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Multiscale mechanics

The mechanical behavior of engineering materials is influenced by their heterogeneous microstructure. Due to large differences in length scale, it is usually not possible to explicitly model this influence in component simulations. This is why multiscale approaches are used in material modeling. The heterogeneous microstructure is explicitly modeled on a small length scale (within so-called representative volume elements) and its influence on the macroscopic material behavior is determined in average by means of numerical homogenization.

Projects:

The concurrently coupled Quantum Mechanics (QM) - Continuum Mechanics (CM) approach for electro-elastic problems is considered in this proposal. Despite the fact that efforts have been made to bridge different description of matter, many questions are yet to be answered. First, an efficient Finite Element (FE)-based solution approach to the Kohn-Sham (KS) equations of Density Functional Theory (DFT) will be further developed. The h-adaptivity in the FE-based solution with non-local pseudo-potentials,…

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MOCOPOLY is a careful revision of an AdG2010-proposal that was evaluated above the quality threshold in steps1&2. In the meantime the applicant has made further considerable progress related to the topics of MOCOPOLY. Magneto-sensitive polymers (elastomers) are novel smart materials composed of a rubber-like matrix filled with magneto-active particles. The non-linear elastic characteristics of the matrix combined with the magnetic properties of the particles allow these compounds to deform…

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Classical continuum approaches do not explicitly consider the specific atomistic or molecular structure of materials. Thus, they are not well suited to describe properly highly multiscale phenomena as for instance crack propagation or interphase effects in polymer materials. To integrate the atomistic level of resolution, the “Capriccio” method has been developed as a novel multiscale technique and is employed to study e.g. the impact of nano-scaled filler particles on the mechanical…

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Aussagefähige Bauteilsimulationen erfordern eine quantitativ exakte Kenntnis der Materialeigenschaften. Dabei sind klassische Charakterisierungsmethoden
teilweise aufwendig, in der Variation und Kontrolle der Umgebungsbedingungen anspruchsvoll oder in der räumlichen Auflösung begrenzt. Das Projekt beschäftigt sich
deshalb mit der Ertüchtigung hochauflösender Meßmethoden wie Nanoindentation oder Rastkraftmikroskopie und der komplementierenden…

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If metallic powders are used as base materials in selective beam melting processes, the resulting mesostructure of the solidified material, i.e. the geometry (shape, size) of the crystal grains and their orientation (texture), strongly dependent on the direction and magnitude of the temperature gradient at the solidification front. The objective of this project is the continuum-thermo-mechanical modelling and simulation of the material behaviour, taking into account the process-induced mesostructure. For this purpose, a gradient-enhanced crystal plasticity formulation is used on the mesoscale and the mesoscopic variables are transferred by the help of numerical homogenization to the macroscale, both for the isothermal behaviour after the process as well as for the cooling period during the process, which results in residual strains and accompanying residual stresses.

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In a continuum the tendency of pre-existing cracks to propagate through
the ambient material is assessed based on the established concept of
configurational forces. In practise crack propagation is
however prominently affected by the presence and properties of either
surfaces and/or interfaces in the material. Here materials exposed to
various surface treatments are mentioned, whereby effects of surface
tension and crack extension can compete. Likewise, surface tension in
inclusion-matrix interfaces can often not be neglected. In a continuum
setting the energetics of surfaces/interfaces is captured by separate
thermodynamic potentials. Surface potentials in general result in
noticeable additions to configurational mechanics. This is
particularly true in the realm of fracture mechanics, however its
comprehensive theoretical/computational analysis is still lacking.

The project aims in a systematic account of the pertinent
surface/interface thermodynamics within the framework of geometrically
nonlinear configurational fracture mechanics. The focus is especially on
a finite element treatment, i.e. the Material Force Method [6]. The
computational consideration of thermodynamic potentials, such as the
free energy, that are distributed within surfaces/interfaces is at the
same time scientifically challenging and technologically relevant when
cracks and their kinetics are studied.

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The mechanical properties and the fracture toughness of polymers can be
increased by adding silica nanoparticles. This increase is
mainly caused by the development of localized shear bands, initiated by
the stress concentrations due to the silica particles. Other mechanisms
responsible for the observed toughening are debonding of the particles
and void growth in the matrix material. The particular mechanisms depend
strongly on the structure and chemistry of the polymers and will be
analysed for two classes of polymer-silica composites, with highly
crosslinked thermosets or with biodegradable nestled fibres (cellulose,
aramid) as matrix materials.

The aim of the project is to study the influence of different mesoscopic
parameters, as particle volume fraction, on the macroscopic fracture
properties of nanoparticle reinforced polymers.

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In engineering
applications, plastics play an important role and offer new possibilities to
achieve and to adjust a specific material behaviour. They consist of
long-chained polymers and possess, together with additives, an enormous
potential for tailored properties.

Recently,
techniques have been established to produce and to disperse filler particles
with typical dimensions in the range of nanometers. Even for low volume
contents of filler particles, these so-called nanofillers may have significant
impact on the properties of plastics. This can be most likely traced back to
their very large volume-to-surface ratio. In this context, the polymer-particle
interphase is of vital importance: as revealed by experiments, certain
nanofillers may e.g. increase the fatigue lifetime of plastics by a factor of
15.

The effective
design of such nanocomposites quite frequently requires elaborated mechanical
testing, which might - if available - be substituted or supplemented by
simulations. For this purpose, however, continuum mechanics together with the
Finite Element Method (FE) as the usual tool for engineering applications is
not well-suited since it is not able to capture processes at the molecular
level. Therefore, particle-based techniques such as molecular dynamics (MD)
have to be employed. However, these typically allow only for extremely small
system sizes and simulation times. Thus, a multiscale technique that couples
both approaches is required to enable the simulation of so-called
representative volume elements (RVE) under consideration of atomistic effects.

The goal of this
4-year project is the development of a methodology which yields a
continuum-based description of the material behaviour of the polymer-particle
interphase of nanocomposites, whereby the required constitutive laws are
derived from particle-based simulations. Due to their very small dimensions of
some nanometers, the interphases cannot be accessed directly by experiments and
particle-based simulations must substitute mechanical testing. The recently
developed Capriccio method, designed as a simulation tool to couple MD and FE
descriptions for amorphous systems, will be employed and refined accordingly in
the course of the project.

In the first step, the mechanical
properties of the polymer-particle interphase shall be determined by means of
inverse parameter identification for small systems with one and two
nanoparticles. In the second step, these properties shall be transferred to large
RVEs. With this methodology at hand, various properties as e.g. the particles’
size and shape as well as grafting densities shall be mapped from pure
particle-based considerations to continuum-based descriptions. Further
consideration will then offer prospects to transfer the material description to
applications relevant in engineering and eventually suited for the simulation
of parts.

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Nanocomposites have great potential for various applications since their
properties may be tailored to particular needs. One of the most
challenging fields of research is the investigation of mechanisms in
nanocomposites which improve for instance the fracture toughness even at
very low filler contents. Several failure processes may occur like
crack pinning, bi-furcation, deflections, and separations. Since the
nanofiller size is comparable to the typical dimensions of the monomers
of the polymer chains, processes at the level of atoms and molecules
have to be considered to model the material behaviour properly. In
contrast, a pure particle-based description becomes computationally
prohibitive for system sizes relevant in engineering. To overcome this,
only e.g. the crack tip shall be resolved to the level of atoms or
superatoms in a coarse-graining (CG) approach.

Thus, this project aims to extend the recently developed multiscale
Capriccio method to adaptive particle-based regions moving
within the continuum. With such a tool at hand, only the vicinity of a
crack tip propagating through the material has to be described at CG
resolution, whereas the remaining parts may be treated continuously with
significantly less computational effort.

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Fracture is an inherently multiscale process in which processes at all
length- and timescales can contribute to the dissipation of energy and
thus determine the fracture toughness. While the individual processes
can be studied by specifically adapted simulation methods, the interplay
between these processes can only be studied by using concurrent
multiscale modelling methods. While such methods already exist for
inorganic materials as metals or ceramics, no similar methods
have been established for polymers yet.

The ultimate goal of this postdoc project is to develop a concurrent
multiscale modelling approach to study the interplay and coupling of
process on different length scales (e.g. breaking of covalent bonds,
chain relaxation processes, fibril formation and crazing at
heterogeneities,…) during the fracture of an exemplary thermoset and its
dependence on the (local) degree of cross-linking. In doing so, this
project integrates results as well as the expertise developed in the
other subprojects and complements their information-passing approach.

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Materials such as solid foams, highly-porous cohesive granulates, for
aerogels possess a mode of failure not available to other solids. cracks
may form and propagate even under compressive loads (‘anticracks’,
‘compaction bands’). This can lead to counter-intuitive
modes of failure – for instance, brittle solid foams under compressive
loading may deform in a quasi-plastic manner by gradual accumulation of
damage (uncorrelated cell wall failure), but fail catastrophically under
the same loading conditions once stress concentrations trigger
anticrack propagation which destroys cohesion along a continuous
fracture plane. Even more complex failure patterns may be observed in
cohesive granulates if cohesion is restored over time by
thermodynamically driven processes (sintering, adhesive aging of newly
formed contacts), leading to repeated formation and propagation of zones
of localized damage and complex spatio-temporal patterns as observed in
sandstone, cereal packs, or snow.

We study failure processes associated with volumetric compaction in
porous materials and develop micromechanical models of deformation and
failure in the discrete, porous microstructures. We then make a scale
transition to a continuum model which we parameterise using the discrete
simulation results.

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In previous works, the dependence of
failure mechanisms in composite materials like debonding of the
matrix-fibre interface or fibre breakage have been discussed.  The
underlying model was based on specific cohesive zone elements, whose
macroscopic properties could be derived from DFT. It has been shown that
the dissipated energy could be increased by appropriate choices of
cohesive parameters of the interface as well as aspects of the fibre.
However due to the numerical complexity of applied simulation methods
the crack path had to be fixed a priori. Only recently models allow
computing the full crack properties at macroscopic scale in a
quasi-static scenario by the solution of a single nonlinear variational
inequality for a
given set of material parameters and thus model based optimization of
the fracture properties can be approached.

The goal of the project is to develop an optimization method, in the
framework of which crack properties (e.g. the crack path) can be
optimized in a mathematically rigorous way. Thereby material properties
of matrix, fibre and interfaces should serve as optimization variables.

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The current research project aims to develop microstructurally
motivated mechanical models for brain tissue that facilitate early diagnostics
of neurodevelopmental or neurodegenerative diseases and enable the development
of novel treatment strategies. In a first step, we will experimentally
characterize the behavior of brain tissue across scales by using versatile
testing techniques on the same sample. Through an accompanying microstructural
analysis of both cellular and extra-cellular…

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This project involves manufacturing biopolymer hydrogels and
cataloguing their mechanical properties. They serve as replacement
materials in order to understand and model the highly-complex behaviour
of soft biological tissue. The aim is to generate a catalogue of
replacement materials for various soft tissue that links the specific
characteristics of their mechanical responses with the relevant
modelling approach. This catalogue could make the process of selecting
suitable materials for 3D printing of artificial organs or generating
suitable models for prognostic simulations considerably easier in the
future.

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Participating Scientists: