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Instabilities and nonlocal multiscale modelling of materials

Final Report Summary - INSTABILITIES (Instabilities and nonlocal multiscale modelling of materials)

Bifurcations, instabilities, and the mechanical conditions preluding and accompanying these phenomena are observed at several different length scales in materials and in a great number of natural and man-made systems. Through a systematic study and development of the mechanics of instabilities, we have explained several natural deformation patterns: the shatter cones found in shocked rocks near meteorite impact, the folding which occurs in geological formations or in some marine shells, and the formation of intense shear zones in ductile materials. Material instabilities are precursors of failure in several materials, so that their knowledge and simulation through computer codes is important for the design of materials of superior mechanical performances. Therefore, modeling and simulation of shear band nucleation, growth, interaction, and coalescence has been achieved during the project, all aspects never challenged before, which include dynamics and wave propagation. We have shown how to reduce and even annihilate stress concentrations in materials, in an effort of defining conditions for superstrength. This effort has been accompanied by our original extension of material models in which a length scale enters the formulation and allows to describe size effects often found in the mechanics of nano-structures. In this way, we have introduced materials approaching extreme mechanical behavior, in an attempt of overcoming limitations encountered in ordinary materials. For instance, we have been able to define the condition for folding of a solid, thus opening a new way to origami materials (the paper gained the cover of the Proceedings of the Royal Society A). Our research lent itself to elastic metamaterials and invisibility cloak; here we found a new and unexpected way to obtain flexural wave invisibility, a result which finds application in the seismic protection of buildings and in vibration shielding. We have been able to obtain structured materials by design, which are able to filter and achieve control of waves so to display total reflection, negative refraction, flat lens focusing, and wave channeling, all features which can be activated ‘on demand’.
The research in solid materials has led us to several unexpected new results in the mechanics of highly deformable structures. Here we have harnessed instability and bifurcation to discover propulsive forces in elastic systems, in the form of torsional and snake locomotion, to analyze the behavior of flexible systems governed by curved constraints, fluttering rods and self-oscillating systems. The research on flutter instability has led to the first experimental proof of the detrimental effect of dissipation on the instability load, an unexplained fact which is so counterintuitive that was previously referred as ‘paradoxical’, and has de facto opened a new field of research. We have designed and realized several proof-of-concept prototypes: (i.) the elastica arm scale, (ii.) the torsional actuator, (iii.) the dripping elastic rod, (iv.) the elastica catapult, (v.) the snake channel, (vi.) the flutter machine, and (vii.) the self-restabilizing system. All these devices (three have been featured on the cover of the Proceedings of the Royal Society A) have been invented by us and vividly show how bifurcation and instability can be exploited to generate flexible systems for applications in actuation and soft robotics. Finally, our results have also extended for applications in interdisciplinary research areas such as the design of stents for blood vessels, and the mechanics of living cells.