Steinmann, Paul, Prof. Dr.-Ing. habil.

SoftFrac will revolutionise geometrically nonlinear fracture mechanics of soft materials (in short soft fracture) by capitalising on configurational mechanics, an unconventional continuum formulation that I helped shaping over the past decades. Mastering soft fracture will result in disruptive progress in designing the failure resilience of soft devices, i.e. soft robotics, stretchable electronics and tissue engineering applications. Soft materials are challenging since they can display moduli as low as only a few kPa, thus allowing for extremely large deformations. Geometrically linear fracture mechanics is well established, nevertheless not applicable for soft fracture given the over-restrictive assumptions of infinitesimal deformations. The appropriate geometrically nonlinear, finite deformation counterpart is, however, still in its infancy. By combining innovative data-driven/data-adaptive constitutive modelling with novel configurational-force-driven fracture onset and crack propagation, I will overcome the fundamental obstacles to date preventing significant progress in soft fracture. I propose three interwoven research Threads jointly addressing challenging theoretical, computational and experimental problems in soft fracture. The theoretical Thread establishes a new constitutive modelling ansatz for soft in/elastic materials, and develops the transformational configurational fracture approach. The computational Thread provides the associated novel algorithmic setting and delivers high-fidelity discretisation schemes to numerically follow crack propagation driven by accurately determined configurational forces. The experimental Thread generates and analyses comprehensive experimental data of soft materials and their geometrically nonlinear fracture for properly calibrating and validating the theoretical and computational developments. Ultimately, SoftFrac, for the first time, opens up new horizons for holistically exploring the nascent field soft fracture.

X01 befasst sich mit dem Problem widersprüchlicher Ergebnisse mechanischer Eigenschaften von ultraweichen Materialien wie Hirngewebe, wenn unterschiedliche ex vivo und in vivo Testverfahren verwendet werden. Unsere Hypothese ist, dass es ein kontinuumsbasiertes Simulationsmodell ermöglichen wird, die verschiedenen experimentell beobachtbaren Regime in vivo und ex vivo zu vereinen. Damit können wir erstmals mechanische ex vivo Parameter verwenden, die aus verschiedenen Testmodalitäten gewonnen wurden, um das mechanische in vivo Verhalten des menschlichen Gehirns zu erklären.

Thecentral nervous system (CNS) is our most complex organ system. Despite tremendousprogress in our understanding of the biochemical, electrical, and geneticregulation of CNS functioning and malfunctioning, many fundamental processesand diseases are still not fully understood. For example, axon growth patterns inthe developing brain can currently not be well-predicted based solely on thechemical landscape that neurons encounter, several CNS-related diseases cannotbe precisely diagnosed in living patients, and neuronal regeneration can stillnot be promoted after spinal cord injuries.

Duringmany developmental and pathological processes, neurons and glial cells aremotile. Fundamentally, motion is drivenby forces. Hence, CNS cells mechanicallyinteract with their surrounding tissue. They adhere to neighbouring cells and extracellular matrix using celladhesion molecules, which provide friction, and generate forces usingcytoskeletal proteins.  These forces aretransmitted to the outside world not only to locomote but also to probe themechanical properties of the environment, which has a long overseen huge impacton cell function.

Onlyrecently, groups of several project leaders in this consortium, and a few other groupsworldwide, have discovered an important contribution of mechanical signalsto regulating CNS cell function. For example, they showed that brain tissuemechanics instructs axon growth and pathfinding in vivo, that mechanicalforces play an important role for cortical folding in the developing humanbrain, that the lack of remyelination in the aged brain is due to an increasein brain stiffness in vivo, and that many neurodegenerative diseases areaccompanied by changes in brain and spinal cord mechanics. These first insights strongly suggest thatmechanics contributes to many other aspects of CNS functioning, and it islikely that chemical and mechanical signals intensely interact at the cellularand tissue levels to regulate many diverse cellular processes.

The CRC 1540 EBM synergises the expertise of engineers, physicists,biologists, medical researchers, and clinicians in Erlangen to explore mechanicsas an important yet missing puzzle stone in our understanding of CNSdevelopment, homeostasis, and pathology. Our strongly multidisciplinary teamwith unique expertise in CNS mechanics integrates advanced invivo, in vitro, and in silico techniques across time(development, ageing, injury/disease) and length (cell, tissue, organ) scalesto uncover how mechanical forces and mechanical cell and tissue properties,such as stiffness and viscosity, affect CNS function. We especially focus on(A) cerebral, (B) spinal, and (C) cellular mechanics. Invivo and in vitro studies provide a basic understanding ofmechanics-regulated biological and biomedical processes in different regions ofthe CNS. In addition, they help identify key mechano-chemical factors forinclusion in in silico models and provide data for model calibration andvalidation. In silico models, in turn, allow us to test hypotheses without the need of excessive or even inaccessibleexperiments. In addition, they enable the transfer and comparison of mechanics data and findingsacross species and scales. They also empower us to optimise processparameters for the development of in vitro brain tissue-like matricesand in vivo manipulation of mechanical signals, and, eventually, pavethe way for personalised clinical predictions.

Insummary, we exploit mechanics-based approaches to advance ourunderstanding of CNS function and to provide the foundation for futureimprovement of diagnosis and treatment of neurological disorders.

Das Hauptziel dieses Projekts ist die Erweiterung des in dem Vorgängerprojekt entwickelten numerischen Modells (starre Mikropartikel in verdünnt dispergierter Zweiphasenströmung unter Verwendung des Lagrange-Euler-Ansatzes) auf ein numerisches Modell für die Translations- und Rotationsimpulsübertragung von weichen verformbaren Mikropartikeln. Der erste Teil ist der Entwicklung eines direkten numerischen Simulationswerkzeugs (DNS) gewidmet, das die strömungsinduzierten Spannungsvektoren und die daraus resultierenden Kräfte und Momente, die auf ein weiches verformbares Partikel endlicher Abmessung wirken, gemeinsam mit der Partikelverformung lokal bestimmt. Darüber hinaus wird die Kopplung zwischen einem CFD-Löser für die Strömung auf globaler Ebene und der Lagrangschen Partikelverfolgung auf der Grundlage des neuartigen Punktpartikelansatzes für weiche verformbare Partikel hergestellt. Diese Kombination wird sowohl durch einen Online-Ansatz unter Verwendung der DNS-Ergebnisse als auch durch einen Offline-Ansatz, d.h. durch ein maschinell erlerntes (ML) Surrogatmodell, erreicht. In dem ML Rahmen wird eine große Datenbank mit strömungsinduzierten Kräften und Momenten für verschiedene Partikelformen, Ausrichtungen und Strömungsbedingungen erstellt. Diese erlaubt die Anwendung auf numerisch anspruchsvolle Strömungsprobleme mit hunderttausenden von weichen verformbaren Partikeln. Schließlich wird das abgeleitete Modell auf ein technologisch relevantes Beispiel einer verdünnen Mehrphasenströmung mit linsenförmigen Vesikeln angewendet.

Knochen ist ein lebendes Material, das auf mechanische und nicht-mechanische Reize reagiert. OP ist die häufigste Altersknochenerkrankung und stellt eine Bedrohung für unsere alternde Gesellschaft dar. OP ist eine Knochenstoffwechselstörung, die zu einer erhöhten Knochenporosität führt und das Frakturrisiko erhöht. Die damit einhergehende Abnahme der Knochendichte ist charakteristisch für den Knochenverlust.
Wir schlagen ein Multiskalenmodell zur prädiktiven numerischen Simulation der OP vor. Dies wird es Klinikern ermöglichen, patientenspezifische Behandlungs- und Medikamentenoptionen virtuell zu analysieren und so z.B. eine schädliche 0berexposition des Patienten durch Röntgenbestrahlung zu vermeiden.
Wir beschreiben Knochenumbau simultan auf der Gewebeskala und auf der Zellskala. Knochenumbau verändert die Knochendichte mit der Möglichkeit ihrer stimulusinduzierten Zu- oder Abnahme. Die Gewebeskala ermöglicht patientenspezifische Simulationen der OP und ihres Verlaufs. Wir erfassen die Knochendichte durch ein Kontinuumsfeld und modellieren ihre Entwicklung durch einen Stimulus und einen Attraktor. Der Stimulus ist mechanischen und nicht-mechanischen Ursprungs, letzterer z.B. durch die Verfügbarkeit von Nahrung und/oder Medikamenten. Auf der Zellskala werden biochemische Signale und ihre Auswirkungen auf die Genese und Mortalität von Knochenzellen betrachtet.
Knochenzellen nehmen ihre mechanische Umgebung wahr und reagieren darauf. Daher koppelt PP 2 (FAU+QUT) die makroskopische mechanische Reaktion direkt mit dem Gleichungssatz, der die zelluläre Knochenenlwicklung auf der Zellskala erfasst. Komplementär koppelt PP 1 (THN+QUT) die Modellierung auf der Zellskala an die Gewebeskala, indem es ein 'zelluläres Knochenbildungs-Resorptionsmodell in den Stimulus und Attraktor der makroskopischen Knochendichteentwicklung einbezieht. So wird die Dynamik der zellulären Knochenenlwicklung auf der Zellskala direkt den Knochenumbauprozess auf der Gewebeskala diktieren.

The goal of this project is to develop a modelling and simulation technique enabling:
(i) the generation of nonwoven unit cell models according to a given set of structure parameters (size, density/grammage, orientation distribution function, fiber properties, …) and relying on a sophisticated beam discretization and formulation extended to contact treatment
(ii) the simulation of the relevant processing steps, i.e. the densification and bond point genera-tion, whereby, for simplicity, only isothermal processes are initially considered and the newly formed bond points are introduced via Dirichlet boundary conditions confining the nonwoven unit cell
(iii) deformation simulations (uniaxial, biaxial, bending,…) under due consideration of fiber proper-ties and contact behavior, validation against experimental data

The overarching objective of our proposal is to develop a revolutionary seamless horizontally coupled multiscale method for meso-heterogeneous materials. For capturing the macroscopic mechanical behaviour of meso-heterogeneous materials by modelling and simulation, which is of utmost importance from an engineering perspective, computational challenges arise from the overwhelming geometric complexity and detail of the meso-structure. This urgently asks for multiscale coupling methods that enable to reduce the computational cost of simulations at the engineering scale, however without sacrificing accuracy when capturing the influence of the meso-structure on the macroscopic mechanical response. Our approach will not rely on scale-separation in order to be suited for problems involving singularities, e.g. at crack tips, and it will use a sole and uniform description of the underlying mesoscopic material behaviour in terms of its material properties and meso-structure in macro- and mesoscopically resolved sub-domains. To achieve this goal, we take inspiration from the quasi continuum (QC) method for crystalline materials that seamlessly bridges fully resolved atomistic domains with quasi continuum domains in which the majority of the atoms are enslaved to follow the motion of only a few representative atoms (Rep-Atoms). We thus propose to substitute the notion of atoms and Rep-Atoms as used in the QC method for the case of crystalline materials by the notion of nodes and Rep-Nodes for the case of meso-heterogeneous materials. Then, the underlying material meso-structure is fully represented everywhere within a macroscopic engineering structure. However, only a much smaller sub-set of the total amount of nodes and corresponding dofs is retained for the simulation of the engineering structure. We will distinguish between the underlying sub-discretization build on all nodes to capture the meso-structure and the overlaying Sup-Discretization build on only the much lesser number of Rep-Nodes used for the simulation of the macroscopic engineering structure. The assignment of sub-discretization nodes to Sup-Discretization Rep-Nodes and the definition of the corresponding Sup-Discretization follows adaptively. A versatile approach to mesh complex domains that allows for arbitrary polygons/polyhedra is the virtual element (VE) approach based on VE Ansatz functions. Noteworthy, VE Ansatz functions are not restricted to interpolate nodal dofs merely linearly along element edges/faces. This freedom in arbitrarily choosing the polynomial degree of the Ansatz functions makes VE conceptually also amenable to p-adaptivity. Of particular interest for our current proposal is moreover that the vertexes of the arbitrary polygons/polyhedra representing a VE and carrying the nodal dofs may also lay on straight lines/planar surfaces. Thus, VE elegantly and straightforwardly enables transition between sub-domains with strongly varying discretization densities.

Die Kontinuumsmechanik ist eine wichtige Grundlagenwissenschaft in den Ingenieur- und Naturwissenschaften, die den Zusammenhang zwischen Kräften und Deformationen (und Bewegungen) in Materialien und Strukturen modelliert. Ihre numerische Umsetzung z.B. in der Finiten Element Methode ist aus dem Alltag von Berechnungsabteilungen von technologieorientierten Unternehmen aufgrund ihrer hervorgehobenen Relevanz heutzutage nicht mehr wegzudenken. Das hier beantragte Vorhaben zielt, motiviert durch Konzepte der Hamiltonschen Dynamik auf die erstmalige Etablierung eines völlig neuartigen, sogenannten symplektischen Zugangs zur geometrisch nichtlinearen Kontinuumsmechanik mit zunächst speziellem Fokus auf die nichtlineare Elastizität. Die symplektische Formulierung der geometrisch nichtlinearen Kontinuumsmechanik verspricht neben ihrer Eleganz dabei insbesondere zahlreiche Vorteile im Rahmen ihrer numerischen Umsetzung. Die nichtlineare Elastizität hat vielfältige bedeutende Modellierungsanwendungen im Bereich weicher und weichster Materialien mit größter aktueller Bedeutung beispielweise für die Mechanik biologischer Gewebe, die Soft-Robotik sowie zahlreicher derzeit entwickelter high-tech Metamaterialien. In Summe wird hier sehr vielversprechendes aber auch riskantes thematisches Neuland betreten, wobei die Erfolgsaussichten des Vorhabens aufgrund der komplementären Expertise der Projektpartner als sehr hoch einzuschätzen sind.

Computational homogenization requires two separate finite element models: a model at the macroscale and a model of the materials’ underlying structure at the microscale. Computational homogenization involves two main ingredients: the transfer of the macroscopic loading to the microscale and averaging the corresponding response of the microstructure to obtain the effective macroscopic properties. A challenging aspect for computational homogenization is the proper modelling of material with uncertainty in the microstructure, as considered in this project. Uncertainties in the macroscopic response of heterogeneous materials result from various sources: the natural variability in the microstructure’s geometry and its constituent’s material properties and the lack of sufficient knowledge regarding the microstructure. The first type of uncertainty is denoted as aleatoric uncertainty and may be characterized by probabilistic approaches. The second type of uncertainty is denoted as epistemic uncertainty and may be described using fuzzy arithmetic. Models considering both sources of uncertainty are denoted polymorphic, requiring some combination of stochastic and fuzzy methods.In Phase I we developed methods for the accurate and efficient propagation of polymorphic uncertainty through the material’s microstructure and applied all proposed approaches to a benchmark problem. The objectives of the Phase II are further development of modelling techniques and their application to the engineering design of structures. The outcome of Phase II will be an accomplished methodology allowing the uncertainty propagation from the lowest level of a material microstructure through the macroscopic structure simulation to the engineering design and decision making. More precisely in Phase II the following challenges are considered:- We continue the development of advanced fuzzy-stochastic benchmark RVE for the microstructure of heterogeneous materials, resulting thus in a more realistic and precise description of polymorphic uncertainty in the material’s microstructure. - Modelling techniques for spectral non-deterministic finite element analysis will be enriched to non-deterministic eXtended Isogeometric Analysis.- The computational cost of full-order large scale simulations of systems in the presence of uncertainty is unacceptably high, in particular considering many-query or real-time applications. Thus, reduced order modeling is an essential tool which allows a speed up microscale simulations. - Reduced order models and metamodels provide a necessary bridge to the final stage of the project, in which a suitable metamodel will be used on the macroscale to run large size simulations of engineering structures. - Finally, the influence of uncertainty in the macrostructure on the static and the dynamic behavior of engineering structures under random loading will be analyzed.

Computational homogenization requires two separate finite element models: a model at the macroscale and a model of the materials’ underlying structure at the microscale. Computational homogenization involves two main ingredients: the transfer of the macroscopic loading to the microscale and averaging the corresponding response of the microstructure to obtain the effective macroscopic properties. A challenging aspect for computational homogenization is the proper modelling of material with uncertainty in the microstructure, as considered in this project. Uncertainties in the macroscopic response of heterogeneous materials result from various sources: the natural variability in the microstructure’s geometry and its constituent’s material properties and the lack of sufficient knowledge regarding the microstructure. The first type of uncertainty is denoted as aleatoric uncertainty and may be characterized by probabilistic approaches. The second type of uncertainty is denoted as epistemic uncertainty and may be described using fuzzy arithmetic. Models considering both sources of uncertainty are denoted polymorphic, requiring some combination of stochastic and fuzzy methods.In Phase I we developed methods for the accurate and efficient propagation of polymorphic uncertainty through the material’s microstructure and applied all proposed approaches to a benchmark problem. The objectives of the Phase II are further development of modelling techniques and their application to the engineering design of structures. The outcome of Phase II will be an accomplished methodology allowing the uncertainty propagation from the lowest level of a material microstructure through the macroscopic structure simulation to the engineering design and decision making. More precisely in Phase II the following challenges are considered:- We continue the development of advanced fuzzy-stochastic benchmark RVE for the microstructure of heterogeneous materials, resulting thus in a more realistic and precise description of polymorphic uncertainty in the material’s microstructure. - Modelling techniques for spectral non-deterministic finite element analysis will be enriched to non-deterministic eXtended Isogeometric Analysis.- The computational cost of full-order large scale simulations of systems in the presence of uncertainty is unacceptably high, in particular considering many-query or real-time applications. Thus, reduced order modeling is an essential tool which allows a speed up microscale simulations. - Reduced order models and metamodels provide a necessary bridge to the final stage of the project, in which a suitable metamodel will be used on the macroscale to run large size simulations of engineering structures. - Finally, the influence of uncertainty in the macrostructure on the static and the dynamic behavior of engineering structures under random loading will be analyzed.

Mechano-electrical (ME) energy conversion is a promising and versatile option for devices that demand novel perspectives in energy supply and/or require non-invasive noise and vibration reduction. The objective of this project is twofold. Firstly, we tackle the challenge of autonomous energy supply for the operation of remotely located electrical devices. These include measuring devices in meteorology or environmental monitoring that are oftentimes located offshore or in the remote locations and that only consume low energy to support their measuring function and/or for further processing of the measured data. Secondly, electric motors for pure and hybridized electric vehicles (PEV, HEV), which often exhibit undesired noise and vibration characteristics during operation. Here, ME energy conversion is highly
viable for simultaneous energy harvesting and reduction of operation-induced vibrational energy.

This project focuses on novel excitation-conforming ME energy converters, which are able to efficiently exploit the energy contained in the EF spectrum of natural (e.g. wind or water) or defined technical excitations of actuator-driven shape-adaptation. This project will develop advanced continuum modeling, computational optimization and simulation tools that enable the design of shape-adaptive energy harvesting structures by combined shape and topology optimization. Thereby, the overarching goal is to optimize the energy harvesting efficiency of a ME system by adapting its natural frequency spectrum to a given excitation EF spectrum via suited stiffness modulations. We will affect stiffness modulations based on a feedback control via actuation of the shape-adaptive ME system at only a few distinct actuation points.

Based on the gained knowledge of projects B4 and C5,the aim of this project is to account for the influence of part borders on theresulting material/part-mesostructure for powder- and beam-based additivemanufacturing technologies of metals and to model the resulting meso- andmacroscopic mechanical properties. The mechanical behavior of thesemesostructures and the influence of the inevitable process-based geometricaluncertainties is modelled, verified, quantified and validated especially forcellular grid-based structures.

Biological tissues such as blood vessels, skin, cartilage or nervous tissue provide vital functionality
to living organisms. Novel computational simulations of these tissues can provide insights
into their biomechanics during injury and disease that go far beyond traditional approaches. This
is of ever increasing importance in industrial and medical applications as numerical models will
enable early diagnostics of diseases, detailed planning and optimization of surgical procedures,
and not least will reduce the necessity of animal and human experimentation. However, the extreme
compliance of these, from a mechanical perspective, particular soft tissues stretches conventional
modeling and testing approaches to their limits. Furthermore, the diverse microstructure
has, to date, hindered their systematic mechanical characterization. In this project, we will, as a
novel perspective, categorize biological tissues according to their mechanical behavior and identify
biofabricated proxy (substitute) materials with similar properties to reduce challenges related
to experimental characterization of living tissues. We will further develop appropriate mathematical
models that allow us to computationally predict the tissue response based on these proxy
materials. Collectively, we will provide a catalogue of biopolymeric proxy materials for different
soft tissues with corresponding modeling approaches. As a prospect, this will significantly facilitate
the choice of appropriate materials for 3D biofabrication of artificial organs, as well as modeling
approaches for predictive simulations. These form the cornerstone of advanced medical
treatment strategies and engineering design processes, leveraging virtual prototyping.

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.

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.

Das Ziel des Teilprojekts ist die Modellierung und Simulation der Plastizität und Schädigung während mechanischer Fügeprozesse vor dem Hintergrund der angestrebten Wandlungsfähigkeit der Verfahren. Dazu werden einerseits Materialmodelle entwickelt, robust und effizient numerisch umgesetzt und experimentell validiert. Andererseits wird eine numerische Methode, die sogenannte Parametrische Finite Elemente Methode (PFEM), problemangepasst weiterentwickelt, um die effiziente Berechnung einer großen Anzahl verschiedener Prozessvarianten zu ermöglichen. Die PFEM stellt damit das ideale Lösungsverfahren zur Simulation wandlungsfähiger Prozesse dar.

The RTG aims to improve understanding of fracture in brittle heterogeneous materials by developing simulation methods able to capture the multiscale nature of failure. With i) its rooting in different scientific disciplines, ii) its focus on the influence of heterogeneities on fracture at different length and time scales as well as iii) its integration of highly specialised approaches into a “holistic” concept, the RTG addresses a truly challenging cross-sectional topic in mechanics of materials. Although various simulation approaches describing fracture exist for particular types of materials and specific time and length scales, an integrated and overarching approach that is able to capture fracture processes in different – and in particular heterogeneous – materials at various length and time resolutions is still lacking. Thus, we propose an RTG consisting of interdisciplinary experts from mechanics, materials science, mathematics, chemistry, and physics that will develop the necessary methodology to investigate the mechanisms underlying brittle fracture and how they are influenced by heterogeneities in various materials. The insights obtained together with the methodological framework will allow tailoring and optimising materials against fracture. The RTG will cover a representative spectrum of brittle materials and their composites, together with granular and porous materials. We will study these at length and time scales relevant to science and engineering, ranging from sub-atomic via atomic and molecular over mesoscale to macroscopic dimensions. Our modelling approaches and simulation tools are based on concepts from quantum mechanics, molecular mechanics, mesoscopic approaches, and continuum mechanics. These will be integrated into an overall framework which will represent an important step towards a virtual laboratory eventually complementing and minimising extensive and expensive experimental testing of materials and components. Within the RTG, young researchers under the supervision of experienced PAs will perform cutting-edge research on challenging scientific aspects of fracture. The RTG will foster synergies in research and advanced education and is intended to become a key element in FAU‘s interdisciplinary research areas “New Materials and Processes” and “Modelling–Simulation–Optimisation”.

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 socalled 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.

Due to the potential of forming induced residual stresses to influence component properties, a deeper understanding of the mechanisms of residual stress generation and stability is required. Therefore, the approach to the research project is structured into the phases of component manufacturing (generation of residual stresses), component operation (residual stress stability) and process design (exploitation of residual stresses). As reference process the forward rod extrusion is used, which is established as standard process in industrial use. Due to the trend towards component materials with higher strength and corrosion resistance, two stainless steels are used in the project. The investigations include parallel experimental and numerical analyses of the process and its synthesis.

During the first phase, the necessary experimental equipment for component manufacture and testing was set up, material and friction parameters were identified, components were formed under consideration of different parameter variants and their residual stresses were determined by X-ray diffraction. In a complementary approach, macroscopic finite element models with subroutines for an extended post-processing of residual stresses were developed on the simulation side and applied in the context of numerical parameter variations. Furthermore, differential geometric and continuum mechanical relationships of residual stresses were investigated and the material modelling was extended to crystal plasticity. The predictivity of the numerical results was quantified on the basis of experimental results.

The second phase concentrates on the residual stress stability in component use and the process robustness during component manufacture. The knowledge gained will be used at the end of the second and in the third phase to specifically influence the operating behaviour and to control the cyclic strength.

The objective in the second phase is the experimental and numerical determination of the mechanical and thermal residual stress stability. As a requirement for the targeted influencing, relevant parameters will be identified. These cause-and-effect relationships are to be plausibilised by means of fundamental physical effects, whereby a recourse is made to effects described in the literature and numerical methods for the derivation of basic model ideas. Based on the experience gained so far, fluctuations of input variables and previously known disturbance variables are to be taken into account in all investigations. A further prerequisite for a systematic investigation of the fundamental mechanisms relevant to residual stresses is an increase in the numerical modeling and prediction accuracy of the deformation-induced residual stresses. In analogy to the generation phase, a constant comparison of simulation and experiment is therefore also carried out in the operating phase in the sense of an assessment of the prognosis quality of the numerical approaches and the plausibility of the experimental laboratory results.

The Project is part of the DFG priority programm SPP2013 "Targeted Use of Forming Induced Internal Stresses in Metal Components". Within the priority program, the subproject takes part in the expert groups Production technology (thick-walled) and Mechanics and simulation.

The operational behavior of steel components is significantly influenced by their residual stress state. On the basis of forward rod extrusion of stainless steel, methods for the controlled generation of residual stresses are being investigated, their stability under typical operating conditions is being analyzed and their effects on the operating behavior are being identified in this research project. In the first phase, basic mechanisms of the generation of residual stresses were identified. In the current second phase, parameters for a robust adjustment of the residual stress state during forming were developed, whereby lubrication in particular was identified as relevant. Furthermore, the influence of thermal and mechanical loads on the stability of the residual stresses in the components is being investigated.

The Project “Multi-scale Modeling, Simulation and Optimization for Energy, Advanced Materials and Manufacturing” aims at academic and research cooperation between the FAU and the Indian Institute of Technology Delhi (IITD) on the thematic areas of multiscale modeling and simulations for advanced materials, multiphase flows relevant to energy processes, numerical simulations of advanced metal forming processes, adaptive wavelet methods, and more.

With the development in the field of supercomputing and several breakthroughs in multi-scale theory, the focus has shifted towards development of new materials having extreme properties such as ultra-lightweight yet strong fiber reinforced composites. These new materials require development of new theories catering to large deformation, growth, fracture and most significantly the multi-scale effects. Besides, faithful constitutive models for these new materials (ranging from ultra-soft to ultra-tough and incorporating structure at all length scales) require bridging structural and deformation phenomena at nano-, micro- as well as macro-scales. This has increased the complexity of the governing equations.

One of the recent trends in designing lightweight high performance materials for extreme loading conditions is on development of architectured materials which have engineered architecture at the micro-scale. The various parameters of this architecture such as its repeating length, constituent unit cell morphology etc. affect the mechanical properties (stiffness, toughness, ductility etc.) at the macro-scale. In fact, the constituent unit cell is often comprised of nanorods which provide additional parameters to tune the macroscopic mechanical properties. For example, the length of the constituent nanorod, its diameter and thickness are some of the parameters which govern whether the constituent nanrod would undergo Euler buckling or shell-type buckling or just fracture. The transition from buckling to fracture at micro-scale would lead to transition from ductility to brittleness at the macroscopic level. Detailed analysis of these structures through multi-scale elasto-plastic simulation will be carried out as well as concurrent atomistic-continuum simulation to better understand the mechanisms of failure and buckling at nano- and micro-scales.

The governing equations which capture various multi-scale phenomena in heterogeneous materials have become highly non-linear and complex. The real challenge lies in how to efficiently and accurately capture the phenomena which occur at both multiple time scale and length scale in complex heterogeneous materials. The existing numerical tools would simply fail in such situations. The aim is to develop an efficient and stable time marching scheme to capture the multiple time scale events that occur in complex heterogeneous materials. Another challenge lies in implementation of the concurrent atomistic-continuum methods to accurately capture fracture in heterogeneous materials. The challenges here lie in the implementation of the hand shake region, the efficiency of the finite element discretization near the transition region etc. New and efficient finite elements, shape functions will be developed to cater to it.

It is expected that a comprehensive multi-scale theory and numerical tool will be in place to computationally design novel high performance materials displaying architectured non-classical mechanical properties and that are. This will pave the way to provide important input parameters to experimentalist to verify and develop such materials.

The overarching goal of the proposed project at the methodological side is to establish a computationally tractable numerical method that is suited to capture polymorphic uncertainties in large-scale problems (as arising from the numerical analysis of heterogeneous materials microstructures). On the one hand the method will allow for fuzzy probability distributions of the random parameters (describing a microstructures geometry) and on the other hand the method will be based on only a few reduced basis modes. These ingredients will enable to capture epistemic uncertainties in addition to aleatoric uncertainties in a computationally accessible manner. The overarching goal of the proposed project at the application side is to establish a non-deterministic macroscopic material model. On the one hand the model accounts for the heterogeneity of the underlying material's microstructure by computational homogenization, and on the other hand it captures polymorphic uncertainties in the geometry description of the microstructure. The non-deterministic macroscopic material model then represents the necessary input for the mechanical design of macroscopic (engineering) structures under due consideration of polymorphic uncertainties in the heterogeneous materials microstructure.

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, as well as the mesh transformation during the structural optimization and formulation of the deformation map are the main topics to be studied. It should be noted that until now there exists no open-source implementation of the DFT approach which uses a FE basis and provides hp-refinement capabilities. A FE basis is very attractive in the context of the DFT theory because of its completeness, refinement possibility as well as good polarization properties based on domain decomposition. Second, QM quantities will be related to their CM counterparts (e.g. displacements, deformation gradient, the Piola stress, polarization, etc). This will be achieved using averaging in the Lagrangian configuration. To that end the full control over a FE-based solution of the KS equations is required. The procedure is then to be tested on a representative numerical example - bending of a single wall carbon nanotube. On the CM side, the surface-enhanced continuum theory will be utilized to properly capture surface effects. It should be noted that although several theoretical works exist on this matter, no numerical attempts have been made to check their validity on test examples. Lastly, based on the correspondence between different formulations, a concurrently coupled QM-CM method will be proposed. Coupling will be achieved in a staggered way, i.e. QM and CM problems will be solved iteratively with a proper exchange of information between them. A test-problem of crack propagation in a graphene sheet will be considered. As a long term goal of the project, coupling strategies for electro-elastic problems will be developed. To the best of my knowledge, non of the QM-CM coupling method is capable to handle electro-elastic problems.

The overarching goal of the proposed Mercator project is to establish a numerical model of translational and rotational momentum transfer of small non-spherical rigid particles in fluid dominated two-phase flows. Thereby the main aims are threefold:The first aim is to establish an accurate numerical model for particle-fluid interaction. It will in particular take into account the translational and rotational effects in the fluid flow field, and will put a special focus on the resulting particle rotational motion in terms of the accurate determination of its orientation and angular velocity. Here, the development of an advanced Lagrangian particle tracking algorithm for the tracking of non-spherical particles in a velocity-vorticity resolved fluid flow field and the development of a two-way coupling algorithmwithin a suited BEM framework, based on an advanced source distribution modelwithin the fluid phase, are planned.The second aim is to incorporate non-spherical particle force and torque models to capture the momentum transfer between particles and the fluid flow field. Here special attention will be paid to particle shapes in terms of generic ellipsoidal geometries. In the context of the envisioned rigid body modelling for the particles this will be accompanied by the development of a particle preprocessor in order to provide particle inertia properties.The third aim is to devise accelerated parallel numerical algorithms which will enable accurate and fast computations of the vortical part of the fluid flow field within the previously established BEM framework as well as the efficient solution of the set of DAEs related to the particle motion.The developed algorithms will be validated by comparison with independent computational results and will eventually be applied to the experimentally verified test case of sludge flocsedimentation.

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 Entwicklung numerischer
Verfahren zur Kalibrierung (Parameteridentifikation) inelastischer Stoffgesetze aus den Meßdaten. Inhärent anspruchsvoll sind dabei die geeignete Gestaltung der
Probekörper und ihrer Fixierung, die den gesuchten Eigenschaften angepaßte Versuchsführung und die hinreichend genaue Reproduktion derselben im Rahmen der zur
Parameteridentifikation erforderlichen Finite-Elemente-Simulationen.
 

Aluminium-Metall-Matrix-Composltes (Al-MMC) zählen zu einer Gruppe komplexer zweiphasiger Hochleistungswerkstoffe, für die aufgrund Ihrer hervorragenden Funktionseigenschaften zukünftig stark ansteigende Verwendung prognostiziert wird. Bei der Bearbeitung von Werkstücken aus Al-MMC treten prozessbedingt hohe Temperaturen auf. Abhängig von der Höhe der eingebrachten Temperatur können diese zu Werkstückverformungen sowie zu Änderungen im Werkstoffgefüge führen. Um Prozessparameter zu finden, die diese Veränderungen im Werkstück vermeiden, sind heute zeit- und materialintensive experimentelle Untersuchungen notwendig. Aufgrund der hohen Herstellkosten von Al-MMC ist die Reduzierung der Zahl experimenteller Untersuchungen für diese Werkstoffgruppe von besonderer Relevanz. Im Rahmen des hier beantragten Forschungsvorhabens soll daher ein Modell für das thermomechanische Materialverhalten von Al-MMC entwickelt werden, welches eine FE-Simulation des thermischen Einflusses auf das Werkstück bei der Drehbearbeitung ermöglicht. Anhand der Simulationsergebnisse wird eine Kompensation thermischer Einflüsse durch gezielte Prozessführung vorgenommen. In der ersten Antragsphase dieses Vorhabens wird grundlegend die Auswirkung des Temperatureintrags bei der Drehbearbeitung von homogenen Werkstoffen untersucht. Aufbauend auf diesen Untersuchungen erfolgt dann in der zweiten und dritten Antragsphase die Betrachtung mehrphasiger Al-MMC. Dabei wird auch der Einfluss einer variierenden Partikelverteilung auf das thermische Verhalten berücksichtigt werden.

The numerical modeling and simulation of the behavior of EEAPs (Electronic Electro-Active Polymers) under electric loading is considered in this proposal. Despite the fact that efforts have been made to simulate the behavior of EEAPs, work still needs to be done to model the electro-thermo-mechanical interaction in a body undergoing large deformation and being subjected to the influence of the free space surrounding the material body. First of all, until now there exists no thermo-dynamically consistent model that at the same time accounts for large deformations, nonlinear electric polarization, visco-elasticity and the temperature-dependent electro-mechanical properties of EEAPs. At the moment, there exists no software that is capable of simulating these effects simultaneously. In addition, almost all works in the literature related to EEAPs did not consider the effect of the free space surrounding a body of interest and as a consequence can only be used in the case of simulating condensator-like structures whose thickness is very small in comparison with other dimensions. In this proposal, the behavior of EEAPs will be modeled using the theory of electro-thermo-visco-elasticity and will be simulated by using the finite element method (FEM) coupled with the boundary element method (BEM). The FEM will be used to model the material body and the BEM will be used to model the surrounding free space. Besides the numerical simulation of the electro-thermo-mechanical interaction in EEAPs, the numerical evaluation of material forces in structures with defects made of EEAPs, taking into account the electro-thermo-visco-elastic effect, is also considered. These forces can be used, for example, in the prediction of the propagation of cracks, which can take place in EEAP-based structures under electric loads.

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.

Diffusionsprozesse, insbesondere deren Kopplung mit Verformungen, sind von großer wissenschaftlicher und technologischer Bedeutung in verschiedensten Feldern der Ingenieur-, Material- und Naturwissenschaften und deren Schnittmengen. Hervorstechende Beispiele sind etwa die Modellierung und Simulation von Lötverbindungen, die Entwicklung von Mikrostrukturen in modernen Materialien, wie sie z.B in hochentwickelten sowie zukünftigen einkristallinen Turbinenblättern verwendet werden, mineralische Entmischungen in der Geologie, Schadstoffausbreitung im Umweltbereich, sowie der Arzneimitteltransport in biologischem Gewebe. In vielen dieser Fälle werden die beobachteten Phänomene jedoch durch ein klassisches Ficksches Diffusionsmodell nicht ausreichend genau beschrieben, sondern erfordern die Modellierung als nichtklassische Diffusion. Typische Beispiele für nichtklassische Diffusionsmodelle sind die Cahn-Hillard Gleichung sowie die sogenannte Mikrokräftebilanz von Gurtin. Die übergreifenden Ziele dieses Vorhabens sind daher (i) die Formulierung und die Simulation einer generischen Klasse von nichtklassischen Diffusionsmodellen, (ii) die Ermittlung ihres mikromechanischen Ursprungs, und (iii) ihre Kopplung mit der Deformation. Es sei dabei daran erinnert, dass höhere Gradienten- sowie mikromorphe Formulierungen als Paradigmen erweiterter Kontinuums-modelle eng miteinander verbunden und mit unterschiedlichen Vor- und Nachteilen verknüpft sind. Es ergibt sich daher die Erforschung von Gradienten- und mikromorphen Diffusionsformulierungen als unmittelbares Ziel der Phase I. Um dabei deren mikromechanischen Ursprung zu ergründen, sollen dann die relevanten Antwortgrößen, die in die zugrundeliegenden Feldgleichungen auf der Makroebene eingehen, aus den entsprechenden Größen auf der Mikroebene durch numerische Homogenisierung zweiter Ordnung bestimmt werden. Das erwartete Ergebnis dieses Vorhabens in Phase I ist somit die Klärung des zugrundeliegenden mikromechanischen Ursprungs einer generischen Klasse von nichtklassichen Diffusionsmodellen. Phase II wird sich dann hauptsächlich auf die Kopplung von Diffusion und Verformungen konzentrieren. Insgesamt wird erwartet, dass die Ergebnisse dieses Vorhabens für unterschiedliche Gebiete der Ingenieur-, Material- und Naturwissenschaften aus wissenschaftlicher und technologischer Sicht von großer Bedeutung sein werden. Insbesondere sollen die Entwicklung und das Verständnis im Bereich neuartiger Materialien durch die erwarteten Erkenntnisse dieses Vorhabens unterstützt werden.

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 dramatically in response to relatively low external magnetic fields. The rapid response, the high level of deformations achievable, and the possibility to control these deformations by adjusting the external magnetic field, make these materials of special interest for the novel design of actuators for a fascinating variety of technological applications. It is the overall objective of this proposal to uncover the process-microstructure-properties relations of the emerging novel multi-scale, multi-physics material class of magneto-sensitive polymers with the aim to better exploit its promising potential for future, currently unimagined technological applications. This objective will only be achieved by performing integrated multi-disciplinary research in fabrication, characterisation, modelling, simulation, testing and parameter identification. This proposal therefore sets up a work programme consisting of nine strongly interconnected work packages that are devoted to:1) Fabrication of magneto-sensitive polymers2) microstructure characterisation by modelling and simulation3) microstructure characterisation by CT-scanning4) continuum physics modelling at the micro-scale5) computational multi-physics homogenisation6) continuum physics modelling at the macro-scale7) testing at the macro-scale8) multi-scale parameter identification9) macro-scale parameter identification.The work programme is therefore characterised by various feedback loops between the work packages.

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.

This proposal aims at an extension of a recently developed, hybrid MD-FE simulation scheme towards its application to materials dominated by polymer-solid interphases. Only particle-based methods are able to intrinsically resolve microstructure and mechanical behavior of interphases. Therefore, we proceed with the following setup: A coarse-grained MD domain, which contains a single nanoparticle and as much polymer as necessary to ensure bulk behavior at the boundary, is included into a FE do-main. The FE boundary is used to apply various types of deformations and to record the overall stress responses of particle, surrounding interphase and bulk. With these data, the parameters of a purely continuous counterpart to the hybrid setup are iteratively adjusted until it behaves identically. As its main feature, the continuous ersatz-model substitutes the interphase between particle and polymer by an interface governed by a surface energy in the sense of Gibbs. This can be understood as a condensation of micro-scale property profiles within the 3-D interphase into a 2-D continuum mechanical model. Ultimately, after homogenizing the continuous ersatzmodel, macroscopic structure simulations allowing for a due consideration of interphase effects as occurring around nanoparticles are to be realized.

Aluminium-Metall-Matrix-Composltes (Al-MMC) zählen zu einer Gruppe komplexer zweiphasiger Hochleistungswerkstoffe, für die aufgrund Ihrer hervorragenden Funktionseigenschaften zukünftig stark ansteigende Verwendung prognostiziert wird. Bei der Bearbeitung von Werkstücken aus Al-MMC treten prozessbedingt hohe Temperaturen auf. Abhängig von der Höhe der eingebrachten Temperatur können diese zu Werkstückverformungen sowie zu Änderungen im Werkstoffgefüge führen. Um Prozessparameter zu finden, die diese Veränderungen im Werkstück vermeiden, sind heute zeit- und materialintensive experimentelle Untersuchungen notwendig. Aufgrund der hohen Herstellkosten von Al-MMC ist die Reduzierung der Zahl experimenteller Untersuchungen für diese Werkstoffgruppe von besonderer Relevanz. Im Rahmen des hier beantragten Forschungsvorhabens soll daher ein Modell für das thermomechanische Materialverhalten von Al-MMC entwickelt werden, welches eine FE-Simulation des thermischen Einflusses auf das Werkstück bei der Drehbearbeitung ermöglicht. Anhand der Simulationsergebnisse wird eine Kompensation thermischer Einflüsse durch gezielte Prozessführung vorgenommen. In der ersten Antragsphase dieses Vorhabens wird grundlegend die Auswirkung des Temperatureintrags bei der Drehbearbeitung von homogenen Werkstoffen untersucht. Aufbauend auf diesen Untersuchungen erfolgt dann in der zweiten und dritten Antragsphase die Betrachtung mehrphasiger Al-MMC. Dabei wird auch der Einfluss einer variierenden Partikelverteilung auf das thermische Verhalten berücksichtigt werden.

Im Fokus dieses Vorhabens steht die mechanische Mehrskalenmodellierung und -simulation von Materialien mit heterogener Faserstruktur (z.B. schaumartige Filterstrukturen oder Dämmungs-materialien aus der Automobilindustrie) unter besonderer Berücksichtigung des Kontakts zwi-schen den einzelnen Fasern. Das Problem wird dabei durch die Berücksichtigung der verschie-denen geometrischen Längenskalen so komplex, dass eine direkte numerische Simulation nicht mehr möglich ist. Für eine effektive Berechnung ist daher ein Mehrskalenzugang erforderlich. Das Vorhaben soll daher zum einen die Anwendungsgrenzen der asymptotischen Homogenisie-rung auf die mechanische Analyse von Kontaktproblemen in der Mikrostruktur von Fasermate-rialien erweitern und damit ein geeignetes effektives phänomenologisches Konstitutivgesetz herleiten. Aufgrund des Kontaktes zwischen den Fasern ist das resultierende effektive phäno-menologische Konstitutivgesetz nichtlinear. Das effektive phänomenologische Konstitutivgesetz soll dabei insbesondere für verschiedene Kontaktgesetze in der Mikrostruktur hergeleitet und umfassend analysiert werden. Zum anderen soll das Mehrskalenproblem inklusive Kontakt in der Mikrostruktur basierend auf dem Konzept eines Repräsentativen-Volumen-Elementes (RVE) direkt berechnet und die nume-rischen Ergebnisse nach einer Volumenmittelung mit dem vorgeschlagenen effektiven phäno-menologischen Konstitutivgesetz gefittet werden. Als Werkzeug zur Simulation eines RVEs (bzw. einer Periodizitätszelle) dient hierbei die Finite-Element-Methode, die sowohl mit 3D Vo-lumenelementen als auch mit Balkenelementen umgesetzt und auf die Behandlung des Kon-takts zwischen den Fasern erweitert werden soll. Das Gesamtvorhaben soll in einer engen Kooperation zwischen den beteiligten Antragstellern mit den jeweiligen Kernkompetenzen im Bereich der asymptotischen Homogenisierung und der Kontinuumsmechanik bzw. Numerischen Mechanik bearbeitet werden.

The main goal of this proposal is the computational modeling of solvent penetration in glassy polymers. For most engineering applications, Fick s law accurately describes diffusive processes, but one of the applications where it miserably fails is in glassy polymers near the glass transition temperature. In the vicinity of the glass transition temperature, when a low molecular weight solvent diffuses into a glassy polymer, the latter is caused to undergo a rubber-glass phase transition. The diffsive process follows non-Fickian behavior. Whereas the classical Fickian diffusion is referred to as case I diffusion, diffusion in glassy polymers is known as non-Fickian „case II diffusion“. A typical system undergoing case II diffusion is polymethylmethacrylate (PMMA) and methanol, for example.Modeling polymers which undergo case II diffusion is of particular interest in pharmaceutical and automotive industries, for example. Due to the importance of diffusion in many industrial and biological processes, a complete examination from a variety of perspectives and techniques is necessary. One tool at hand is the computational modeling at which this project aims. Hereby, an all-embracing theoretical model is to be set up extending existing approaches. Thus the very challenging modeling of non-Fickian behavior is one main task of this project. The numerical implementation of this ambitious theory is to be done subsequently in order to computationally model distinct typical applications from engineering or biomechanics.

Die mechanischen Eigenschaften von Polymerwerkstoffen hängen nicht nur von der chemischen Komposition und den Umgebungsbedingungen (Temperatur, Feuchte,...) ab,
sondern sie variieren teilweise erheblich mit dem verwendeten Aushärteregime und der Temperaturhistorie. Sie sind darüber hinaus vor allem in Verbundsituationen
u.U. sogar ortsabhängig von den Eigenschaften der Kontaktpartner beeinflußt, bilden also Eigenschaftgradienten (sog. Interphasen) aus.
Um diese Effekte bei der Simulation von Bauteilen korrekt abbilden zu können werden im Rahmen des Projektes Modelle entwickelt und erweitert,
die zeit-, orts- und umgebungsabhängige Materialeigenschaften wie Steifigkeitsevolutionen und -gradienten, Aushärteschrumpf und verschiedene Arten von
Inelastizität (Viskoelastizität, Elastoplastizität, Viskoplastizität, Schädigung) berücksichtigen können.

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 properties of polymer-nanocomposites. Further research activities focus on adaptive particle-based regions moving within the continuum, which is essential for multiscale simulation of crack propagation.

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 properties of polymer-nanocomposites. Further research activities focus on adaptive particle-based regions moving within the continuum, which is essential for multiscale simulation of crack propagation.

The mechanical response of electronic electro-active polymers (EEAP) under electric loading is influenced both by mechanical and electric properties of the material. Understanding the behavior of EEAP is vital in the development and design of EEAP based actuators and artifical muscles. Despite the fact that applications of EEAP are very promising, until now only a handful of experimental works have been realized to characterize their material properties. Moreover, so far only one-sided coupled models were used to explain experimental data and there exist discrepancies between meausrement, modeling and simulation. In this proposal, first experimental work will be performed to determine the material characteristics of a typical EEAP material then the electro-mechanical coupling phenomenon exhibited by EEAP will be modeled within the frameof hyperelasticity and viscoelasticity. Finally, by using a variational approach, a formulation representing the fully coupled problem will be derived, discretized, linearized and solved by the Finite Element Method in order to simulate the behavior of EEAP. Benchmark simulations will be performed to validate the applicability of the coupled model. Efforts will also be directed to the study of defects of EEAP by the Material Force Method and with the help of some recent developments in the spatial and material setting of nonlinear electro-elasticity. Especially the Material Force Method will be applied in numerical studies of cracked structures made of EEAP.

Magneto-sensitive-elastomers are smart materials which are composed of a rubber-like basis matrix filled with magneto-active particles. Due to the highly elastic properties of the rubberlike material, these compounds are able to deform significantly, i.e. geometrically non-linearly by the application of external magnetic fields. The rapid response, the high level of deformations that may be achieved, and the possibility of controlling these deformations by varying an external magnetic field, make these materials of special interest; e.g., for vibration and noise suppression. Thus, there is an urgent need for research on this novel material class in terms of modelling within the framework of geometrically nonlinear continuum physics and in the area of suitable computational methods in order to simulate technologically relevant benchmark problems. In this proposal, three main objectives are pursued: (i) the discussion and formulation of appropriate boundary conditions for the coupled magneto-elastic problem, in particular the correct acknowledgement of the influence of the magnetic field on the mechanical boundary conditions; (ii) the development of simple and at the same time realistic forms for the constitutive equations, respecting the microstructural features and including a careful analysis of the ellipticity (or infinitesimal rank-one convexity) condition; and, finally, an objective of utmost importance is (iii) to solve relevant nonlinear boundary value problems by resorting to a newly developed finite element method.

Aufgrund des mikroskopischen Materialabtrags haben beim Schleifen bereits kleine Schwingungsamplituden und Strukturverlagerungen eine große Bedeutung für das Prozessverhalten und -ergebnis. Vor diesem Hintergrund werden in diesem Forschungsvorhaben Schleifprozess und Schleifmaschine gemeinsam simulativ und experimentell betrachtet, um auftretende Wechselwirkungen und deren Einflüsse auf Prozessverhalten und -ergebnis zu erfassen. In der dritten Projektphase sollen die entwickelten Strategien zur gekoppelten Simulation der Prozess- und Maschinenmodelle detailliert analysiert und optimiert werden. Des Weiteren wird das gekoppelte Simulationssystem an eine weitere Werkzeug-Werkstoff- Paarung angepasst, um dessen Adaptionsfähigkeit zu untersuchen. Dadurch sind weitere messtechnisch überwachte Schleifexperimente zur Verifikation und Kalibrierung notwendig, in denen sowohl Prozessgrößen zur Beschreibung des Maschinenverhaltens als auch Qualitätsmerkmale erfasst werden. Durch Einbeziehung thermischer Effekte sollen das Maschinenmodell verfeinert und die Ergebnisse der gekoppelten Simulation verbessert werden. Die Gesamtheit der durchgeführten experimentellen und numerischen Untersuchungen gewährleistet die Parametrierung und Verifikation der gekoppelten Simulation und ihrer Modelle und ermöglicht die Prognose von Stabilitätskarten zur Korrelation von Qualitätsmerkmalen und Prozessparametern. Diese bieten im Wesentlichen eine Unterstützung bei der Parameterauswahl in der vorbereitenden Prozessauslegung.