Periodic Reporting for period 2 - META-LEGO (Learning to play LEGO with metamaterials !)
Reporting period: 2023-03-01 to 2024-08-31
The presence of boundaries in metamaterials strongly affects their response when coming in contact with mechanical loads.
Yet, an exhaustive model to predict the static/dynamic response of finite-size metamaterials was still lacking: current homogenization methods are unsuitable to provide a coherent transition from infinite- to finite-size metamaterials modeling which includes well-posed macroscopic boundary conditions.
Until today, this prevented us from exploring realistic structures combining metamaterials’ and classical-materials’ bricks of finite size.
META-LEGO shows that the mechanical response of finite-size metamaterials can be explored going beyond classical homogenization.
Instead, an elastic- and inertia-augmented micromorphic model with embedded internal lengths has been conceived at the macro-scale to describe the main metamaterials’ fingerprint characteristics, such as anisotropy, dispersion, band-gaps, size-effects, etc.
A fundamental breakthrough brought about by META-LEGO is that the new concept of interface forces must necessarily be introduced if one wants to use homogenized models to describe the response of finite-size metamaterials.
It has been shown that ignoring this concept may lead to dramatically wrong homogenized solutions when considering metamaterials' specimens of finite size.
Despite the importance of the concept of interface forces arising at macroscopic (homogenized) interfaces, this issue is practically disregarded in the current literature.
META-LEGO brings the knowledge needed to design large-scale metamaterials/classical-materials structures that control elastic waves.
For this,it develops, implements and validates a new paradigm for finite-size metamaterials’ modeling, by leveraging the relaxed-micromorphic model that the PI has contributed to pioneer and enriching it with the concept of macroscopic interface forces to make it suitable for the description of both infinite and finite-size metamaterials.
The reduced model’s structure (free of unnecessary parameters), coupled with adapted boundary and interface conditions, allows us to unveil the static/dynamic response of metamaterials’ bricks of arbitrary size and shape.
Playing LEGO with such bricks, we are able to design and optimize large-scale meta-structures, such as meta-panels controlling noise and vibrations for future application in Civil Engineering.
Yet, an exhaustive model to predict the static/dynamic response of finite-size metamaterials was still lacking: current homogenization methods are unsuitable to provide a coherent transition from infinite- to finite-size metamaterials modeling which includes well-posed macroscopic boundary conditions.
Until today, this prevented us from exploring realistic structures combining metamaterials’ and classical-materials’ bricks of finite size.
META-LEGO shows that the mechanical response of finite-size metamaterials can be explored going beyond classical homogenization.
Instead, an elastic- and inertia-augmented micromorphic model with embedded internal lengths has been conceived at the macro-scale to describe the main metamaterials’ fingerprint characteristics, such as anisotropy, dispersion, band-gaps, size-effects, etc.
A fundamental breakthrough brought about by META-LEGO is that the new concept of interface forces must necessarily be introduced if one wants to use homogenized models to describe the response of finite-size metamaterials.
It has been shown that ignoring this concept may lead to dramatically wrong homogenized solutions when considering metamaterials' specimens of finite size.
Despite the importance of the concept of interface forces arising at macroscopic (homogenized) interfaces, this issue is practically disregarded in the current literature.
META-LEGO brings the knowledge needed to design large-scale metamaterials/classical-materials structures that control elastic waves.
For this,it develops, implements and validates a new paradigm for finite-size metamaterials’ modeling, by leveraging the relaxed-micromorphic model that the PI has contributed to pioneer and enriching it with the concept of macroscopic interface forces to make it suitable for the description of both infinite and finite-size metamaterials.
The reduced model’s structure (free of unnecessary parameters), coupled with adapted boundary and interface conditions, allows us to unveil the static/dynamic response of metamaterials’ bricks of arbitrary size and shape.
Playing LEGO with such bricks, we are able to design and optimize large-scale meta-structures, such as meta-panels controlling noise and vibrations for future application in Civil Engineering.
META-LEGO achieved a topical breakthrough with respect to the modeling of mechanical metamaterials of finite size through homogenized (macroscopic, or effective) models.
It was shown, for the first time, that, when considering metamaterials' specimens of finite size, the classical homogenized interface and/or boundary conditions (e.g. continuity of tractions ) must be enhanced so as to allow the presence of interface forces arising at the considered macroscopic interfaces.
These interface forces are directly driven by the presence of the underlying microstructure and their specific expression depends on the way in which a metamaterial is connected to another material.
In particular, we showed that, when the same metamaterial is cut differently at the boundary and then connected to a homogeneous material, surface forces must necessarily be accounted for at the considered interface to achieve the correct homogenized modeling of the considered metamaterial's structure.
While crucial for the successful use of homogenized models, this finding is practically overlooked in the literature.
Simple control structures have been designed as benchmarks for the model’s validation.
The new model’s performances have been validated on these benchmarks, thanks to finite-element simulations. The micromorphic model performed well, especially for larger specimens.
Due to the topical breakthrough concerning « effective interface forces », we were able to extend the effectiveness of the micromorphic model also to smaller finite-size specimens.
We explicitly showed that homogenized models ignoring the presence of interface forces can lead to dramatically wrong solutions when considering metamaterials’ specimens of finite size.
The new finding related to the introduction of interface forces in micromorphic elasticity led us to explore and design additional control structures for the model’s validation.
A labyrinthine unit-cell has been chosen for prototype manufacturing and experimental testing.
Coupling FE simulations and experimental campaigns allowed us to confirm that the metamaterial’s connection to another material can drastically change the structure’s performances (a given metamaterial can pass from being less effective to be by far more effective than existing solutions, just by changing the way in which it is connected to the rest of the structure).
The breakthrough related to the effect of interfaces on finite-size metamaterials’ response allowed us to optimize the interface’s metamaterial design so as to maximize the metamaterials’ absorbing performances.
Experimental tests have been performed on the manufactured metamaterials’ specimens showing that the designed structures hold huge potential for applications in vibration and noise control.
This discovery allowed us to start considering some of the designed structures for applications in civil engineering and patenting purposes.
It was shown, for the first time, that, when considering metamaterials' specimens of finite size, the classical homogenized interface and/or boundary conditions (e.g. continuity of tractions ) must be enhanced so as to allow the presence of interface forces arising at the considered macroscopic interfaces.
These interface forces are directly driven by the presence of the underlying microstructure and their specific expression depends on the way in which a metamaterial is connected to another material.
In particular, we showed that, when the same metamaterial is cut differently at the boundary and then connected to a homogeneous material, surface forces must necessarily be accounted for at the considered interface to achieve the correct homogenized modeling of the considered metamaterial's structure.
While crucial for the successful use of homogenized models, this finding is practically overlooked in the literature.
Simple control structures have been designed as benchmarks for the model’s validation.
The new model’s performances have been validated on these benchmarks, thanks to finite-element simulations. The micromorphic model performed well, especially for larger specimens.
Due to the topical breakthrough concerning « effective interface forces », we were able to extend the effectiveness of the micromorphic model also to smaller finite-size specimens.
We explicitly showed that homogenized models ignoring the presence of interface forces can lead to dramatically wrong solutions when considering metamaterials’ specimens of finite size.
The new finding related to the introduction of interface forces in micromorphic elasticity led us to explore and design additional control structures for the model’s validation.
A labyrinthine unit-cell has been chosen for prototype manufacturing and experimental testing.
Coupling FE simulations and experimental campaigns allowed us to confirm that the metamaterial’s connection to another material can drastically change the structure’s performances (a given metamaterial can pass from being less effective to be by far more effective than existing solutions, just by changing the way in which it is connected to the rest of the structure).
The breakthrough related to the effect of interfaces on finite-size metamaterials’ response allowed us to optimize the interface’s metamaterial design so as to maximize the metamaterials’ absorbing performances.
Experimental tests have been performed on the manufactured metamaterials’ specimens showing that the designed structures hold huge potential for applications in vibration and noise control.
This discovery allowed us to start considering some of the designed structures for applications in civil engineering and patenting purposes.
In the last decades, many homogenization techniques have emerged trying to establish how to derive suitable macroscopic PDEs for mechanical metamaterials starting from specific microscopic unit-cells.
In the last 50 years countless efforts have been deployed to develop reliable effective models for the description of heterogeneous materials.
This has mainly been done in view of the tremendous advantage that an effective model would bring in terms of new possibilities for meta-structural design at the large scales which are relevant for engineers (it is well known that fully microstructured simulations become unaffordable in terms of computational costs already for relatively few unit cells).
However, only very few authors seem to be aware of the crucial role that interface forces must play to develop realistic effective models for metamaterials, especially when considering samples of finite size.
Even if it is evident that interfaces at metamaterials’ boundaries must play a predominant role in the mechanical response of finite-size metamaterials, this issue is often disregarded and thus remained, until now, an open scientific challenge.
To deal with such complexity, META-LEGO adopted a different perspective with respect to bottom-up homogenization techniques and postulated the problem directly at the macro-scale.
Leveraging the relaxed micromorphic model that largely showed its performances for the description of metamaterials’ bulk propagation problems at the macro-scale, we complemented it with the possibility of macroscopic traction discontinuities at the considered macroscopic boundaries, which take the form of ≪ interface forces ≫.
Refraining from trying to obtain a general expression of these interface forces via a bottom-up approach, we explored the nature of such interface forces based on a semi-phenomenological/in-silico approach.
We showed that our procedure is able to bring new answers about the numerical implementation and simulation of realistic bounded metamaterials’ domains and that it opens new perspectives to inspire the targets for bottom-up homogenization approaches.
In the last 50 years countless efforts have been deployed to develop reliable effective models for the description of heterogeneous materials.
This has mainly been done in view of the tremendous advantage that an effective model would bring in terms of new possibilities for meta-structural design at the large scales which are relevant for engineers (it is well known that fully microstructured simulations become unaffordable in terms of computational costs already for relatively few unit cells).
However, only very few authors seem to be aware of the crucial role that interface forces must play to develop realistic effective models for metamaterials, especially when considering samples of finite size.
Even if it is evident that interfaces at metamaterials’ boundaries must play a predominant role in the mechanical response of finite-size metamaterials, this issue is often disregarded and thus remained, until now, an open scientific challenge.
To deal with such complexity, META-LEGO adopted a different perspective with respect to bottom-up homogenization techniques and postulated the problem directly at the macro-scale.
Leveraging the relaxed micromorphic model that largely showed its performances for the description of metamaterials’ bulk propagation problems at the macro-scale, we complemented it with the possibility of macroscopic traction discontinuities at the considered macroscopic boundaries, which take the form of ≪ interface forces ≫.
Refraining from trying to obtain a general expression of these interface forces via a bottom-up approach, we explored the nature of such interface forces based on a semi-phenomenological/in-silico approach.
We showed that our procedure is able to bring new answers about the numerical implementation and simulation of realistic bounded metamaterials’ domains and that it opens new perspectives to inspire the targets for bottom-up homogenization approaches.