• Describe the most important research tasks to be coordinated by the Action.
• Provide a structured, but not too detailed work plan flexible enough to permit the inclusion, at the implementation stage, of disciplinary perspectives and activities not foreseen during the preparation of the proposal. Keep the framework of the Action open and flexible.
• Explain the human and technical means to achieve the objectives described in section C.
• Remember that this section must be clear to non-specialists (even if the description may be more “technical”).

This Action seeks to promote, and coordinate at European level, research efforts which aim to relate macroscopic properties of amorphous materials to microscopic features, based on an understanding of the underlying physical mechanisms. It focuses on the mechanical behaviour of amorphous materials, with on the one hand the visco-elastic response in the regime of small deformation, and on the other, large deformation and flow. The latter regime includes homogeneous flows but also the transition to failure via shear-banding and localization. The most important research tasks are the following:

1. Gather information about the elementary mechanisms of deformation via experiments and numerical simulations that can access microscopic scales
2. Identify coarse-grained observables (stress, strain, density, texture, distributions of material properties etc.) which allow one to characterize the internal material state prior to and during deformation
3. Construct equations of motion which govern the relevant fields describing the material state
4. Identify limiting cases (hard/soft particles, slow/fast deformation etc) where existing concepts can be shown to work accurately or conversely to break down
5. Construct scenarios that interpolate between disparate domains, e.g. going from hard (colloidal) to soft (metallic) interactions to clarify commonalities and differences between diverse amorphous materials

The laboratories which have been involved in the preparation of this proposal bring wide-ranging expertise in experimental, numerical, and theoretical studies of a variety of amorphous solids. In many cases, more than one laboratory is involved in similar work, but to date there has been little collaborative effort. Experimental domains of expertise cover metallic glasses, colloidal glasses, and foams, and include a vast array of fabrication protocols and experimental methods.

For experimental studies of metallic glasses, Action participants have the capability to produce metallic glasses of various compositions and glass forming ability, in bulk form or as ribbons. They own a range of experimental apparata for: structural characterization (X-Ray Diffraction, Scanning Transmission Electron Microscopy) to distinguish amorphous vs crystalline structures; chemical characterization from the nanometer to the micrometer scale (Energy Dispersive X-ray spectrometry, Electron Energy Loss Spectroscopy, Electron Probe MicroAnalyser); and thermodynamic characterization (Differential Scanning Calorimetry). The mechanical properties, finally, can be studied through various methods, such as macroscopic compression tests – in homogeneous or inhomogeneous conditions, nanoindentation, or a broad range of mechanical spectroscopy techniques (including Double Paddle Oscillator or Atomic Force Acoustic Microscope).

For colloidal glasses, the Action partners have complementary expertise in the synthesis of colloidal particles with controlled particle size, polydispersity and material from hard-sphere to temperature-sensitive soft particle systems, allowing to explore a range of glassy behaviour from fragile to strong glasses. They can also vary the particle interactions from repulsive to attractive by adding depletant, and control the particle pair potential directly by using temperature-dependent binary solvents. Investigation techniques include conventional and Fourier transform rheology to probe the frequency-dependent mechanical response, static and dynamic light scattering to measure structure factor and diffusion coefficient, and confocal microscopy to image the individual particles and follow their motion directly in three dimensions and real-time. Combined rheo-confocal setups allow even simultaneous rheological measurement and three-dimensional particle imaging to explore a direct link between macroscopic rheology and microscopic particle dynamics.

For foams, the teams included in the Action so far have a range of complementary instruments permitting the fabrication and analysis of monodisperse and polydisperse 2- and 3-dimensional foams. Available characterization methods include a custom-built strain-controlled 2D rheometer and sensitive strain and stress-controlled 3D rheometers. Structural information for the bubble rearrangements in flowing foams can be obtained using diffusing wave spectroscopy or by direct optical observations. Detailed characterization methods of the surface rheological properties (both dilatational and shear) in foaming solutions are also available.

A magnetic resonance imaging (MRI) facility complements these methods. It permits to characterize the internal state of possibly inhomogeneous flows (density, velocity profile, etc.) of sheared colloidal pastes, foams, and other complex systems in rheometry experiments. In this way one can assess what is actually measured in macroscopic rheometry – a key characterization tool in industry – and provide guidelines to industrial partners concerning the interpretation of these measurements.

The Action participants identified so far also possess very significant expertise and equipment for numerical simulation, from the point of view of both software and hardware. Algorithmic expertise covers methods ranging from plain molecular dynamics simulations, to minimization or saddle-node tracking methods which grant access to key properties of the disordered structure, or can accelerate simulations so as to access macroscopically relevant time and space scales. Hardware capacities include local clusters (usually comprising up to several hundreds of cores), and time allocations on supercomputing centres.

Finally, preparation of the Action has already gathered a large panel of theoretical teams, covering the major existing theories of deformation in amorphous materials:

• The mode-coupling theory (MCT) is a successful description of the approach to the glass transition from the liquid state, and is based on equations that describe the dynamics of density fluctuations in a liquid. It has been adapted to sheared system and has been shown to provide a good description of bulk rheology in soft systems not too far above their jamming density.
• “Isomorphic” curves in the phase diagram can be deduced from specific properties of the particle-particle interactions. They predict relationships between a number of thermodynamic, static, and dynamic properties of glasses. But such “isomorphic invariants” have so far been studied only in the absence of deformation.
• The soft glassy rheology (SGR) model introduces a stochastic description at the mesoscopic level that tracks the evolution of local strains in a material, as well as the local barriers to irreversible mechanical rearrangements during which energy is dissipated. It has been used to make qualitatively accurate predictions for a wide range of steady and non-steady (ageing) deformation scenarios, in particular in soft materials such as colloidal glasses and emulsions or foams.
• The shear transformation zone (STZ) theory describes flow in a glassy solid as an accumulation of local rearrangements or “shear transformations” occurring in specific defects (“zones”). These events are assumed uncorrelated. Equations of motion for zone densities are derived from thermodynamic principles, and lead to predictions for macroscopic stress under various deformation conditions.
• The avalanche behaviour theory (ABT) proposes that in a material under shear, basic relaxation events self-organize as avalanches; this leads to predictions for the functional form of the stress-strain-rate relation in homogeneous, steady-state flows. The theory is based on simulation results, and will benefit from experimental investigations into whether the postulated avalanche behaviour occurs in physical systems.
• Elasto-plastic models are not dissimilar to e.g. SGR in that they consider local strains or stresses and plastic rearrangement events, but track in more detail how stresses redistribute after such events, leading to spatial correlations, and possibly avalanches and/or shear bands. They generally neglect the large scale motion of the material and so are better suited to the study of small deformations.

This Action will welcome any new participants from related fields in materials science, physics, and engineering, who can help advance its goals. This includes researchers with expertise in other types of amorphous materials which are not currently covered, or other characterization or simulation techniques, or alternative theoretical approaches.

• Do not mention explicitly the names of individual scientists, specific research institutions or other bodies (only exceptionally, if the Action cannot be implemented without the participation of a specific Institution, you should clearly mention this with the relevant explanation); Always remember that scientists who have not participated in the preparation are also entitled to join if their countries accept the MoU.
• Focus on work plan and methods of the Action and not on its organisation.
• If you plan Working Groups, you may mention their objectives and what they will achieve.

Advances on the above tasks require to reach across, and break down, traditional boundaries between Physics, Material Science and Engineering. This Action thus rests on a collaborative effort, with at the core the transversal communication of theoretical concepts and data analysis techniques across communities. Its success will depend, in particular, on the very close interaction between theory, experiments, and numerical simulations. To spur progress this Action plans to encourage all researchers to direct their specific efforts so that they contribute to the foundation of a coherent field of research, including:

• compare and analyse existing theories for deformation and flow; analyse in detail which assumptions they make and whether these assumptions are specific or not to a given material; delineate as precisely as possible their domains of applicability
• define benchmark experimental or numerical tests that can discriminate between the existing scenarios; promote their usage for a broad and diverse range of materials whenever possible; collect relevant experimental data
• construct databases of both material macroscopic behaviour and microstructural information, which are accessible online, are as complete as possible, and cover homogeneous and inhomogeneous flow regimes.
• promote the usage of identical experimental models (this is often the case in metallic glasses, less so with colloidal materials, which have broad variability) that can be studied by a broad ranges of investigation techniques.

This process requires to help experimental groups become more aware of recent, often technically demanding, theoretical developments, and conversely, to encourage theorists to adapt models to reflect details of new materials for advanced technology being pursued by experimentalist participants.

Examples of collaborative projects that will be supported by this Action are listed below. To emphasize how these involve cross-interactions between teams spread all over Europe, we provide further details of some projects [marked PWP] in the Preliminary Work Program, listing for these only titles with a brief explanation.

• Compare existing theories systematically against deformation data on both metallic glasses – in homogeneous flow, near the glass transition – and colloidal glasses and similar soft materials (emulsions, microgel suspensions); make tests more stringent by focussing on domains outside those motivating those theories (metallic glasses for STZ, soft materials for SGR etc.)
• Extend the “liquid isomorphs” approach to predict the pressure-dependence of metallic glass behaviour
• “Connecting the high temperatures and low temperature pictures” [PWP]: Understand the relationships between liquid-based (MCT) and solid-based (elasto-plastic) models
• “Mode-coupling and mechanical fields” [PWP]: Understand how mechanical forces (i.e. stress and strain fields) can enter the framework of MCT
• “Rheology, inhomogeneities and evolution of thermodynamic properties with plastic deformation and structural relaxation of metallic glasses” [PWP]: Linking local mechanical properties to thermodynamics
• “Model experimental systems with controlled governing parameters” [PWP]: Complete rheological characterization of model systems across a wide range of parameters
• “Role of structural and compositional order parameters in glassy rheology” [PWP]: Tracking composition, density and effective temperature variations in space, in experiment and theory
• “Experimental insight into the microscopic mechanisms of deformation” [PWP]: Quantifying, understanding and exploiting correlations between plastic events

These efforts will be coordinated by five working groups with the following remits:

1.WG1 “Microstructures”: address the identification, using both experiments and numerical simulations, of elementary mechanisms of deformation, primarily in low temperature conditions, i.e. in the solid state. Determine which form of data analysis best permits to access key information about the underlying phenomenology (→ tasks 1 & 2)

2.WG2 “Across the glass transition”: connect research on amorphous materials under strain to work on glassy relaxation in supercooled liquids. This connection is established both ways: what can be borrowed from theories developed for glassy relaxation; what do features emerging from studies of sheared systems allow us to learn about relaxation in the absence of deformation (→ tasks 4,5)

3.WG3 “Multiscale methods”: focus on the passage from mesoscopic to macroscopic scales: how can microscopic mechanisms such as those detected in WG1&WG2 lead to constitutive equations like those used in WG4; how do these then predict material behaviour under inhomogeneous deformation, or the transition towards shear-banding and localization (→ tasks 2 & 3)

4.WG4 “Constitutive equations”: put together and compare existing theoretical work on material deformation; determine which specific predictions are made by these theories at the macroscopic scale and how they can be tested in experiments; connect research performed in this Action to the material engineering community (→ tasks 3 & 4 in Sec. D.1 above)

These working groups correspond to several identifiable angles of attack of the scientific problems described above. The coordination between them will also be important – and implemented via regular joint WG meetings – as the information gained from WG1&WG2 relating to needs to feed into WG3, which itself feeds into WG4. Finally we add a WG5 which will permit the transfer of this knowledge towards industrial partners:

5.WG5 “Knowledge Transfer to Industry” will be in charge of encouraging the participation of industrial partners, facilitating the transfer of knowledge from public research efforts towards applied research laboratories, and conversely communicating to the public sector industrial problems where the fundamental knowledge on amorphous materials can lead to technological breakthroughs. WG5 will be responsible in particular for the invitation of industrial participants to Action meetings; to monitor and report scientific progress on applied research projects; to ensure, in collaboration with the STSM coordinator, that a proper component of STMSs facilitate the transfer of knowledge from fundamental to applied projects, and from applied research to industry.