Mathematical design of new materials: strategies and algorithms for the design of alloys and metamaterials
1115 March 2019
ICMS, The Bayes Centre, 47 Potterrow, Edinburgh EH8 9BT
Scientific Organisers
 John Ball, HeriotWatt University
 Kaushik Bhattacharya, Caltech
 Xian Chen, The Hong Kong University of Science and Technology
 Richard James, University of Minnesota
Many recent and spectacular advances in the world of materials are related to complex materials having extraordinary and unique features, usually determined by their specific microstructure. Such materials are key to much technology appearing in our daily lives: they are in liquid crystal displays, in miniaturised phones, special steels in cars, plastics and composites in the construction of modern airplanes, in biological implants in human bodies, and so on.
However, despite the impressive technological applications of these materials, the theoretical understanding and modelling of them are still inadequate. The need for models and basic understanding is not just of theoretical interest, but indeed a key requirement for being able to access and further develop the true potential of these materials, to optimise them, to combine them into new materials, and to use them for creating new devices, with predefined abilities and behaviours.
This workshop will bring together mathematicians and scientists working in various areas of materials science and applied mathematics in order to initiate a systematic study of the optimal design of new complex materials
This is a satellite workshop of the The mathematical design of new materials programme at the Isaac Newton Institute. The workshop will begin at lunchtime on Monday 11 March and close at lunchtime on Friday 15 March. On Wednesay, 13 March, the workshop will include a minisymposium on Machine learning and atomistic simulations organised by Graeme Ackland, University of Edinburgh with the generous support of the ERC (HECATE).
Invited speakers include:
Graeme Ackland, University of Edinburgh
Virginia Agostiniani, Università di Verona
David Bourne, HeriotWatt University
Eric Cancès, Ecole des Ponts ParisTech
Gabor Csányi, University of Cambridge
Francesco Della Porta, Max Planck Institute for Mathematics in the Sciences, Leipzig
Adriana Garroni, Sapienza, Università di Roma
Sandrine Heutz, Imperial College London
Thomas Hudson, University of Warwick
Tomonari Inamura, Tokyo Institute of Technology
Raz Kupferman, Hebrew University, Jerusalem
Paul Plucinsky, University of Minnesota
Eckhard Quandt, Kiel University
Angkana Rüland, Max Planck Institute for Mathematics in the Sciences, Leipzig
Lucia Scardia, HeriotWatt University
Hanuš Seiner, Czech Academy of Sciences
Yang Xiang, Hong Kong University of Science and Technology
Giovanni Zanzotto, Università di Padova
Recordings from the meeting are available here
Invited Speakers
Invited speakers were sent invitations out in January.
Public applications
The public applications are now closed.
Arrangements
This workshop will commence at 12:30 on Monday 11 March and finish on Friday 15 March at 13:00.
On Monday 11 March, you should aim to arrive at ICMS, for registration at 12:30  13:20. Tea/coffee will be served. The workshop will begin with a welcome talk at 13:20 followed by the first talk art 13:30.
Travel
Please note that it is your responsibility to have adequate travel insurance to cover medical and other emergencies that may occur on your trip.
Please see the Visiting ICMS page for details of our location.
A taxi directly from the airport will cost approximately 20.00 to 25.00 GBP to the city centre for a oneway journey.
There is also a bus service direct from the airport to the city centre which will cost 4.50 GBP single or 7.50 GBP return  the Airlink 100. This is a frequent service (every 10 minutes during peak times) and will bring you close to Waverley Railway Station, only a short walk to the workshop venue.
Lothian buses charge £1.70 for a single, £4.00 for a day ticket. Please note that the exact fare is required and no change is given.
If travelling by train, please note that Edinburgh has several railway stations  Waverley Railway Station being the main station and closest to the workshop venue. If you alight at Edinburgh Waverley, the workshop venue is an easy 15 minute walk away
ICMS does NOT use third parties to arrange accommodation. If you are approached by a third party (e.g. Business Travel Management) asking for booking details, please ignore. If you have any concerns please contact ICMS.
Accommodation
If you are booking your own accommodation for this workshop, here are a few suggestions below which are close to ICMS and reasonably priced.
 Masson House Pollock Halls of Residence, The University of Edinburgh, 18 Holyrood Park Road, Edinburgh EH16 5AY 0800 028 7118 (UK only)  +44 (0)131 651 2189  University of Edinburgh accommodation. Pollock Halls is about a 2025 minute walk
 Ibis Hotel on South Bridge (not Hunter Square) A 2 minute walk from ICMS.
 Motel One Edinburgh (Please note that Motel One has two hotels in the city centre  Motel One Royal or Motel One Princes. Both are within 5 to 10 minutes walk from ICMS)
 Jurys Inn Edinburgh, 43 Jeffrey Street, Edinburgh EH1 1DH +44 (0)131 200 3300  A 5 minute walk from ICMS.
 Edinburgh City Hotel, 79 Lauriston Place, Edinburgh, EH3 9HZ +44 (0)131 622 7979  Also around a 5 minute walk from ICMS
 St Christophers Hostel, 913 Market Street, Edinburgh EH1 1DE (approx 25.00 or less depending on offers available)+44 (0)20 7407 1856  bookings@stchristophers.co.uk This is Youth Hostel accommodation.
There are of course many more hotels, guest houses, hostels and selfcatering flats in Edinburgh. The Visit Scotland page is a good place to start looking for them.
POSTERS
There will be a poster session on Monday 11 March, 17:0018.30. Posters should be no larger an A1 size and preferably portrait. You will be asked to hand over your poster at Registration when you arrive at ICMS and staff will display the poster for you in time for the poster session. There will be an informal wine reception to coincide with the poster session.
Provisional Programme
Monday 11 March 2019
12.3013.20 
Registration with Tea/Coffee 
13.2013.30 
Welcome remarks 
13.30 14.30 
Eric Cancès ((Ecole des Ponts ParisTech) 
14.3015.30 
Hanuš Seiner (Czech Academy of Sciences) 
15.3016.00 
Tea/Coffee break in the catering space 
16.0017.00 
Sandrine Heutz (Imperial College London) 
17.0018.30 
Poster session and Informal wine reception 
Tuesday 12 March 2019
09.3010.30 
Eckhard Quandt (Kiel University) 
10.3011.00 
Tea/Coffee break in the catering space 
11.0012.00 
Francesco Della Porta (Max Planck Institute, Leipzig) 
12.0013.30 
Lunch in the catering space 
13.3014.30 
Lucia Scardia (HeriotWatt University) 
14.3015.30 
Virginia Agostiniani (University of Verona) 
15.3016.00 
Tea/Coffee break in the catering space 
16.0017.00 
Tomonari Inamura, (Tokyo Institute of Technology) 
Wednesday 13 March 2019
Minisymposium  Machine learning and atomistic simulations (organised by Graeme Ackland)
09.3010.30 
Xian Chen (Hong Kong University of Science and Technology) 
10.3011.00 
Tea/Coffee break in the catering space 
11.0012.00 
Gabor Csányi (University of Cambridge 
12.0013.30 
Lunch in the catering space 
13.3014.30 
Albert BartokPartay (University of Cambridge) Learning interactions from microscopic observables 
13.3014.30 
Graeme Ackland (University of Cambridge) 
15.3016.00 
Tea/Coffee break in the catering space 
Thursday 14 March 2019
# THERE WILL BE A FIRE ALARM TEST AT 11:30 TODAY. THIS WILL ONLY LAST FOR A FEW SECONDS. PLEASE REMAIN SEATED. THERE IS NO NEED TO EVACUATE.
09.3010.30 
Adriana Garroni (Sapienza, Università di Roma) 
10.3011.00 
Tea/Coffee break in the catering space 
11.0012.00 
David Bourne (HeriotWatt University) 
12.0013.30 
Lunch in the catering space 
13.3014.30 
Raz Kupferman (Hebrew University, Jerusalem) 
14.3015.30 
Thomas Hudson (University of Warwick)

15.3016.00 
Tea/Coffee break in the catering space 
16.0017.00 
Paul Plucinsky (University of Minnesota) 
19:00 
Workshop dinner at Blonde Restaurant, 75 St. Leonard’s Street, Edinburgh 
Friday 15 March 2019
09.3010.30 
Yang Xiang (Hong Kong University of Science and Technology) 
10.3011.00 
Tea/Coffee break in the catering space 
11.0012.00 
Angkana Rüland (Max Planck Institute, Leipzig) 
12.0013.00 
Giovanni Zanzotto (Università di Padova) 
13.00 
Close of workshop 
Mathematical design of new materials: strategies and algorithms for the design of alloys and metamaterials
11 – 15 March 2019
International Centre for Mathematical Sciences, Edinburgh
Abstracts
Graeme J. Ackland
Phase transformations in microstructure under extreme shear stress
I will discuss how material behaviour is affected by phase transitions occurring at extreme shear rate. Two regimes are considered, shock waves and machining. The atomiclevel processes involved are investigated using large scale molecular dynamics. High shear rates are obtained during machining, causing materials to fracture. An interesting feature is shear banding, where the applied shear strain leads to a microstructure containing bands of even higher shear rate. We describe a dynamical phase transition occurring within a shear band at high temperature and under extremely high shear rates. With increasing temperature, dislocation deformation and grain boundary sliding is supplanted by amorphization in a highly localized nanoscale band, which allows massive strain and fracture. The mechanism is similar to shear melting and leads to liquid metal embrittlement at high temperature. We show liquid metal embrittlement, can be utilized to improve machinability of materials like titanium alloy by adding add rare earth metals (REMs). Under high shear, the REM becomes mixed with the titanium, lowering the melting point within the shear band and triggering the shearmelting transition. This in turn generates heat which remains localized in the shear band due to poor heat conduction. In a lathe, the new material fractures easily along the shear band. High shear rates are also observed as shock waves pass through a material. The timescales associated with shockwaves are of order nanoseconds: small, but still much longer than typical atomic vibrations. Conventionally, it was assumed that shocked materials would behave as if at thermodynamic equilibrium. Very recent experiments using femtosecond pulsed lasers show that this is not the case, the phase diagram under shock may be very different from the thermodynamics states at equivalent PT conditions. We present a combined calculation + experiment analysis showing how and why phases absent in the thermodynamic phase diagram can be accessed and observed in shock wave experiments.
Virginia Agostiniani
Minkowski inequality for mean convex domains and sharp constant for nearly umbilical estimates
The classical Minkowski inequality states that for any convex domain with smooth boundary it holds
where is the mean curvature of computed with respect to the outward unit normal. Moreover, the equality holds iff is a ball. The same inequality is nowadays known to hold either for mean convex and starshaped domains or for outward minimising ones. In this talk, we outline the main ideas underlying a recent result obtained in collaboration with M. Fogagnolo and L. Mazzieri, which states that the Minkowski inequality can be extended under the mere assumption of mean convexity. As a byproduct, we find the best constant in the rigidity estimate for nearly umbilical surfaces due to C. De Lellis and S. Muller.
Albert BartokPartay
Learning interactions from microscopic observables
Designing new materials needs a detailed understanding of the structure and processes of matter on the atomistic scale, because all macroscopic properties ultimately depend on microscopic interactions. For such studies, quantum mechanical modelling combined with atomistic simulations has been proven to be predictive in addition to being able to explain experimental phenomena. However, larger length and timescales are not easily accessible due to the nonlinear growth in computational resources required to numerically solve the quantum mechanical equations. We would like to enable fast simulations without a compromise in accuracy by using machine learning techniques to fit the quantum mechanical model. To realise this aim, we have developed the Gaussian Approximation Potentials framework, which uses microscopic data from quantum mechanical calculations on small systems to create fast, accurate and scalable models. Apart from data, the other main ingredient needed to fit Gaussian Processes are kernels. In my talk I will discuss kernels that are designed to compare atomic structures and show examples from molecular and condensed matter systems. These kernels are used to define a set of interatomic potentials or models, and a Bayesian approach determines which is the most likely, based on the data as evidence.
David Bourne,
Optimal transport theory meets the steel industry
In this talk I will show how optimal transport theory can be used to generate representative volume elements (RVEs) for modelling the grain structure of metals.
Eric Cances
Computing the properties of multilayer 2D materials: a method based on noncommutative geometry
2D materials such as graphene have fascinating electronic and optical properties. Multilayer 2D materials are obtained by stacking several layers of possibly different 2D materials. Their study is one of the current hot topics in physics and materials science. The numerical simulation of such systems is made difficult by incommensurabilities originating from lattice mismatches and twisting angles. In this talk, I will first present the most common framework, based on Kubo formula, for deriving the frequencydependent electrical conductivity tensor of a given material from its molecular structure. For periodic systems (perfect crystals), Bloch theory allows one to numerically compute the conductivity from Kubo formula in an efficient way. The situation is much more involved for aperiodic systems such as incommensurate multilayer 2D materials. However, it can be handled by relying on tools from noncommutative geometry introduced in the 80's and 90's by Jean Bellissard and coworkers following ideas of Alain Connes.
Xian Chen
Datadriven approach for indexingfree Xray crystallography
We propose a novel datadriven approach for analyzing the synchrotron Xray microdiffraction scans based on machine learning algorithms. The basic architecture and major components of the method are formulated mathematically. We demonstrate it through the typical examples including polycrystalline solids, multiphase phase transforming alloys and finely twinned martensite. The computational pipeline is implemented for the Beamline 12.3.2 at the Advanced Light Source, Lawrence Berkeley National Lab. The conventional analysis of Xray diffraction is based on the crystallographic study and the patternbypattern indexing processing. This work underlies a new way of Xray diffraction analysis independent of the indexing results. It motivates further studies of Xray diffraction patterns from the prospective of machine learning for suitable feature extraction, clustering and labeling algorithms. Authors: Xian Chen (presenter), Yintao Song, Nobumichi Tamura
Gabor Csányi
Advances in interatomic potentials for metals and alloys
Modelling the deformation of metals is one of the success stories of atomic scale modelling over the past four decades. Increasingly complex functional forms, from pair potentials to embedded atom models and bond order potentials, allowed the quantitative description of different crystal structures, point and line defects, shedding light on many elementary processes governing failure, phase stability, surface phenomena etc. Interestingly, the accuracy with which these models describe the potential energy surface corresponding to the electronic ground state has not changed over the decades and is rather limited. The success is thus largely empirical in nature  and follows from the sophistication of the modeller and the judicious compromises made in order to solve specific problems. The parallel developments in electronic structure theory on the other hand provided exquisite quantitative agreement with experiments e.g. for thermomechanical properties, phase stability, and defect energetics. I will report on recent work of a growing community, who have managed to bring these two worlds together, and construct extremely accurate functional representations of the interatomic potential. These developments rely on a very large amount of highly accurate electronic structure data, on nonparametric function fitting, and on sophisticated representation theory that brings with it guarantees of completeness and convergence.
Francesco Della Porta
Different behaviour of materials closely satisfying supercompatibility
This talk will survey some recent results on the cofactor conditions, conditions of supercompatibility between phases in martensitic transformations which are believed to influence reversibility. We highlight how different metrics can give contradicting results on whether or not a material closely satisfies the cofactor conditions. Finally we study some incompatible junctions between martensitic variants which are observed in a material that satisfies these conditions closely, but not too closely.
Adriana Garroni
Derivation of 3D line tension models for dislocations from geometrically nonlinear models
We study a nonlinear three dimensional elastic model which includes incompatibilities of the deformation matrix. In particular it provides a nonlinear semidiscrete model for dislocations in 3d which incorporates invariance under rigid motions. For the logarithmic regime, in the limit as the lattice parameter tends to zero, we derive a line tension model which can be characterised using the linearised elastic energy, validating the accuracy of the linear approximation for dilute configurations of dislocations.
Sandrine Heutz
Mathematical challenges for molecular films: from structure to function
The introduction of transition metals into molecular semiconductors has opened up tremendous opportunities for the implementation of new properties in flexible devices. Molecular semiconductors have experienced a rapid rise from fundamental properties to commercial applications such as organic light emitting devices (OLEDs). While their function is mainly attributed to the delocalized πelectrons, coordinated transition metals have been previously used, for example to increase the yield of triplet excitons.[1]
This talk will focus on the strategies used to exploit the transition metal of organic semiconductor thin films in a range of applications. Metal phthalocyanines are a particularly suitable system as they exist with a large number of different transition metal substituents, which can have very similar crystal structures. Thin film growth techniques have therefore been developed to exploit the spin of the transition metal, both in the strongly coupled and weakly coupled regimes. In the former, magnetic couplings could be observed above the boiling point of liquid nitrogen, which opens up possibilities in spintronics.[2] In the latter, the spins have long lifetimes that render them useful for classical or quantum information processing.[3] The talk will centre on experimental methods, and review simulations done by collaborators and others to understand and optimize the functional properties.
1. J. S. Wilson; A. S. Dhoot; A. Seeley; M. S. Khan; A. Kohler; R. H. Friend, Nature 2001, 413, 828.
2. M. Serri; W. Wu; L. R. Fleet; N. M. Harrison; C. F. Hirjibehedin; C. W. M. Kay; A. J. Fisher; G. Aeppli; S. Heutz, Nat. Commun. 2014, 5, 3079.
3. M. Warner; S. Din; I. S. Tupitsyn; G. W. Morley; A. M. Stoneham; J. A. Gardener; Z. Wu; A. J. Fisher; S. Heutz; C. W. M. Kay; G. Aeppli, Nature 2013, 503, 504.
Thomas Hudson
Modelling dislocation motion via discrete dislocation dynamics
Dislocations are line defects found in crystals, and act as the carriers of irreversible (or plastic) deformation for these materials. Understanding and accurately modelling the complex collective evolution of dislocations is therefore viewed as a key challenge in obtaining predictive models of plasticity. Since the 1960s, a wide variety of models described is location motion have been proposed, and with the growth of computer power in the 1990s, Materials Scientists began using these models computationally. In this talk, I will present mathematical results which link a particular class of dislocation evolution model (Discrete Dislocation Dynamics) to microscopic principles, and discuss the precise mathematical formulation and wellposedness of the relevant evolution problem in three dimensions.
Tomonari Inamura
Incompatible microstructure of martensite and kink deformation
Not only in martensite, but also in deformation microstructure, incompatibility plays significant role. LongPeriod Stacking Ordered (LPSO) Mg alloys exhibit high strength owing to kink deformation, though detailed mechanism of the strengthening has not been understood. Existence of disclination is shown by the analysis of the rank1 connection at kink boundaries and the origin of the strengthening is discussed.
Raz Kupferman
The bending energy of bucked edgedislocations
The study of elastic membranes carrying topological defects has a longstanding history, going back at least to the 1950s. When allowed to buckle in threedimensional space, membranes with defects can totally relieve their inplane strain, remaining with a bending energy, whose rigidity modulus is small compared to the stretching modulus.
It was suggested in the 1980s that a disc endowed with a single edge dislocation can totally relieve its stretching energy on the expense of a bending energy, whose magnitude is independent of the size of the system. In this lecture, I will show that this is not true: the minimum bending energy associated with strainfree configurations diverges logarithmically with the size of the system.
Paul Plucinsky
Active and architectured sheets: From nematic elastomers to rigidlyfoldable origami
Thin and slender structures exhibit a broad range of mechanical responses as the competition between stretching and bending in these structures can result in buckling, localized deformations like folding, and tension wrinkling. Active and architectured materials also exhibit a broad range of mechanical responses as features that manifest at the micro and mesoscale in these materials result in mechanical couplings at the engineering scale (thermal/electrical/dissipative/...) with novel function (the shape memory effect/ferroelectricity/enhanced fracture toughness/...). Given this richness in behaviors, my research broadly aims to address the following questions: What happens when active and architectured materials are incorporated into thin and slender structures? Do phenomena inherent to these materials compete with or enhance those inherent to these structures? Does this interplay result in entirely new and unexpected phenomena? And can all this be exploited to design new functionality in engineering systems?In this talk, I will explore these questions in the context of thin sheets of an active material in nematic elastomer as well as architectured sheets designed to fold continuously as origami. For the latter, I will completely characterize all rigidly and atfoldable origami, and describe an efficient algorithm to compute their designs and deformations. For the former, I will show that a material instability inherent to nematic elastomers at the micron scale is capable of suppressing a structural instability (wrinkling) at the engineering scale. These results provide novel, yet concrete, design guidance for membrane structures (where wrinkling can diminish functionality), as well as tools to efficiently investigate robust and elegant concepts for deployable space structures, reconfigurable antennas, and soft robotics using origami.
Eckhard Quandt
TiNiCu and TiNiCuCo thin films for elastocaloric cooling
Chair of Inorganic Functional Materials, Institute for Materials Science, Faculty of Engineering, University of Kiel, Germany The elastocaloric effect is a promising alternative for the replacement of conventional vapor compression cooling which suffers from a high environmental impact and limited efficiency improvement possibilities. Instead of a vaporliquid transition in a conventional cooling, the elastocaloric effect is based on a stress induced structural phase transition usually from a high symmetry to a low symmetry phase. At adiabatic conditions this results in a temperature change of the material. For a continuous use of this effect in a cooling cycle, several requirements have to be fulfilled. Transformation temperatures, effect size and efficiency have to be suitable, but most importantly a high functional and structural fatigue resistance is necessary.Highly fatigue resistant Tirich TiNiCu compositions prepared by thin film technology have been found that can withstand 10 million transformation cycles without functional degradation. Within this talk the reasons for the fatigue resistance will be discussed. In situ synchrotron and TEM investigations have been conducted to investigate the underlying microstructural mechanisms that ensure the reversible transformation. Cobalt and iron addition is used to adjust the transformation temperature to a suitable range to enable the use of this compositions at room temperature. The compositional influence on the elastocaloric parameters is investigated by temperature dependent tensile tests, infrared (IR) thermography and differential scanning calorimetry. Due to the small hysteresis of TiNiCubased compositions an improved elastocaloric cooling efficiency is found in comparison to binary NiTi thin films. Considering also the high fatigue resistance, this class of materials is promising for future elastocaloric cooling applications. Lars Bumke, Christoph Chluba, Eckhard Quandt
Angkana Rüland
A compactness and structure result for a discrete multiwell problem with so(n) symmetry in arbitrary dimension
In this talk I will discuss a compactness and structure result for a quite general class of phase transformationswith SO(n) symmetry in the regime of surface energy scaling. This includes for instance martensitic transformations but also phaseantiphase transformations, whose limiting structures are described. Mathematicallythe argument relies on a combination of a "spinargument" with a reduction of the multiwell problem to anincompatible one wellproblem. This is joint work with G. Kitavtsev, G. Lauteri and S. Luckhaus.
Lucia Scardia,
Equilibrium measures for nonlocal energies: The effect of anisotropy
Nonlocal energies are continuum models for large systems of particles with longrange interactions. Under the assumption that the interaction potential is radially symmetric, several authors have investigated qualitative properties of energy minimisers. But what can be said in the case of anisotropic kernels? Motivated by the example of dislocation interactions in materials science, we pushed the methods developed for nonlocal energies beyond the case of radially symmetric potentials, and discovered surprising connections with random matrices and fluid dynamics.
Hanus Seiner
Microstructures in modulated martensites – experimental observations and theoretical models Modulated martensites of NiMnGa ferromagnetic shape memory alloys are able to form complex, hierarchical microstructures of twins and macrotwin interfaces. Some of the macrotwins in this material exhibit a very unique property called super mobility, i.e. such interfaces can be set into motion by as small mechanical stress as 0.01MPa and can be also easily driven by external magnetic fields. The origin of the super mobility is not fully understood yet. It is, however, believed that this phenomenon may be related to the ability of NiMnGa to form martensitic microstructures at very fine spatial scales, and thus, to specific lattice parameter and crystal structure of this alloy. The talk will summarize the recent experimental observations of microstructures in 10 M modulated NiMnGa, and outline the main theoretical tools used for describing their formation. It will be shown that these microstructures exhibit several unique features, not observed in any shape memory alloy before, which opens a discussion whether other alloys with super mobile interfaces could be, in future, designed based on the knowledge gained on NiMnGa.
Yang Xiang
Energy and dynamics of grain boundaries based on underlying microstructure
Grain boundaries are the interfaces of grains with different orientations in polycrystalline materials. Energetic and dynamic properties of grain boundaries play essential roles in the mechanical and plastic behaviours of the materials. These properties of grain boundaries strongly depend on their microscopic structures. We present continuum models for the energy and dynamics of grain boundaries based on the continuum distribution of the line defects (dislocations or disconnections) on them. The longrange elastic interaction between the line defects is included in the continuum models to maintain stable microstructure on grain boundaries during the evolution. The continuum models is able to describe both normal motion and tangential translation of the grain boundaries due to both coupling and sliding effects that were observed in atomistic simulations and experiments.
Giovani Zanzotto
Deformation avalanches in crystalline materials: some experimental, empirical, and modelling results
We describe recent experimental and empirical studies of the bursty strain behavior of memory alloys undergoing thermically and mechanicallyinduced reversible martensitic transformations. Work in progress also investigates the intermittent evolution of the phase microstructure simultaneously by fullfield strain measurements and by acoustic emission. Powerlawtype behavior for the deformation avalanching of different materials is reported, highligting the role of kinematic compatibility in these phenomena. We finally present some crystallographicallyinformed modelling approaches and results on the strain intermittency in crystalline materials.
POSTERS
Noemi Barrerra
Intermittency and compatibility in martensitic transformations
Detection of events in twodimensional maps for the characterisation of intermittency in various kinds of martensitic material. Particular attention is payed to the comparison between materials which satisfy compatibility conditions and classical incompatible materials.
Luisa Wunner
$\Gamma$convergence and relaxation results in nonlinear elasticity with constraints on the determinant and the cofactor matrix
The Saint VenantKirchhoff energy density is often used to model the deformation of elastic materials. Unfortunately, the corresponding energy allows nonphysical behavior and one cannot guarantee that the corresponding energy has minimizers. This motivates to study a modification of the Saint VenantKirchhoff energy density which is gradient polyconvex and overcomes the drawbacks. The modifications involve the term $\alpha (\nabla \operatorname{Cof} \nabla u + \nabla \det \nabla u)$, where $u$ is the function that describes the deformation. We study what happens as $\alpha \rightarrow 0^+$ by means of the $\Gamma$convergence and present a relaxation result that is motivated by the result we get for the $\Gamma$limit. This master's thesis was supervised by A. Schlömerkemper (Würzburg) and M. Kru\v{z}\'{i}k (Prague).