Geometric Mechanics of Solids: new analysis of modern engineering materials

Lead Research Organisation: University of Manchester
Department Name: Mechanical Aerospace and Civil Eng


The cost and safety of the important elements of our life - energy, transport, manufacturing - depend on the engineering materials we use to fabricate components and structures. Engineers need to answer the question of how fit for purpose is a particular component or a system: a pressure vessel in a nuclear reactor; an airplane wing; a bridge; a gas turbine; at both the design stage and throughout their working life. The current cost of unexpected structural failures, 4% of GDP, illustrates that the answers given with the existing engineering methods are not always reliable. These methods are largely phenomenological, i.e. rely on laboratory length- and time-scale experiments to capture the overall material behaviour. Extrapolating such behaviour to real components in real service conditions carries uncertainties. The grand problem of current methods is that by treating materials as continua, i.e. of uniformly distributed mass, they cannot inherently describe the finite nature of the materials aging mechanisms leading to failure. If we learn how to overcome the constraint of the lab-based phenomenology, we will be able to make predictions for structural behaviour with higher confidence, reducing the cost of construction and maintenance of engineering assets and thus the cost of goods and services to all individuals and society. For example, by extending the life of one civil nuclear reactor the produced electricity each hour will cost £10k-15k less than from a new built nuclear reactor, or from a conventional power plant.
This project is about the creation of a whole new technology for high-fidelity design and assessment of engineering structures. I will explore an original geometric theory of solids to overcome the phenomenological constraint, produce a pioneering software platform for structural analysis, validate the theory at several length scales, and demonstrate to the engineers how the new technology solves practical problems for which the present methods ar inadequate.
In contrast to the classical methods, the engineering materials will be seen as discrete collections of finite entities, or cells; importantly this is not a discretization of a continuum, such as those used in the current numerical methods, but a reflection of how materials organise at any length scale of observation - from atomic through to the polycrystalline aggregates forming engineering components. The cellular structure is characterised by distinct elements - cells, faces, edges and nodes - and the theory proposes an inventive way to describe how such a structure behaves by linking energy and entropy to the geometric properties of these elements - volumes, areas, lengths, positions. This theory will be implemented in a highly efficient software platform by adopting and modernising existing algorithms and developing new ones for massively parallel computations, which will enable engineers and scientists to exploit the impending acceleration in hardware power. With the expected leaps of computing power over the next five years (1018 operations per second by 2020) the new technology will allow for calculating the behaviour of engineering components and structures zooming in and out across length-scales from the atomic up to the structural. The verification and validation of the theory at multiple length-scales are now possible due to exceptionally powerful experimental techniques, such as lab- or synchrotron-based tomography, combined by image analysis techniques, such as digital volume correlation. Once verified, the technology will be applied to a series of engineering problems of direct industrial relevance, such as cleavage and ductile fracture and fatigue crack growth, providing convincing demonstrations to the engineering community. The product of the work will make a step change in the modelling and simulation of structures, suitable for the analysis of high value, high risk high reward engineering cases.

Planned Impact

Important industries, such as energy, manufacturing, construction and transport, can reduce the cost of their products and services by improved analysis of their engineering systems and structures. For example, advanced knowledge of the life-long behaviour of a particular component can improve its design and reduce the cost of its manufacturing. Scientifically-underpinned methods can demonstrate for how long a component, already in service, will be fit for purpose. To a large extend, the current engineering practices for design and assessment have reached their limits of applicability due to inherent difficulties to incorporate new experimentally derived knowledge at length scales below the classical laboratory size specimens - from single crystals down to individual atoms. This proposal is about resolving these inherent difficulties by a new theory of solids, and providing an unique computational platform by which experimental evidence across the length scales can be incorporated to provide high-fidelity assessments of structural performance.
I am offering a step change in capability over a 10-20 year period that will open up all the benefits of high-fidelity structural design. This is not a replacement for routine finite element analysis, but a much more sophisticated approach that will suit certain high value, high risk, high reward situations - the life extension of power plant, ageing aircraft, energy efficient designs for low environmental impact, new materials for specialist applications, to name a few. In one specific case, the low-carbon nuclear energy sector will benefit in the UK and internationally, with impact on environmental sustainability and protection. New understanding and predicting degradation of plant components in Advanced Gas-cooled Reactors and Pressurised Water Reactors (PWR) are relevant to the UK ONR, EdF Energy NG, as well as world-leading engineering consultancy companies, such as AMEC FW. The new-build programme also involves PWR and Boiling Water Reactor systems, where this research and development will inform more efficient inspection planning. Improved design methods, underpinned by this project's outputs, will increase the confidence in structural integrity and improve the monitoring of material ageing. In another case, the vendors of scientific and engineering software will benefit internationally with a positive impact on the knowledge society evolution and job generation. The prominent vendors of engineering software, members of NAFEMS, are presently engaged in incremental improvements of well-established numerical methods, such as the finite element method. In the majority of the cases the software platforms are not capable of taking full advantage of the expected leaps in computing power. The development of a new software platform, directly for massively parallel computations, will create significant opportunities for growth of scientific and engineering software vendors, such as Simpleware, and start-up companies, such as PlayGen.
The postdoctoral researchers will gain unique skills, benefiting from the cross-disciplinary approach with close links between theory, software and engineering applications. Planned academic collaborations will enhance the profile and influence of the team by sharing original theoretical advances, innovative modelling tools, important insights into real-world phenomena, and by giving exposure to wider networks of academic partners. Further impact will be ensured by publications in international journals and conferences relevant to advanced materials, engineering structural integrity and computational modelling of materials. The outputs will be disseminated to industry and its stakeholders through interactions with the steering board members and own networks, and through workshops. The general public will be engaged via active participation in science festivals.


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Description To date we have explored the very few previously published approaches for discrete formulation of elasticity and found a number of deficiencies or omitted aspects. As a result, we developed a new consistent mathematical formulation that conserves both linear and angular momentum (not clear from past works) and this is now coded and tested successfully on small models on personal computer. Subsequently, the team discovered deficiencies in the approach developed during the first year, namely it was not applicable to all possible cases. This lead to the development of our first collaboration with Prof Hirani from the University of Illinois, with whom we discussed all options available mathematically to proceed. Different possibilities for discrete (geometric) formulation have been explored to date, including representations of continuum elasticity theory. We have come to the conclusion that the way forward is to fully decouple the discrete formulation from any continuum considerations, including the usual for other numerical methods requirement for convergence. We are currently at the final stages of testing the new approach and preparing for publication.
Exploitation Route As soon as we confirm the discrete (geometric) formulation of elasticity, we are prepared to introduce dissipative mechanisms that change the topological structure of solids and once this is accomplished and coded, the software will provide the means to analyse the multi-physical effects on materials' behaviour in structures.
Sectors Aerospace, Defence and Marine,Construction,Energy,Manufacturing, including Industrial Biotechology,Transport

Description EdF-NNL LA
Amount £326,000 (GBP)
Organisation National Nuclear Laboratory 
Sector Public
Country United Kingdom
Start 04/2018 
End 03/2021
Description RAEng Newton Fund
Amount £24,000 (GBP)
Funding ID NRCP1617/6/19 
Organisation Royal Academy of Engineering 
Sector Learned Society
Country United Kingdom
Start 03/2017 
End 02/2018
Description University of Illinois at Urbana-Champaign 
Organisation University of Illinois
Country United States 
Sector Academic/University 
PI Contribution Three members of the team visited Prof Anil Hirani, Department of Mathematics, one of the pioneers of discrete exterior calculus (DEC) and its application to physical problems. The visit lead to the development of a joint paper, which is still under preparation. The application of DEC to solid mechanics is an entirely new area and requires the joined efforts of the two teams to resolve a number of challenges. Our team contribution is in clarifying the physical significance of all operators involved in the mathematical description and test a number of different approaches numerically.
Collaborator Contribution Prof Anil Hirani visited Manchester at the start of the collaboration. He delivered a lecture to the entire research group of the PI and clarified in discussions with us a number of possible mathematical approaches to the problem at hand.
Impact Multi-disciplinary collaboration between solid mechanics and mathematics teams, the first output is under preparation
Start Year 2018
Description University of Saint Petersburg 
Organisation Saint Petersburg State University
Country Russian Federation 
Sector Academic/University 
PI Contribution Members of my research team have contributed to modelling efforts to understand better and predict the evolution of microstructures during severe plastic deformations
Collaborator Contribution Partners have contributed with experimental data and numerical modelling
Impact 10.1016/j.matchar.2018.05.002 Multidisciplinary research - physics and mechanics of solids
Start Year 2018
Title Elasticity with DEC 
Description Software based on discrete exterior calculus for calculation of elasticity problems define on discrete topological spaces 
Type Of Technology Software 
Year Produced 2019 
Open Source License? Yes  
Impact Possibility to explore different options for development of new geometric mechanics of solids 
Description Group webpage with project dedicated space 
Form Of Engagement Activity Engagement focused website, blog or social media channel
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact Created a web-space for the Mechanics and Physics of Solids Research Group with dedicated space to the Fellowship projects GEMS looking at engaging the general public, student population, media and other researchers (specialised space for industrial project partners is also created). Activity attracted interest from students and researchers around the world, inquiring more information regarding research possibilities and collaborations. Information attracted media attention too and a company Science Impact Ltd is presently preparing an impact article for Ingenta Connect dedicated to the projecy and the group
Year(s) Of Engagement Activity 2017,2018
Description Interview by Science Impact Ltd 
Form Of Engagement Activity A press release, press conference or response to a media enquiry/interview
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Public/other audiences
Results and Impact I and selected members of my research group were interviewed by Research Impact Ltd for the production of publication dedicated to GEMS and the wider activities of the group. The publication will come out in April 2017 with anticipated wide international reach.
Year(s) Of Engagement Activity 2018
Description Talk at MMU 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Other audiences
Results and Impact Presentation of project GEMS aims, methodology and anticipated outcomes to academic staff and postgraduates of MMU by invitation. The talk was visited by about 40 people and was followed by a lively discussion of the ideas presented and potential for collaboration later on in the project.
Year(s) Of Engagement Activity 2017
Description Talk at University of Sao Carlos, Brazil 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact A talk on GEMS during a visit to USC attracted about 40 participants, academic and PhD students, who expressed particular interest during the discussion about the opportunities to collaborate on this topic in the future.
Year(s) Of Engagement Activity 2017
Description Workshop at the University of Sao Paulo, Brazil 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact A workshop organised in relation to my visit to the USP was attended by about 50 participants from industry, military, academic staff and PhD students. The talk related to GEMS attracted significant interest and was followed by a discussion of anticipated applications to industrial problems.
Year(s) Of Engagement Activity 2017