Geometric Mechanics of Solids: new analysis of modern engineering materials

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

Abstract

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 are 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.

Publications

10 25 50
 
Description The purpose of this project is to create an "ab initio" mathematical formulation of solid mechanics, in order to resolve and explain phenomena, which cannot be tackled by the classical continuum formulations. One important problem is the initiation of cracks in solids. The classical continuum solid mechanics deals with situations where a solid region already contains a crack and to some extent can answer questions related to the stability of this crack, but it cannot answer the question about the conditions that led to its emergence. The fundamental issue is that the continuum description does not involve any length scale, each point of the solid is infinitesimal (infinitely small) and is surrounded by infinitely many (also infinitesimal) neighbours, so there is no way to formulate a criterion by which a crack of naturally finite size will emerge from an infinitesimal point. More generally, there is no way to formulate a criterion for emergence of finite size internal free surfaces, which include voids or pores in addition to cracks. The meaning we attach to "ab initio", is that the formulation must obey the most fundamental physics principles. The two key principles dictate that such a formulation should be background independent (i.e. it should not depend on fixed structures that do not interact with the system being described) and relational (i.e. it should involve only relations between parts of the system being described). From here, and the need to describe and explain the emergence of discontinuities, it follows that the fundamental description of solids should be discrete, i.e. solids should be considered as a system of interacting finite entities at any length scale we wish to look at. To this end, we started with descriptions of solids as discrete topological manifolds, using the tools of one area of mathematics called algebraic topology. These tools allow us not only to describe the solids, but also to analyse all important topological characteristics of their structures. We have created a code for calculating a number of such characteristics and it is open domain. These can be linked to the emergent (macroscopic) physical and mechanical properties of the solid material and provide information for improved design. We have used this part of the work already to investigate the relation between sub-structures and properties of metals undergoing severe plastic deformation (e.g. during metal forming), and to optimise the mechanical and electrical performance of nano-ceramic composite, enhanced by reduced graphene oxide inclusions. For the analysis of processes in solids we needed operations on such discrete topological manifolds, which is to say calculus, or notions of differentiation and integration. Our project started with the understanding that one development, called discrete exterior calculus (DEC), offers this capability. Working closely with the originator of DEC from University of Illinois' Mathematics Department, we developed a DEC-based formulation appropriate for physical processes characterised by scalar primary variables, such as temperature, concentration, pressure and electric potential. This is now implemented in an efficient code for massively parallel computations, allowing for analysis of systems with as many discrete entities as the hardware allows. The code is open domain. The advantage of our new formulation over the classical methods based on continuum mathematics is that we can model easily emerging and growing discontinuities in the material and their effect on the macroscopic material properties. Combined with the algebraic topological analysis of the evolving discrete manifolds, this new utility offers a method to investigate relations between topological characteristics and emergent behaviour. However, in the course of our work, and after exploring several avenues, we realised that DEC is not suitable for mechanical problems, i.e. problems involving deformation which are classically based on displacements of points (vectors). Thanks to several new collaborations with Mathematics Departments, starting with the Jagiellonian University in Polland, through Durham University, to Harvard University, we were able understand in detail DEC's limitations. The critical one is that DEC does not offer a framework for an "ab initio" formulation due to its underlying assumption for the presence of an absolute smooth background space. Our newest developments are now based on the proper notion of discrete vector fields and differential forms, introduced independently around the time of DEC development (2000-2003). At the moment, we have created rigorous procedures for calculation of exterior differentials of discrete differential forms, exterior products of such forms, and interior product along a vector field. All these operations are independent of any metric, i.e. they are purely topological, and allow us to construct Lie derivatives of differential forms, as well as the curvature and torsion differential forms, similarly to the smooth (continuous) case. This is a preparation for describing real materials, where it is known that the curvature is a measure of disclination density, and the torsion is a measure of dislocation density. One very interesting consequence of our new formulation is that we can analyse transport (heat, mass, charge) processes which are operating differently on solid parts of different dimensions, e.g. we can analyse diffusion in a polycrystalline material, where the diffusion happens at different rates through the grains (3D or bulk diffusion), along the grain boundaries (2D or surface diffusion) and even along the junctions between grain boundaries (1D or line diffusion). This capability is unmatched by methods based on continuum formulations, but such distinct processes are operational in real materials. We are currently working on an appropriate formulation of a metric, based on geometric invariants of our discrete topological manifold, such as lengths, areas and volumes, which will give us a canonical way to construct the discrete co-differential and from there to calculate the system Laplacian. For the moment, we have established firmly that the Laplacian has the same algebraic structure as the Lie derivative, despite the former being a second order and the later a first order operator. We remain extremely positive that a complete "ab initio" formulation is achievable, and we will be able to demonstrate the advantages of our new theory over the existing continuum mathematical formulations and numerical methods for their solution.
Exploitation Route The 3D formulation for physical problems is implemented and can be used by all researchers dealing with heat, mass, or charge transport in media with complex and evolving microstructures. Furthermore, the software for calculating various topological characteristics of discrete manifolds can be used by researchers analysing microstructures obtained e.g. by EBSD or 3D EBSD. The combination of the two available tools offers a method to link emergent physical properties with appropriate structural characteristics. The ability to calculate deformation and failure, when ready, will make the largest impact, as it will allow for natural coupling all physical and mechanical processes on the discrete topology, and from there a fundamentally new way to model multi-physics.
Sectors Aerospace, Defence and Marine,Construction,Digital/Communication/Information Technologies (including Software),Energy,Manufacturing, including Industrial Biotechology,Transport

URL https://mapos.manchester.ac.uk
 
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 Charity/Non Profit
Country United Kingdom
Start 03/2017 
End 02/2018
 
Title Finite element analysis results from simulation of fusion energy heat exchange component: hybrid CAD/IBSim model including a graphite foam interlayer 
Description Temperature profile data from a finite element analysis of a conceptual design for a fusion energy heat exchange component (monoblock). The mesh is a hybrid from a computer aided design (CAD) drawing for the pipe and armour and IBSim for the interlayer. The IBSim interlayer is generated directly from a 3D volumetric image of a graphite foam block (KFoam). The 3D image was generated with an X-ray tomography scan performed by Dr Llion Evans with Manchester X-ray Imaging Facility equipment, which was funded in part by the EPSRC (grants EP/F007906/1, EP/F001452/1 and EP/I02249X/1). Conversion of the data to FE mesh was achieved using ScanIP, part of the Simpleware suite of programmes, version 7 (Synopsys Inc., Mountain View, CA, USA). The mesh used for the analysis is available as a separate dataset: https://doi.org/10.5281/zenodo.3522319 This data was used originally for the following publications (please cite if re-using the data): Ll.M. Evans, L. Margetts, P.D. Lee, C.A.M. Butler, E. Surrey, "Image based in silico characterisation of the effective thermal properties of a graphite foam", Carbon, Vol. 143, pp. 542-558, 2018. https://doi.org/10.1016/j.carbon.2018.10.031 Ll.M. Evans, L. Margetts, P.D. Lee, C.A.M. Butler, E. Surrey, "Improving modelling of complex geometries in novel materials using 3D imaging", Proceedings of NEA International Workshop on Structural Materials for Innovative Nuclear Systems, Manchester, UK, July 2016. https://www.oecd-nea.org/science/smins4/documents/P1-18_LlME_SMINS4_paper_reviewed.pdf 
Type Of Material Database/Collection of data 
Year Produced 2019 
Provided To Others? Yes  
 
Title Finite element analysis results from simulation of fusion energy heat exchange component: hybrid CAD/IBSim model including a graphite foam interlayer 
Description Temperature profile data from a finite element analysis of a conceptual design for a fusion energy heat exchange component (monoblock). The mesh is a hybrid from a computer aided design (CAD) drawing for the pipe and armour and IBSim for the interlayer. The IBSim interlayer is generated directly from a 3D volumetric image of a graphite foam block (KFoam). The 3D image was generated with an X-ray tomography scan performed by Dr Llion Evans with Manchester X-ray Imaging Facility equipment, which was funded in part by the EPSRC (grants EP/F007906/1, EP/F001452/1 and EP/I02249X/1). Conversion of the data to FE mesh was achieved using ScanIP, part of the Simpleware suite of programmes, version 7 (Synopsys Inc., Mountain View, CA, USA). The mesh used for the analysis is available as a separate dataset: https://doi.org/10.5281/zenodo.3522319 This data was used originally for the following publications (please cite if re-using the data): Ll.M. Evans, L. Margetts, P.D. Lee, C.A.M. Butler, E. Surrey, "Image based in silico characterisation of the effective thermal properties of a graphite foam", Carbon, Vol. 143, pp. 542-558, 2018. https://doi.org/10.1016/j.carbon.2018.10.031 Ll.M. Evans, L. Margetts, P.D. Lee, C.A.M. Butler, E. Surrey, "Improving modelling of complex geometries in novel materials using 3D imaging", Proceedings of NEA International Workshop on Structural Materials for Innovative Nuclear Systems, Manchester, UK, July 2016. https://www.oecd-nea.org/science/smins4/documents/P1-18_LlME_SMINS4_paper_reviewed.pdf 
Type Of Material Database/Collection of data 
Year Produced 2019 
Provided To Others? Yes  
 
Title Finite element mesh of fusion energy heat exchange component: hybrid CAD/IBSim model including a graphite foam interlayer 
Description Image-Based Simulation (IBSim) mesh:
A finite element mesh of a conceptual design for a fusion energy heat exchange component (monoblock). The mesh is a hybrid from a computer aided design (CAD) drawing for the pipe and armour and IBSim for the interlayer. The IBSim interlayer is generated directly from a 3D volumetric image of a graphite foam block (KFoam). The 3D image was generated with an X-ray tomography scan performed by Dr Llion Evans with Manchester X-ray Imaging Facility equipment, which was funded in part by the EPSRC (grants EP/F007906/1, EP/F001452/1 and EP/I02249X/1). Conversion of the data to FE mesh was achieved using ScanIP, part of the Simpleware suite of programmes, version 7 (Synopsys Inc., Mountain View, CA, USA). The FE mesh data uses the EnSight Gold file format and may be visualised using Paraview (https://www. paraview.org). The CT data used for the mesh is available as a separate dataset: This data was used originally for the following publications (please cite if re-using the data):
Ll.M. Evans, L. Margetts, P.D. Lee, C.A.M. Butler, E. Surrey, "Image based in silico characterisation of the effective thermal properties of a graphite foam", Carbon, Vol. 143, pp. 542-558, 2018. https://doi.org/10.1016/j.carbon.2018.10.031 Ll.M. Evans, L. Margetts, P.D. Lee, C.A.M. Butler, E. Surrey, "Improving modelling of complex geometries in novel materials using 3D imaging", Proceedings of NEA International Workshop on Structural Materials for Innovative Nuclear Systems, Manchester, UK, July 2016. https://www.oecd-nea.org/science/smins4/documents/P1-18_LlME_SMINS4_paper_reviewed.pdf 
Type Of Material Database/Collection of data 
Year Produced 2019 
Provided To Others? Yes  
 
Title Finite element mesh of fusion energy heat exchange component: hybrid CAD/IBSim model including a graphite foam interlayer 
Description Image-Based Simulation (IBSim) mesh:
A finite element mesh of a conceptual design for a fusion energy heat exchange component (monoblock). The mesh is a hybrid from a computer aided design (CAD) drawing for the pipe and armour and IBSim for the interlayer. The IBSim interlayer is generated directly from a 3D volumetric image of a graphite foam block (KFoam). The 3D image was generated with an X-ray tomography scan performed by Dr Llion Evans with Manchester X-ray Imaging Facility equipment, which was funded in part by the EPSRC (grants EP/F007906/1, EP/F001452/1 and EP/I02249X/1). Conversion of the data to FE mesh was achieved using ScanIP, part of the Simpleware suite of programmes, version 7 (Synopsys Inc., Mountain View, CA, USA). The FE mesh data uses the EnSight Gold file format and may be visualised using Paraview (https://www. paraview.org). The CT data used for the mesh is available as a separate dataset: This data was used originally for the following publications (please cite if re-using the data):
Ll.M. Evans, L. Margetts, P.D. Lee, C.A.M. Butler, E. Surrey, "Image based in silico characterisation of the effective thermal properties of a graphite foam", Carbon, Vol. 143, pp. 542-558, 2018. https://doi.org/10.1016/j.carbon.2018.10.031 Ll.M. Evans, L. Margetts, P.D. Lee, C.A.M. Butler, E. Surrey, "Improving modelling of complex geometries in novel materials using 3D imaging", Proceedings of NEA International Workshop on Structural Materials for Innovative Nuclear Systems, Manchester, UK, July 2016. https://www.oecd-nea.org/science/smins4/documents/P1-18_LlME_SMINS4_paper_reviewed.pdf 
Type Of Material Database/Collection of data 
Year Produced 2019 
Provided To Others? Yes  
 
Title Finite element meshes of graphite foam samples for Image-Based Simulation (IBSim) of experimental laser flash analysis 
Description Image-Based Simulation (IBSim) meshes:
Finite element mesh of laser flash analysis (LFA) disc samples made of a graphite foam material (KFoam). The IBSim meshes are generated directly from a 3D volumetric image of a graphite foam block. The 3D image was generated with an X-ray tomography scan performed by Dr Llion Evans with Manchester X-ray Imaging Facility equipment, which was funded in part by the EPSRC (grants EP/F007906/1, EP/F001452/1 and EP/I02249X/1). Segmentation of the data into a binarized image was achieved with ImageJ. Conversion of the segmented data to FE mesh was achieved using ScanIP, part of the Simpleware suite of programmes, version 7 (Synopsys Inc., Mountain View, CA, USA). The graphite foam has anisotropic properties partly due to its microstructure. This dataset contains three meshes, one for each alignment along cartesian axes. The FE meshes use the EnSight Gold file format and may be visualised using Paraview (https://www.paraview.org). The CT data used for the mesh is available as a separate dataset: This data was used originally for the following publications (please cite if re-using the data):
Ll.M. Evans, L. Margetts, P.D. Lee, C.A.M. Butler, E. Surrey, "Image based in silico characterisation of the effective thermal properties of a graphite foam", Carbon, Vol. 143, pp. 542-558, 2018. https://doi.org/10.1016/j.carbon.2018.10.031 
Type Of Material Database/Collection of data 
Year Produced 2019 
Provided To Others? Yes  
 
Title Finite element meshes of graphite foam samples for Image-Based Simulation (IBSim) of experimental laser flash analysis 
Description Image-Based Simulation (IBSim) meshes:
Finite element mesh of laser flash analysis (LFA) disc samples made of a graphite foam material (KFoam). The IBSim meshes are generated directly from a 3D volumetric image of a graphite foam block. The 3D image was generated with an X-ray tomography scan performed by Dr Llion Evans with Manchester X-ray Imaging Facility equipment, which was funded in part by the EPSRC (grants EP/F007906/1, EP/F001452/1 and EP/I02249X/1). Segmentation of the data into a binarized image was achieved with ImageJ. Conversion of the segmented data to FE mesh was achieved using ScanIP, part of the Simpleware suite of programmes, version 7 (Synopsys Inc., Mountain View, CA, USA). The graphite foam has anisotropic properties partly due to its microstructure. This dataset contains three meshes, one for each alignment along cartesian axes. The FE meshes use the EnSight Gold file format and may be visualised using Paraview (https://www.paraview.org). The CT data used for the mesh is available as a separate dataset: This data was used originally for the following publications (please cite if re-using the data):
Ll.M. Evans, L. Margetts, P.D. Lee, C.A.M. Butler, E. Surrey, "Image based in silico characterisation of the effective thermal properties of a graphite foam", Carbon, Vol. 143, pp. 542-558, 2018. https://doi.org/10.1016/j.carbon.2018.10.031 
Type Of Material Database/Collection of data 
Year Produced 2019 
Provided To Others? Yes  
 
Description Aberystwyth University 
Organisation Aberystwyth University
Country United Kingdom 
Sector Academic/University 
PI Contribution Provided introduction to the mathematical methods we are developing to make the discrete formulation of solid mechanics
Collaborator Contribution Provided advise and insights in the potential avenues to be explored in the continuation of the work
Impact This collaboration led to the idea of applying the mathematical tools being developed in GEMS to additively manufactured (3D printed) materials and to the preparation of a ERC Advanced Grant application by the PI. The collaboration continues.
Start Year 2019
 
Description Durham University 
Organisation Durham University
Country United Kingdom 
Sector Academic/University 
PI Contribution Explained the GEMS project and the associated mathematical problems with developing a purely discrete formulation of solid mechanics, instigated and maintained a discussion on the specific topics of curvature and torsion of discrete topological spaces.
Collaborator Contribution The partner's expertise in discrete curvature contributed to our in-depth understanding of the operators that we had to develop in order the address non-linear problems in GEMS, since curvature is associated with disclinations and torsion with dislocations in real materials.
Impact This is a collaboration between an algebraic topologist and a group of theoretical solid mechanicians. It has not led to joint outputs yet, but the direction of work on GEMS has been influenced.
Start Year 2020
 
Description Harvard University 
Organisation Harvard University
Country United States 
Sector Academic/University 
PI Contribution Explained the potential of purely discrete and intrinsic formulation of solid mechanics and outlined the outstanding mathematical issues related to formulation of proper discrete exterior forms and operations on these.
Collaborator Contribution The collaborator's expertise in development of purely topological (combinatorial) description of operators helped us to create a proper formulation of exterior and interior products of discrete differential forms, and from there all possible operators that do not include metric properties, such as discrete Lie derivatives, and curvature and torsion forms (discrete versions of Cartan forms)
Impact This is a collaboration between a mathematician and a group of theoretical solid mechanicians. It has not led to any outputs yet, but the recent developments in the GEMS group based on these discussions are very promising for a paper.
Start Year 2021
 
Description Jagiellonian University 
Organisation Jagiellonian University
Country Poland 
Sector Academic/University 
PI Contribution Delivered a lecture on Geometric Mechanics of Solids to establish first contact, followed by regular online discussions on the GEMS project.
Collaborator Contribution Hosting the PI with discussions during the first contact, followed by regular discussions on GEMS project.
Impact This is a collaboration between a group of algebraic topologists (mathematicians) and and a group of theoretical solid mechanicians. It has not led to joint outputs yet, but the discussions instigated a new line of thinking about the mathematical description of discrete topological spaces, more specifically about precise description of discrete differential forms and operations with these. The collaboration continues.
Start Year 2020
 
Description NINT China 
Organisation Nuclear Threat Initiative
Country United States 
Sector Charity/Non Profit 
PI Contribution Contributed to the development of models for glass dissolution and non-Fickian transport trough porous media
Collaborator Contribution Provided experimental data for models development and tested different models
Impact [1] Ma T, Jivkov AP, Li W, Liang W, Wang Y, Xu H, Han XY (2017). A mechanistic model for long-term nuclear waste glass dissolution integrating chemical affinity and diffusion barrier. Journal of Nuclear Materials, 486, 70-85. (http://dx.doi.org/10.1016/j.jnucmat.2017.01.001) [2] Liu D, Jivkov AP, Wang L, Si G, Yu J (2017). Non-Fickian dispersive transport of strontium in laboratory-scale columns: Modelling and evaluation. Journal of Hydrology, 549, 1-11. (http://dx.doi.org/10.1016/j.jhydrol.2017.03.053) [3] Liu D-X, Zuo R, Jivkov AP, Wang J-S, Hu L-T, Huang L-X (2019, 15 September). Effect of colloids on non-Fickian transport of Strontium in sedimentary rocks elucidated by continuous-time random walk analysis. Environmental Pollution, 252, 1491-1499. (https://doi.org/10.1016/j.envpol.2019.06.064) *Multidisciplinary research - materials chemists and mechanicians
Start Year 2015
 
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 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, there are three significant outputs under review in three journals, noting that the review process in mathematically-inclined journal is substantially longer than in natural sciences.
Start Year 2018
 
Description University of Ljubljana 
Organisation University of Ljubljana
Country Slovenia 
Sector Academic/University 
PI Contribution Provided theoretical basis and computational tool for the development of geometric elastoplasticity
Collaborator Contribution Tailored the code and executed simulations to demonstrate the approach in a publication
Impact [1] Seruga D, Kosmas O, Jivkov AP (2020). Geometric modelling of elastic and elastoplastic solids with separation of volumetric and distortional energies and Prandtl operators. International Journal of Solids and Structures, 198, 136-148. (https://doi.org/10.1016/j.ijsolstr.2020.04.019) This is collaboration between theoretical solid mechanicians and experimental engineers, where the new modelling techniques developed within GEMS are being applied to practical engineering problems. It has led to the preparation of a grant application in the collaborator's home country. We are currently seeking routes to join a Horizon Europe grant application to use and the develop the methodology created to date.
Start Year 2019
 
Description University of Saint Petersburg 
Organisation Belgorod National Research 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 [1] Borodin EN, Bratov VV (2018). Non-equilibrium approach to prediction of microstructure evolution for metals undergoing severe plastic deformation. Materials Characterization, 141, 267-278. (https://doi.org/10.1016/j.matchar.2018.05.002) [2] Borodin EN, Morozova A, Bratov V, Belyakov A, Jivkov AP (2019). Experimental and numerical analyses of microstructure evolution of Cu-Cr-Zr alloys during severe plastic deformations. Materials Characterization, 156, 109849. (https://doi.org/10.1016/j.matchar.2019.109849) [3] Borodin EN, Jivkov AP (2020). Evolution of triple junctions' network during severe plastic deformation of copper alloys - a discrete stochastic modelling. Philosophical Magazine, 100(4) 467-485. (https://doi.org/10.1080/14786435.2019.1695071) [4] Zhu S, Borodin E, Jivkov AP (2021). Triple junctions network as the key pattern for characterisation of grain structure evolution in metals. Materials & Design, 198, 109352. (https://doi.org/10.1016/j.matdes.2020.109352) Multidisciplinary research - physics and mechanics of solids. This
Start Year 2018
 
Description University of Saint Petersburg 
Organisation Institute of Problems of Mechanical Engineering
Country Russian Federation 
Sector Public 
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 [1] Borodin EN, Bratov VV (2018). Non-equilibrium approach to prediction of microstructure evolution for metals undergoing severe plastic deformation. Materials Characterization, 141, 267-278. (https://doi.org/10.1016/j.matchar.2018.05.002) [2] Borodin EN, Morozova A, Bratov V, Belyakov A, Jivkov AP (2019). Experimental and numerical analyses of microstructure evolution of Cu-Cr-Zr alloys during severe plastic deformations. Materials Characterization, 156, 109849. (https://doi.org/10.1016/j.matchar.2019.109849) [3] Borodin EN, Jivkov AP (2020). Evolution of triple junctions' network during severe plastic deformation of copper alloys - a discrete stochastic modelling. Philosophical Magazine, 100(4) 467-485. (https://doi.org/10.1080/14786435.2019.1695071) [4] Zhu S, Borodin E, Jivkov AP (2021). Triple junctions network as the key pattern for characterisation of grain structure evolution in metals. Materials & Design, 198, 109352. (https://doi.org/10.1016/j.matdes.2020.109352) Multidisciplinary research - physics and mechanics of solids. This
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 [1] Borodin EN, Bratov VV (2018). Non-equilibrium approach to prediction of microstructure evolution for metals undergoing severe plastic deformation. Materials Characterization, 141, 267-278. (https://doi.org/10.1016/j.matchar.2018.05.002) [2] Borodin EN, Morozova A, Bratov V, Belyakov A, Jivkov AP (2019). Experimental and numerical analyses of microstructure evolution of Cu-Cr-Zr alloys during severe plastic deformations. Materials Characterization, 156, 109849. (https://doi.org/10.1016/j.matchar.2019.109849) [3] Borodin EN, Jivkov AP (2020). Evolution of triple junctions' network during severe plastic deformation of copper alloys - a discrete stochastic modelling. Philosophical Magazine, 100(4) 467-485. (https://doi.org/10.1080/14786435.2019.1695071) [4] Zhu S, Borodin E, Jivkov AP (2021). Triple junctions network as the key pattern for characterisation of grain structure evolution in metals. Materials & Design, 198, 109352. (https://doi.org/10.1016/j.matdes.2020.109352) Multidisciplinary research - physics and mechanics of solids. This
Start Year 2018
 
Description University of Sao Paulo 
Organisation Universidade de São Paulo
Country Brazil 
Sector Academic/University 
PI Contribution Members of the team contributed to an experimental programme to understand the effects of residual stress and load history on the apparent fracture toughness of structural steels. Further they participated in the development of an improved local approach to fracture.
Collaborator Contribution Developed numerical models and an improved local approach to fracture.
Impact [1] Beswick J , Sarzosa DFB, Savioli RG, James P, Ruggieri C, Jivkov AP (2018). Applicability of local approaches to assessment of cleavage fracture in complex constraint and load history cases. Procedia Structural Integrity, 13, 63-68. (https://doi.org/10.1016/j.prostr.2018.12.011) [2] Sarzosa DFB, Savioli RG, Ruggieri C, Jivkov AP, Beswick J (2018). A local approach to assess effects of specimen geometry on cleavage fracture toughness in reactor pressure vessel steels. In: Proceedings of the ASME 2018 Pressure Vessel and Piping Conference, July 15-20, Prague, Czech Republic. [3] Ruggieri C, Jivkov AP (2018). A local approach to cleavage fracture incorporating the measured statistics of microcracks. In: Proceedings of the 6th International Conference on Crack Paths (CP2018), September 19-21, Verona, Italy. [4] Ruggieri C, Jivkov AP (2019). A local approach incorporating the measured statistics of microcrack to assess the temperature dependence of cleavage fracture for a reactor pressure vessel steel. Procedia Structural Integrity, 18, 28-35. (https://doi.org/10.1016/j.prostr.2019.08.137) [5] Jivkov AP, Sarzosa Burgos D, Ruggieri C, Beswick J, Savioli R, James P, Sherry A (2019). Use of local approaches to calculate changes in cleavage fracture toughness due to pre-straining and constraint effects. Theoretical and Applied Fracture Mechanics, 104, 102380. (https://doi.org/10.1016/j.tafmec.2019.102380) [6] Jivkov AP, Ford M, Yankova M, Sarzosa D, Ruggieri C (2019). Progress and challenges with local approaches to cleavage fracture. Procedia Structural Integrity, 23, 39-44. (https://doi.org/10.1016/j.prostr.2020.01.060) [7] Yankova M, Jivkov AP, Patel R (2021). Incorporation of obstacle hardening into local approach to cleavage fracture to predict temperature effects in the ductile to brittle transition regime. Materials, 14(5), 1224. (https://doi.org/10.3390/ma14051224)
Start Year 2017
 
Title ParaGEMS 
Description Software based on discrete exterior calculus for calculation of physical (scalar) problems defined on finite discrete topological spaces 
Type Of Technology Software 
Year Produced 2020 
Open Source License? Yes  
Impact The software has been used to demonstrate the benefits of the new discrete approach in comparison with classical numerical approaches based on continuum formulations, such as finite elements, in a work that shows the evolutions of thermal diffusivity in a solid with increasing crack population (applicable to problems with nuclear graphite and other quasi-brittle materials, such as cement-based). The outcomes are in a paper under review. 
 
Title VoroC++Analyser 
Description VoroC++Analyzer (VCA) is a post-processing software that takes polycrystalline microstructures created by the open sources software Voro++ and calculates all necessary operators required to analyse the topological properties of these microstructures, including combinatorial Laplacians and their spectra, as well statistical and entropic parameters characterising them. 
Type Of Technology Software 
Year Produced 2021 
Open Source License? Yes  
Impact The software has been used to characterise and analyse the electrical and mechanical behaviour of nan-crystalline ceramics enhanced by reduced graphene oxide inclusions, aiming at optimal design of such nano-composites, and the outcomes are reported in a paper under review. 
 
Description ESIS Summer School 2021 
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 Delivered a lecture at the 1st Virtual Summer School organised by the European Structural Integrity Society. This was attended at different times by all participants in the 1st Virtual ESIS Conference (which replaced the scheduled European Conference on Fracture ECF23) led to invitations to develop collaborations, to submit an invited paper, and to act as an PhD examiner in France.
Year(s) Of Engagement Activity 2020
URL https://www.vecf1.eu/summer-school/tc8-programme
 
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
URL https://mapos.manchester.ac.uk
 
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