Two different theoretical description have emerged in the last decade to describe the rheology and deformation of glassy materials. On the one hand, the mode coupling approach [Brader2009a], inspired by the successful liquid state based description of the approach to the glass transition, describes the rheology by taking as a starting point equations that describe the dynamics of density fluctuations in a liquid. This description has been shown to provide a good description of global rheology in soft systems not too far above their jamming density. On the other hand, a completely different approach takes as a starting point the existence of shear transformations, which form the elementary ingredients of the dynamics in strongly jammed systems or at low temperatures. Such ideas can be implemented numerically in the form of elasto plastic models [Picard2002] that allow large scale simulations, and have also had support from particle-based quasistatic calculations [Maloney2006]. These models can also be coarse grained to give rise to continuum equations [Bocquet2009]. It is fair to say, however, that there is at present essentially no connection between these two approaches: elasto plastic models are still too simplistic, and mode coupling approaches presumably too 'mean field' in their description of the stress dynamics. The COST approach would be extremely beneficial in bringing together groups that are using these two different approaches to study in parallel such problems as particle diffusion in deformed materials [Martens2011], or the nature and scaling properties of dynamical heterogeneities in actively deformed systems.

This project would involve collaboration between a numerical team in Grenoble and a theoretical team in Konstanz.

Studying the effects of strong external fields in glass forming systems opens a new approach to investigate the glass transition. Experimental, simulational, and theoretical efforts need to be combined in order to unravel the complex structural and transport phenomena under far-from equilibrium conditions. In the theoretical group at Konstanz, mode coupling theory is generalized to incorporate strong external fields into a unified and comprehensive first principles approach to the deformation of amorphous materials. Necessarily, the theoretical developments need to be compared with detailed experimental and simulational investigations, which will greatly benefit from exchange during a COST programme.

Mechanic fields, like strain and stress [Brader2009a], are considered theoretically in Konstanz, which provides insights into (non-linear) elasticity, plasticity, yielding and flow of colloidal dispersions [Siebenbuerger2009,Brader2009b]. Comparisons with metallic systems as studied in Goettingen will be possible in the COST programme and reveal whether different glasses, like metallic and colloidal ones, yield by similar mechanisms. Extensions of the theory building on the Soft Glassy Rheology theory developed in London and Edinburgh will provide insights into the history dependence (ageing) of glass, which may depend on the nature of the applied field. Comparison with theory and simulations of low-temperature glasses as studied in Paris will provide insights into the atomistic motion in amorphous systems during large deformations. The novel technique of 'Active Microrheology' [Gazuz2009] is studied in Konstanz, where a single probe is forced through the glass forming host, so that nonlinear stress-strain and force-velocity relations can be observed. Experiments are performed in Edinburgh and a continued cooperation [Gazuz2001] within the COST programme will be very valuable.

This project would consolidate and extend collaborations involving Konstanz, Goettingen, London, Edinburgh and Paris.

The understanding of the mechanisms responsible for the plastic deformation of glasses is particularly challenging because of the absence of long range order, which prevents the use of electronic microscopy and does not allow one to transpose the usual approaches developed in other fields of materials science such as physical metallurgy. Hence, there is a need to correlate as many properties of the glasses as possible, using various kind of characterization techniques, be they mechanical, structural, or chemical.

An approach particularly well suited to metallic glasses would couple the measurement of local mechanical properties by nanoindentation and atomic force acoustic microscopy for binary glasses of well controlled compositions, coupled with the measurement of local chemical composition using transmission electron microscopy. The evolution of the assumed inhomogeneities with relaxation time at temperature close to the glass transition temperature (Tg) should provide interesting insights on the correlation that exists between local composition and local mechanical properties.

Applying the same approach to more complex bulk metallic glasses (BMG) will then open the possibility to assess the influence of homogeneous deformation on local properties, as it is assumed to promote a so-called rejuvenation of the glass. The structural state of these BMG will then be characterized by differential scanning calorimetry, TEM, nanoindentation, X-ray diffraction and dynamic mechanical analysis, for various times of relaxation (isothermal treatment close to Tg) or various plastic strain levels.

The resulting data set will then be confronted with various theoretical approaches to check their consistency, or to refine their accuracy, in particular by testing their ability to describe the thermodynamic properties and the local distribution of mechanical properties.

This project would involve experimentalists and theoreticians from Goettingen and Paris.

The detailed quantitative verification of rheological models often suffers from the lack of appropriate experimental systems, allowing controlled variation of the main governing parameters. The Sofia group has experience in generating dispersions of soft particles (foams and emulsions) with desired properties [Denkov2009a, Tcholakova2008]. These procedures include appropriate surfactants and surfactant-polymer mixtures, which allow controlled variation of surface fluidity (rigid versus fluid interfaces) and particle-particle interactions (attractive versus repulsive), while preserving the Newtonian viscosity of the continuous phase. These procedures allow also fine control of the mean size, polydispersity, and volume fraction of the dispersed particles. With such systems, the Sofia group has already demonstrated the important effect of surface rigidity on the foam rheological properties [Denkov2005, 2009a] and the role of bubble-bubble attraction for the jamming transition in slowly sheared foams [Denkov2008, 2009b]. In the context of the COST Action, a range of model systems will be designed with controlled major characteristics – particle size, polydispersity and volume fraction, particle interactions and surface rigidity. The properties of these systems will be systematically compared by the rheological methods and surface characterization techniques available in Sofia. Through the STSM implemented in the COST action, the same experimental systems can be run on complementary instruments, available in Action partner groups, such as the MRI in Laboratoire Navier (Paris), 2D Couette rheometer in Leiden, and confocal rheo-imaging in Edinburgh. Thus a complete rheological characterization of a well defined set of systems, covering a wide range of the governing parameters, will be available for comparison with the theoretical models and numerical simulations. In addition, the discussions with the theoretical partner groups (Leiden, Konstanz, London, Zurich, etc.) will provide leads about the most appropriate experimental systems to be designed for verification of the models and simulations. In this way, the COST network will coordinate and enhance the experimental and theoretical efforts in this area, with strong synergistic effect expected.

This project will establish important synergies between experimental groups in Sofia, Paris, Leiden, Edinburgh, and form new links to theoretical partners.

The Edinburgh group plans to understand in more detail the interplay between glassy dynamics and specific mechanical degrees of freedom described by suitable order parameters in materials under flow. These order parameters could address for instance concentration fields; recent theory and experiment in Edinburgh show these to be crucial in colloidal glass flows [Besseling 2010]. But they might also represent the dynamical population of shear-transformation zones (STZ) [Bouchbinder 2009], or other identifiable substructures such as soft modes. Models of soft glassy rheology (SGR) will be further developed to better address the role of a spatially varying mechanical temperature [Fielding 2009]. The relative strengths and weaknesses of SGR models and STZ theory will be explored collaboratively with King's College London and Weizmann, aiming to develop new models capturing more of the physics. In particular the problematic relation between the effective temperature [Lemaitre 2006] that arises in SGR and the (more conventional) subsystem temperature of slow modes in STZ theories will be explored. In collaboration with the Konstanz group [Brader 2008, Brader 2009a], the Edinburgh team will also address whether it is possible to handle additional order parameters within schematic mode coupling theories of colloidal glass rheology. This could create a quantitative avenue to explaining the unexpected occurrence of flow inhomogeneities (shear bands) in isothermal colloidal glasses with monotone stress/strain-rate curves [Besseling 2010].

This project would combine experimental efforts in Edinburgh with theory contributions from London, Israel (Weizmann Institute), Konstanz.

Insight into the microscopic mechanism of deformation is central to the understanding and modeling of macroscopic glass properties. However, for molecular glasses, such experimental insight is challenging. Observation techniques with atomic resolution such as electron microscopy cannot be used due to the lack of translational order. The first insight into the mechanism of plastic deformation has been achieved using models of soft glasses – foams. Direct observations of the rearrangement of soap bubbles in flowing foam have given the first evidence of elementary plastic events in glasses, which were proposed to account also for metallic glasses [Argon1979], and inspired the first physical models of deformation. Simulations confirmed the existence of these plastic events in metallic glasses [FalkLanger1998], and revealed a remarkable similarity between elementary events in foams and hard glasses. Recently, these elementary plastic events have been observed by the Amsterdam group in colloidal glasses, and their direct three-dimensional imaging allowed insight into their topology and thermally activated formation [Schall2007]. This development demonstrates the historic links between hard and soft glasses, and simulations, and the need for establishing an interdisciplinary community. Experimental observations are particularly valuable: they allow determination of important microscopic parameters that can be directly used in physical models of deformation and ageing. Recent years have witnessed a search for common observables. Models that are built on elementary plastic events such as the STZ and SGR models have very recently been applied to an increasing range of amorphous materials from metallic glasses to colloids, foams, emulsions, and granulates with good success. Microscopic observations and simulations have allowed the definition of common observables on the one hand, and system-specific properties on the other. However, very recent experiments and simulations [Maloney2009] have shown that these plastic events are not independent, as assumed by many models, but show strong correlation. These correlations may play a crucial role for important properties of the deformation of glasses such as strain localization and failure; however, the nature of these interactions is far from understood. Identifying these correlations and their common properties in the different glassy materials will be an important challenge for the near future. In this subproject, we seek active collaborations between experimentalists and simulation scientists to meet this challenge. The goal is to compare correlations in the deformation of metallic glasses, colloids, foams and granular materials to identify a common, scale-bridging mechanism of the deformation of glasses. Owing to the ever increasing computer power, simulations can now be performed in sufficiently large systems. Likewise, for experimental systems, sufficiently large sections can now be imaged and analyzed. This offers new opportunities for a universal scale-bridging picture of the deformation of glasses.

This project would involve experiments performed at Amsterdam, Leiden, Göttingen, and Edinburg, and interaction with theoreticians from Paris and Grenoble, to compare direct observations in colloidal glasses with foams, granulates, and metallic glasses. It will be the efficient combination of experimental observations and simulations in a wide range of glassy systems that will allow us to identify the generic mechanism of deformation.

Proposed by the experimental and numerical teams in Montpellier

We propose to investigate both experimentally and numerically the fracture in amorphous soft materials. While significant progress has been made in the last ten years on a plausible scenario of the glass transition [Cavagna2009,Binder2011], little is known on the rheological behavior of matter close to this transition. In can be expected that close to the glass transition the time scales of the viscoelastic processes become comparable with the relaxation times of the glass-former thus giving rise to new dynamical phenomena. Also, the glass transition has been shown to be controlled by the emergence of dynamical heterogeneities, the length-scale of which grows when approaching the transition from above [Berthier2005]. How does this length-scale influence the rheological response? Conversely, do viscoelastic measurements allow to access this length-scale closer to the glass transition than other experiments?

In particular, the fracture behavior of non-crystalline materials is far from being understood, especially on a microscopic scale. Heating up the material, fracture goes from brittle to ductile: fracture of brittle materials absorbs relatively little energy, with no evidence of irreversible deformation prior to failure, while a ductile material can be deformed plastically without breaking. For crystalline materials, the transition is marked at the microscopic level by the emission of mobile dislocations at the crack tip: the solid starts flowing in the vicinity of the tip (the so-called process zone), where stresses are particularly high. Since there is no difference between the structure of a solid glass and its super-cooled liquid, no such disordering mechanism can be invoked for non-crystalline materials. How can one then define a process zone?

Experimentally, we will tackle these issues by studying i) model (nearly Maxwellian) viscoelastic materials with tunable rheological parameters ii) attractive and repulsive glasses. We will take advantage of a well known instability -the Saffman-Taylor instability- to amplify the microscopic fluctuations and heterogeneities and to control the behavior (fragile vs ductile) of the material [Tabuteau2009,Tixer2010]. Experimental methods will include videomicroscopy and space- and time-resolved light scattering [Duri2009].

Within the numerical simulations we will study the viscoelastic and fracture behavior within a model for a telechelic gel-former, a model system which allows to change continuously from a simple (i.e. repulsive) glass-former to a viscoelastic liquid [Hurtado2007]. Since this system can also be realized in a real experiment, we will be able to compare the results from our simulations with real experimental data which will allow to advance the understanding of the results from the simulations as well the one of the experiments.

Recent theoretical work at Roskilde has involved the discovery a key feature of several of the standard model glass-forming liquids: The structure and dynamics are almost invariant along certain curves in the phase diagram, called isomorphs. Liquids has have isomorphs are called “strongly correlating liquids” because of the strong correlation between the configurational parts of pressure and energy fluctuations. This property can be considered equivalent to an effective inverse power-law potential, from which certain scaling properties follow [Pedersen2010]. These are independent of whether a system is in equilibrium and therefore relevant for the amorphous solid as much as the viscous liquid. The group has special computational capabilities, combining a graphics-card based computational cluster and an in-house MD code optimized for small systems and long times. Probably no other group can match us in performance for systems smaller than 10000 particles.

Deformation of an amorphous system necessarily involves taking it out of equilibrium. In fact the term ”rejuvenation” has been used to describe this; it implies the opposite of ageing, the natural approach towards equilibrium of an undriven out-of-equilibrium system. In a driven system the competition between ageing and rejuvenation, manifested in structural and mechanical properties, is governed by the relation between the internal relaxation time and the shear rate. As there exists no general theory for out-of-equilibrium systems, many attempts have been made to characterize the microscopic states, one being the effective temperature, defined via violations of the fluctuation-dissipation theorem (FDT). Work published in the last year [Gnan2010] has investigated the validity of the effective temperature concept for strongly correlating liquids in the context of off-equilibrium behaviour (jumps of temperature and/or density followed by ageing) and found that, in contrast to non-strongly correlating liquids, the ageing behavior is simple, and can be understood be reference to isomorphs. In addition effective temperature has a meaningful interpretation as the temperature corresponding to the energies of the potential energy wells visited during ageing.

The scaling behavior of strongly correlating liquids and glasses under shear has been investigated recently in Israel [Lerner2009], although this work has not made direct connection to the isomorph concept. We propose to study violation and extensions of the (FDT) to sheared systems [Kruger2009] with a view to understanding in detail how the competition between ageing and shear-induced rejuvenation is governed by an effective temperature. The results from Ref. [Gnan2010] suggest that the latter is an especially useful concept particularly in strongly correlating models, although this it is not fully understood why.