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Catastrophic Failure in Flexural Lattice Problems

Periodic Reporting for period 1 - CAT-FFLAP (Catastrophic Failure in Flexural Lattice Problems)

Reporting period: 2017-09-14 to 2019-09-13

Currently, there is a vast amount of research activity taking place into the development of new materials having unconventional properties and the respective technologies have been opening new eras through various applications for society. This new generation of materials, or metamaterials, have led to interesting physical properties previously thought impossible such as cloaking, negative refraction and materials that contract when heated. Most of those properties are realised in the dynamic response of the material. However, in these dynamic processes uncertainty remains as to whether these metamaterials undergo feasible deformations, remaining intact. Research into the latter is limited. Understanding this phenomenon is important in developing new metamaterials. Additionally it is crucial, for example, in larger structures such as multi-span bridges (see Fig 1(a)), pipelines and skyscrapers exposed to earthquakes and terrorist attacks, regularly faced in Europe and their effects can be catastrophic to human life.

The primary scientific objective of CAT-FFLAP is to model dynamic failure propagation in complex structured media. As an example, let us consider a crack propagating in a structure (in Fig 1(b)) composed of periodically placed masses (at the junctions) connected by beams. The structure is loaded remotely by some mechanical or thermal load. Physically, this scenario may represent a flaw propagating in a the deck of a bridge. We ask, can one predict the dynamic failure phenomenon associated with the propagation waves in this structure? More specifically, is the crack propagation regular or non-regular? What speed does it possess? What dynamic processes appear as a result of this failure? Does the fracture process settle to some steady-state? What load is required to initiate and support the fracture propagation? All these questions are of relevance in practical applications, but are largely unaddressed in research into metamaterials.

It is envisaged that addressing these questions within this project will lead to designs for new materials capable of inhibit the initiation and propagation of failure. It will also provide new pathways to controlling the flow of vibrations in structured materials in order to mitigate their effects.
The European Fellow (EF) has achieved theoretical breakthroughs through the analytical and numerical analysis of:
• new models characterising the failure of flexural and elastic structures describing the collapse of long span structures such as bridges, bridge decks, rooftops and pipeline systems.
• novel designs for new gyroscopic metamaterials, or advanced materials with a microstructure, for the purposes of vibration control and seismic protection for civil engineering structures.

The tools developed allow one to identify methods for avoiding failure of structured systems, providing methods for constructing stronger failure resistant materials and frame-like structures found in buildings.

This work has led to the completion of 12 publications (3 conference papers, 9 journal articles). The conference papers were presented at high impact meetings across Europe aimed at discussing new developments in the design of metamaterials. Journal articles have been published in high quality journals of engineering and mathematics with Green or Gold open access or stored in the research depository ArXiv.

In disseminating results related to the outputs, a total of 17 talks have been given at international conferences, workshops and seminars at other universities. The EF also discussed the work with the Italian public the “European Researcher’s Night” at the University of Cagliari. In connection with the project, a minisymposium on “Dynamic Failure and Phase Transition in Structured Media” was organised at ESMC 2018, Bologna, 2nd-6th July 2018, bringing together world experts designing advanced materials to discuss recent advances in analysing failure and vibration in metamaterials.

The Host Supervisor and the EF supervised highly skilled postgraduates and in educating the next-generation of researchers and the EF developed a short course for researchers working in the area of the project, delivered at the University of Cambridge. Accompanying this short course are lecture notes and slides that can be found at the project website (see

An industrial secondment with CAEMATE SRL (contact is M. Penasa, cofounder) allowed the EF to learn essential industrial skills in programming advanced numerical codes for the purposes of modelling failure in structured media. In future, the integration of this software into routines owned by CAEmate will provide engineers with fast and efficient software accessible online from any device and operating system. This software will enable these groups to use novel tools in constructing methods to control waves and failure mechanisms in structured systems.

For frequent and accessible information related to the dissemination of the outputs in the project, see the project website
These results will have the potential to change civil engineering design practices, helping to avoid the catastrophic failure of frame-like systems such as bridges, pipelines and rooftops. The associated designs will also allow civil engineering companies to reduce the costs associated with the maintenance of these structures. As a result, a new breed of stronger and safer structures that can help to avoid the long term closure of transport links will be constructed for society and industry.

In addition, the models tackled in this project have provided new designs for micro-structured materials capable of being adapted for further study by physicists, engineers and mathematicians in the long term. They also act as recipes for experimentalists to adapt, construct and test prototypes of other micro-structured materials. This in turn will also provide valuable information to help improve the existing models. Further, this will lead to new structured materials from which novel mathematical models will arise. In the future, these activities will allow one to address a wider class of problems encountered in engineering.

In particular, a new stream of research has been created during the life of this project. This research concerns the modelling of new structured materials possessing a dynamic chirality. This is imposed by attaching active gyroscopic spinners to elastic elements. These materials offer a completely new range of approaches for controlling vibrations in civil engineering structures and frame-like systems. They have the potential to play a crucial role in how seismic protection systems are constructed for long span bridges, tall buildings or even cities.

In future, this work may also impact techniques used to control the response of other systems exposed to hazardous environmental conditions, such as bridges subjected to high winds and ships at sea, which is important for the safe transportation of people, fuel and goods. Other applications of the gyro-elastic models developed in this project include (i) energy harvesting, where potential new pathways to generating electrical power can appear through the construction of novel gyroscopic-mechanical generators, and (ii) the design of new robotic systems reducing costs of human labour (such as the development of drone taxis).
Fig 1: (a) The Rio-Niterói Bridge. (b) A structured medium containing a propagating crack.