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## Scale transitions in space and time for materials |

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) ---
WZI-University of Amsterdam
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. ---
Laboratory
for Atomistic and Molecular Mechanics, Department of Civil and Environmental
Engineering, Massachusetts Institute of Technology
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. ---
Computational Materials Engineering, RWTH Aachen University
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. ---
Computational Science, University of Amsterdam
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. ---
ETH Zurich, Department of Materials, Polymer Physics
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. ---
Eindhoven
University of Technology
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. ---
WIAS Berlin
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. ---
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. ---
Delft
University of Technology, Faculty of Aerospace Engineering
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. --
The University of Edinburgh
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). ---
Czech Technical University in Prague
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). --- [Back] |