Lorentz Center - Scale transitions in space and time for materials from 19 Oct 2009 through 23 Oct 2009
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    Scale transitions in space and time for materials
    from 19 Oct 2009 through 23 Oct 2009

GENERIC perspective on coarse graining



Onno Bokhove

University of Twente


Supercritical shallow granular and slurry flows through a contraction

Granular or dry particulate flows are important flows in industry and in nature. An industrial example is the controlled inflow of coke, (iron-ore) pellets and sinter via an inclined chute into the melting oven. Landslides are an example in nature. Slurry flows are a mixture of fluid and particles and are important in the chemical industry, and natural examples include mud and debris avalanches of water-saturated soil or rock debris near volcanoes.Idealized laboratory experiments with dry granular matter, water, and slurry flows through a channel with a linear contraction will be presented, followed by a hydraulic-type mathematical analysis of these cases, and two- and three-dimensional numerical simulations of particle and particle-fluid dynamics. Naturally, we advocate the use of these three, often complimentary, types of investigation as the most fruitful. Finally, an outlook will be given on Heterogeneous Multi-scale Modeling of granular flows; the first aim here is to find (numerical) closure laws for granular flows with poly-dispersed and non-uniform particles and increase computational speed.

Note by SL: this approach is one possibility to bridge the scales (from mud and small particles to large scale flows,and from very short time events like collisions, up to large, geological time-scales)




Daniel Bonn

WZI-University of Amsterdam


Large scale events in soft glassy materials

One of the possible ways to define the glass transition is that the

relaxation time of the system exceeds some critical value. The have been

numerous debates on whether the diverging time scale at the glass

transition implies also a diverging length scale. However experimentally,

not much evidence for length scales larger than a few molecules has been

found. I will present a novel way of looking at glasses transition:

instead of using liquid-state theory as is usually done, we use the

central concept from solid-state physics: the Density of States (DOS). We

thus determine the DOS experimentally for the first time for a (colloidal)

glass, and show that a large length scale emerges naturally from the data.






Markus J. Buehler

Laboratory for Atomistic and Molecular Mechanics, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology


Materiomics: Multiscale science of protein materials in extreme conditions and disease 

Biological protein materials feature hierarchical structures, ranging through the atomistic, molecular to macroscopic scales to form functional biological tissues as diverse as spider silk, tendon, bone, skin, hair or cells. Here I will present integrated theoretical, computational and experimental multiscale materiomics studies, focused on how protein materials deform and fail due to extreme mechanical conditions, disease and injuries. Based on a multi-scale atomistic simulation approach that explicitly considers the architecture of proteins including the details of chemical bonding, we have developed predictive models of the deformation and fracture behavior of protein materials across multiple scales, validated through quantitative comparison with experimental results. The utilization of “model materials” and supercomputing approaches enable us to extract fundamental physical concepts that govern the properties of protein materials at multiple scales, from nano to macro. I will present an investigation of several major classes of protein materials, including cellular alpha-helix rich protein networks, beta-sheet structures as found in spider silk and amyloids, as well as collagenous tissues that form tendon and bone.

An overarching aspect that controls the properties of protein materials is the behavior of clusters of H-bonds, biology’s cement. I will discuss deformation mechanisms and the strength limit of H-bonds, confinement effects in protein nanostructures and associated evolutionary driving forces, as well as the role of material hierarchies in defining their properties. Case studies will be presented that illustrate applications in genetic diseases, explain how structural changes at the molecular level can lead to the formation of defects and flaws, and elucidate the role of mechanical driving forces in initiating the onset of material instabilities. Specific diseases to be discussed include osteogenesis imperfecta (brittle bone disease), Alport’s syndrome (kidney disease), and the rapid aging disease progeria. The understanding of how the molecular structure and material properties are linked across hierarchies of length- and timescales may lead to a paradigm shift in the understanding of basic mechanisms in the behavior of biological systems, in the understanding of injuries and genetic diseases, as well as in disease diagnosis and treatment. The transfer towards the design of novel nanostructures may lead to novel multifunctional and mechanically active, tunable and changeable materials.





Heike Emmerich

Computational Materials Engineering, RWTH Aachen University


Bridging the atomic to microscale for nucleation and initial crystal growth via advanced coupling of phase-field, phase-field crystal and kinetic monte carlo methods

Interfaces of condensed matter systems are essential for tooling the material properties and consequently that of derived devices and products in a whole range of applications from everyday household goods to opto-electronics and even further to medicine.  Prominent examples are corrosion resistant surfa-ces of household goods, or likewise noble surfaces of engineering protheses in medical applications. Thus there has been strongly increased effort in deve-loping computational tools to support the understanding and to derive new design concepts for interfaces and surfaces of condensed matter systems during their processing to a materials system.  This comes along with an inherent multi-scale challenge due to the large range of time- and length scales on which essential physical and chemical mechanisms occur. In this talk we present several examples as a representative cross-section of our model portfolio in this topic.






Alfons G. Hoekstra

Computational Science, University of Amsterdam


Complex Automata, multiscale computing, and applications in the Biomedical Sciences

Biomedical systems are multiscale ("from molecule to man") where many biological and physical/chemical processes interact across the scales. Driven by a challenging application in Cardiovascular disease (in-stent restenosis) a multiscale modelling and computing  framework called complex automata was developed. The methodology behind Complex Automata will be highlighted,  followed by a discussion of the in-stent restenosis application where issues related scale transitions and multiscale computing  are addresssed. Prelimary results related to a multiscale model for  blood viscosity are discussed and its application in models for coronary  artery disease. Finally, to trigger discussions, some thoughts on the role of generic concepts as proposed in Complex Automata for the field of  scale transitions for materials will be formulated.





Markus Hütter 

ETH Zurich, Department of Materials, Polymer Physics


GENERIC perspective on coarse graining

Bridging scales is viewed in this contribution from the perspective of nonequilibrium thermodynamics, particularly using the framework known as GENERIC (for “general equation for the nonequilibrium reversible-irreversible coupling”). First, the corresponding systematic coarse-graining scheme is presented, which involves statistical mechanics procedures and projection operator methods. Second, the scheme is applied to obtain a microscopically motivated continuum description of a polymeric liquid. And third, we discuss potential applications of this methodology to other fields (e.g., the plasticity of metals and polymers), in which the formulation of constitutive relations based on microscopic principles is of interest.





Varvara Kouznetsova

Eindhoven University of Technology


Upscaling techniques for evolving microstructures

In this contribution, presently available computational techniques will be discussed for upscaling the behaviour of evolving microstructures, thus enabling the study of structure-property relations.

In general, the overall macroscopic characteristics of heterogeneous media are determined by multi-scale techniques, termed homogenization in the engineering mechanics and mathematics and coarse graining in physics. Classical homogenization methods include (advanced) rules of mixtures, mean-field methods, based on the famous result by Eshelby, variational bounding methods and asymptotic (mathematical) homogenization. The above mentioned methods perform very well for linear problems and static microstructures. Their extension to non-linear regimes is, however, difficult and has only been done for some particular cases. The treatment of path dependent and evolving microstructures is practically infeasible.

Among the advanced homogenization techniques proposed in the past decade, a computational homogenization scheme, also called FE2 in a particular form, is probably one of the most accurate and general techniques for upscaling the nonlinear behaviour of complex, evolving microstructures. Computational homogenization is essentially based on the derivation of the local macroscopic constitutive response (input leading to output, e.g. stress driven by deformation) from the underlying microstructure through the adequate construction and solution of a microstructural boundary value problem, which resolves the microstructural behaviour and evolution in detail. In case the macroscale boundary value problem is solved simultaneously, a fully nested, concurrent, solution of two boundary value problems is obtained, one at each scale.

In this talk, first the main concepts of the computational homogenization scheme will be summarized and illustrated on some representative examples. Next, the attention will be given to the limits of applicability of the standard technique and extensions thereof will be proposed, e.g. for the cases where the microstructural evolution leads to the overall (stress) relaxation and/or severe strain localization and cracking. Finally, some open issues will be discussed, such as the consistent scale transition of time scales.






Alexander Mielke

WIAS Berlin


Multiscale modeling for energy-driven systems
Material models are
often given as generalized gradient flows, as Hamiltonian systems, or as a combination of both. GENERIC is a consistent way of including both effects.  The importance is that the dynamics is driven by functionals and geometric structures, which define the evolution equation.

We address the question how these structures can be used in multiscale modeling. Instead of passing to the limit in the evolution equation (like in homogenization) we want to pass to the limit in the geometric structures and in the functionals (using Gamma convergence).  The general question is under what conditions such a passage leads to the correct limit model.

We will give a few Hamiltonian or dissipative examples and exemplify certain sufficient compatibility conditions between the Gamma convergence of the functionals and the convergence of the geometric structures.






Michael Parks

Peridynamics for Multiscale Materials Modeling

Sandia National Laboratories, Albuquerque


The peridynamic model is a nonlocal reformulation of continuum mechanics based on integral equations. It assumes points in a continuum separated by a finite distances may interact directly. This nonlocal interaction induces length scales, which can be controlled for multiscale modeling. In particular, recent efforts have demonstrated peridynamics as an up scaling of molecular dynamics. Further, classical elasticity has been established as a limiting case of a peridynamic model. I will survey the analytical, numerical, and computational connections between molecular dynamics, peridynamics, and classical continuum mechanics, motivating peridynamics as a multiscale material model.






Akke Suiker

Delft University of Technology, Faculty of Aerospace Engineering 


Continuous and discrete models for simulating granular assemblies

The mechanical behaviour of an assembly of discrete particles can be studied at various levels of observation. In order to keep the computation time manageable, the large-scale mechanical behaviour of assemblies composed of a very large number of particles is typically studied by means of continuum models. Conversely, the small-scale mechanical behaviour of assemblies composed of a moderate to small number of particles is often studied by means of discrete models, which provide a more accurate computational result than continuum models.  This contribution discusses the connection between continuum models and discrete models, both for  elastic problems and for inelastic (frictional) problems. It is demonstrated how homogenization  procedures can provide a coupling between the elastic responses of discrete models and continuum models.  Heterogeneous effects at the particle level are accounted for at the continuum level through the  inclusion of strain-gradients and rotational gradients, which leads to kinematically enhanced  continuum models of the strain-gradient type and the strain-gradient micro-polar type.  The accuracy and stability of these models is discussed through the analysis of body wave  dispersion curves. For frictional assemblies it is demonstrated how the effective frictional resistance  is affected by the local contact friction at the particle level, and by the relative proportion of sliding  and rolling of particles. In addition, the shape of the failure surface is constructed for  an assembly of discrete particles, and compared to well-known phenomenological continuum failure models.    





Michael Zaiser

The University of Edinburgh


Fluctuations across space and time scales: The case of dislocation-mediated plasticity


On macroscopic scales, the deformation of crystalline solids is spatially smooth and temporally continuous, at least in the absence of so-called plastic instabilities. On small scales, dislocation plasticity is localized and jerky. In my talk I address the question how fluctuations in plasticity change as we move from small to large scales and how the spatio-temporal continuum limit is approached. On the way there are several surprising discoveries to be made. These include a new definition of the yield stress, and a size effect on strength that stems neither from strain gradients nor from the influence of surfaces (a bonus for those who are bored with the various versions of the exhaustion argument).






Jan Zeman

Czech Technical University in Prague


Stable Damage Evolution in Discrete Systems: A Consistent Variational Approach


A consistent derivation of non-local damage theories for heterogeneous media remains to be of the most challenging topics in mechanics of materials. The difficulty of the subject arises from the fact that the spatial separation of scales, widely accepted in the well-established homogenization theories, cannot be applied to the localized damage. In the current presentation, this limitation is overcome by a careful combination of recent development in rate independent processes and in Hashin-Shtrikman-Willis variational principles, specialized to discrete finite systems.


In the adopted “energetic” philosophy, an analyzed system is characterized by the total stored elastic energy and the overall energy dissipation. Following the approach pioneered by Francfort and Marigo, the damage evolution in a discrete structure follows from as a time-incremental variational principle, formulated in terms of topology of damaged phase. The resulting combinatorial optimization problem is next replaced with a relaxed formulation by employing appropriate coarse-grained variables. The essential ingredient of this step is a non-local stored-energy estimate, derived using tools developed for finite-size random composites by Luciano and Willis. Such re-formulation results in an incremental convex optimization problem, efficiently solvable using linear programming. Finally, an extension towards stochastic framework will be briefly commented on. This is a joint work with Ron Peerlings and Marc Geers (TU Eindhoven).