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Optimization

Optimization of mechanical structures and systems

Projects:

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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This project targets the formulation and implementation of a method for structural shape and topology optimization within an embedding domain setting. Thereby, the main consideration is to embed the evolving structural component into a uniform finite element mesh which is then used for the structural analyses throughout the course of the optimization. A boundary tracking procedure based on adaptive (or hierarchical) mesh refinement is used to identify interior and exterior elements, as well as such elements that are intersected by the physical domain boundary of the structural component. By this mechanism, we avoid the need to provide an updated finite element mesh that conforms to the boundary of the structural component for every single design iteration. Further, when considering domain variations of the structural component, its material points are not attached to finite element nodal points but rather move through the stationary finite element mesh of the embedding domain such that no mesh distortion is observed. Hence, one circumvents the incorporation of time consuming mesh smoothing operations within the domain update procedure. In order to account for the geometric mismatch between the boundary of the structural component and its non-conforming finite element representation within the embedding domain setting, a selective domain integration procedure is employed for all elements that are intersected by the physical domain boundary. This is to distinguish the respective element area fractions interior and exterior to the structural component. We rely on an explicit geometry description for the structural component, and an adjoint formulation is used for the derivation of the design sensitivities in the continuous setting.

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We consider local refinements of finite element triangulations as continuous graph operations, for instance by splitting nodes and inflating edges to elements. This approach allows for the derivation of sensitivities for functionals depending on the finite element solution, which may in turn be used to define local refinement indicators. Thereby, we develop adaptive algorithms exploiting sensitivities for both hierarchical and non-hierarchical mesh changes, and analyze their properties and performance in comparison with established methods.

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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 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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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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