Beyond hyperelasticity: a virgin land of extreme materials

Informations projet

Beyond

N° de convention de subvention: 101052956

DOI

10.3030/101052956

Date de signature de la CE 16 Juin 2022

Date de début 1 Octobre 2022

Date de fin 30 Septembre 2027

Financé au titre de

• European Research Council (ERC)

Coût total

€ 2 476 084,00

Contribution de l’UE

€ 2 476 084,00

Coordonné par

UNIVERSITA DEGLI STUDI DI TRENTO
Italy

Periodic Reporting for period 1 - Beyond (Beyond hyperelasticity: a virgin land of extreme materials)

Période du rapport: 2022-10-01 au 2025-03-31

Résumé du contexte et des objectifs généraux du projet

Beyond bifurcation, instability, and even hyper-elasticity, there is an unexplored world of superior materials, capable of introducing a high-tech revolution and influencing our daily lives. Surpassing bifurcation and instability yields unprecedented deformational capabilities, leading to new design approaches for architected materials and deformable devices. Going beyond the concept of the elastic potential leads to materials capable of absorbing energy from the environment in a closed cycle of deformation and releasing it upon request. The road to the new paradigm introduced by the project BEYOND is the fusion of concepts of structural mechanics with principles of solid mechanics, both brought to the highly nonlinear realm of extreme deformation. This view opens virgin territory, left unexplored since the 100-year-old definitions of linear structural behaviour and elastic potential, the latter treated until now as inviolable dogma. However, structural engineers know structures capable of suffering extreme deformation without failure, or harvesting energy from the wind, or becoming dynamically unstable when subject to follower or fluidic loads, so that the implantation of these structural concepts in microscale form into a macroscopic solid leads to the creation of materials opening new horizons in the design of new materials. Implementing these concepts at the microscale (with elements subject to extreme forces, or constraints or generating microscopic interactions to suck/deliver energy from/to external sources) leads to architected materials which may display engineered instabilities, harvest energy, or release it to generate actuation, or propagate a signal with amplification, or suffer a Hopf bifurcation and self-oscillate at designed frequency. This is an unexplored field where we expect applications in metamaterials, locomotion devices, wearable technologies, sensors, or interacting devices for use in everyday life and medical applications.

Travail effectué depuis le début du projet jusqu’à la fin de la période considérée dans le rapport et principaux résultats atteints jusqu’à présent

We analysed and exploited the complex interactions between instabilities and nonlinear dynamics of deformable rods, combining different kinds of instabilities, to obtain new structural behaviours.
We invented a bistable and tetrastable metainterface element, exhibiting nonlinear dynamics and providing a structured material interface for a novel approach to vibration attenuation.
An innovative design of a constrained rod led to a multifaceted bifurcation pattern, with single and double restabilizations. We designed a force-limiter capable of delivering a complex force response upon application of a continuous displacement.
We developed a new theory of thin-walled cylinders characterized by nonlinear hyperelastic constitutive laws to model the necking in thin-walled tubes experimentally observed by us for the first time. Results find applications to the mechanics of soft pneumatic robot arms, arteries, catheters, and stents.
We investigated the effects of new loadings on structural elements, involving transverse, fluidic, configurational, and follower forces. These forces were theoretically and experimentally analyzed when applied to the external coating of an elastic disc, in view of their application to coated fibres, mechanical rollers, morphogenesis of fruits, flexible electronics, and cable-actuated robot arms.
Configurational forces on an elastic rod led to the invention of a new Kapitza inverted pendulum, now made elastic, continuous, and of variable length. The pendulum can yield vibration-based devices with an extended frequency range.
We formulated a new homogenization scheme for 2D grids of elastic rods. We demonstrated that it is possible to design a material that loses stability as the load increases, but then regains stability as the load continues to increase. The structural model introduces a key distinction: ‘islands’ of instability emerge within a broad zone of stability. This unique feature leads to unexpected behaviour, where shear bands appear, vanish and reappear along radial stress paths originating from the unloaded state. This is a groundbreaking result in the design of architected materials.
The design of new materials is a challenge for solid mechanics. We focused the latter on instabilities and fracture, the phenomena that we want to analyse with architected materials.
We investigated shear band and fracture formation, growth, and interaction in materials containing inclusions or voids. We found new strategies for the design of super-resistant materials. In addition, we modelled an apatite used for medical applications.
Architected materials are the contact point between solids and structures, where microstructures are designed and conceived to generate materials with outstanding properties, including the possibility of surpassing the concept of hyper-elasticity. We developed a new homogenization approach (which includes rigid elements, sliders, and Timoshenko deformability) to design new materials yielding unprecedented mechanical properties.

Progrès au-delà de l’état des connaissances et impact potentiel prévu (y compris l’impact socio-économique et les conséquences sociétales plus larges du projet jusqu’à présent)

We have introduced the concept of fusion in the design of new structures, thus opening unexpected perspectives. Two structures, stable when separately analyzed, can be fused together to show a dynamic instability that has never been observed before. This breakthrough in structural mechanics is related to the follower loading and broadens the Hopf bifurcation concept. The results have substantial conceptual implications on piecewise-linear mechanics theories such as plasticity and frictional contact. Furthermore, this new concept may be used in designing new mechanical sensors, devices for energy harvesting, and architected materials.
The concept of tensile buckling has led us to a new interpretation of human finger luxation. Exploiting the same concept in a homogenization context has led to a breakthrough in designing architected materials. In fact, a new paradigm has been introduced in materials engineering, namely, the possibility of controlling the failure of a material for every possible stress path.
We invented a new origami-based microstructure, effectively introducing a new rod model, operating in a nonlinear deformation regime. This model generalizes and mechanically motivates the well-known ‘Engesser rod model’. The response beyond bifurcation exhibits the emergence and growth of folding, a feature so far unknown in the rod theory. Results can be applied to achieve objective trajectories with soft robot arms.
A connection between configurational forces acting on structures led to a breakthrough in the contact problem between a punch and a nonlinear elastic solid, showing the existence of a configurational force. We developed an application for dynamic locomotion. Moreover, our results may provide a mechanical explanation for the observed phenomenon of negative durotaxis.
Within the family of variable-length structures, a novel resonator has been invented, capable of self-tuning and thus responding to a frequency range wider than that corresponding to the classical fixed-length resonators. We extended self-tunability to the dynamics of variable-length structures constrained by harmonically oscillating sliding sleeves, also showing the ability to dynamically stabilize previously observed unstable responses.
New results based on rigorous homogenization theory enable the design of architected materials that exhibit programmed shear band formation, growth, subsequent disappearance, and eventual reappearance.