controlling highly dissipative processes such as friction and fracture. The latest was applied to the case of chocolate and the tenability of metamaterials was leveraged to to tune moughtfeel. On active metamaterials, we have demonstrated experimentally for the first time the interplay between topological edge modes and the non-Hermitian skin effect in active metamaterials, as well as unidirectional solitons and patterns.
In conclusion, the Extr3Me has led to 30 peer-reviewed publications in scientific journals, plus 7 still under review. These papers have been published in top journals such as Nature (5x), PNAS (4x), Nature Communications (3x), Nature Physics (2x), Physical Review Letters (3x), Science (1x), etc... and have lead to 50+ (invited) presentations at international conferences and seminars as well as broad societal reach (e.g. our work on edible metamaterials was read by more than 25Million people and has led to public lecture in the Science museum of Amsterdam NEMO).
In the second phase of the project, we will build on the knowledge established up to now to move towards application. We will demonstrate in particular that we can leverage boundary conditions, disorder and dissipative/active effects to create new functionalities such as mechanical memory, vibration and shock damping in stiff structures, on the fly control of shape changes. These results will impact the fields of vibration and shock control and of soft robotics.
Our work has led to many fundamental breakthroughs and technological innovations (2 ERC PoC were granted based on the idea, one patent is pending, and we are in the process of building a startup company), that way exceed the initial goals of the project.
Our work has led to many fundamental breakthroughs and technological innovations (2 ERC PoC were granted based on the idea, one patent is pending, and we are in the process of building a startup company), that way exceed the initial goals of the project.