
TSM for dynamic processesModeling and simulation of materials with stochastic properties is typically computationally expensive especially for nonlinear materials or dynamic simulations. The Timeseparated stochastic mechanics (TSM) can be extended for the dynamic analysis of stochastic viscoelasic materials by incorporation of the transient terms. In transient timedomain simulations a good approximation of the expectation and variance of the reaction force and the stresses for the dynamic response can be observed. A numerical extra cost of 10% compared with one deterministic finite element simulation is reported. However, the Monte Carlo simulation needs a minimum number of 400 finite element computations to arrive at results, that can be considered converged. Therefore, the TSM provides a fast yet accurate procedure for the dynamic simulation of viscoelastic structures witch stochastic properties.Leitung: P. Junker, J. NagelTeam:Jahr: 2022

InsilicoDesign von Implantaten auf der Basis eines MultiskalenansatzesIn der Forschungsgruppe sollen optimierte permanente Implantate entwickelt werden. Durch die additive Fertigung ergibt sich eine große Freiheit in der geometrischen Gestaltung. Dadurch kann die Gitterstruktur im Implantat gezielt eingestellt werden, um das Implantat optimal an den umgebenden Knochen anzupassen. Die Förderperiode 1 konzentriert sich auf permanente Implantate. Dabei muss besonders die Funktionsfähigkeit des Implantats über einen langen Belastungszeitraum garantiert sein. In diesem TP7 wird ein skalenübergreifendes Modell entwickelt, das den Einfluss von Schädigungseffekten auf der Mikroskala, von Kerbeffekten der Gitterstrukturen auf der Mesoskala sowie das Stress Shielding auf der Makroskala berücksichtigt. Dazu wird ein neuartiger Homogenisierungsansatz eingeführt, der mittels Machine Learning eine zeiteffiziente Kopplung der Skalen erlaubt. Zusätzlich wird die Thermodynamische Topologieoptimierung weiterentwickelt, um skalenübergreifend das optimale digitale Implantat unter Berücksichtigung von prozessbedingten Schädigungs und belastungsinduzierten Ermüdungseffekten zu bestimmen. Um das Optimum zwischen Gitterstruktur und Funktionsfähigkeit zu finden, wird ein effizienter MultiskalenAlgorithmus entwickelt. Das Ermüdungsverhalten bei Beanspruchung bei hohen (HCF, engl. High Cycle Fatigue) und sehr hohen Lastspielzahlen (VHCF, engl. Very High Cycle Fatigue) wird auf der Mikroskala modelliert. Dabei wird angenommen, dass das Versagen hauptsächlich an den Korngrenzen auftritt. Die Untersuchung des Einflusses der Gitterstruktur auf die SpannungsDehnungsBeziehung findet auf der Mesoskala statt. Die Optimierung des Implantats hinsichtlich Betriebsfestigkeit, Tragfähigkeit und Morphologie wird schlussendlich auf der Makroskala durchgeführt. Der Datentransfer zwischen den einzelnen Skalen soll auf speziell entwickelten künstlichen neuronalen Netzen basieren.Leitung: Philipp Junker, Peter WriggersTeam:Jahr: 2022

Characterization and Simulation of Biofilm Growth and Degradation (SIIRI  DFG TRR 298)Leitung: Meisam Soleimani, Philipp Junker, Peter WriggersTeam:Jahr: 2022

Virtual element formulation for trusses and beamsThe virtual element method (VEM) was developed not too long ago, starting with the paper Beirao da Veiga et al. (2013) related to elasticity in solid mechanics. The virtual element method allows to revisit the construction of different elements in solid mechanics, however, has so far not been applied to one dimensional structures like trusses and beams. In this project, several VEM elements suitable for trusses and beams are derived. It could be shown that the virtual element methodology produces elements that are equivalent to well know finite elements but also elements that are different, especially for higher order ansatz functions, like 2nd and 3rd order for the truss and 4th order for the beam. It will be shown that these elements can be easily incorporated in classical finite element codes since they have the same nodal degrees of freedom as finite beam elements. Furthermore, the formulation allows to compute nonlinear structural problems undergoing large deflections and rotations.Leitung: P. WriggersJahr: 2021

Virtual KirchhoffLove plate elements for isotropic and anisotropic materialsThe virtual element method allows to revisit the construction of KirchhoffLove elements because the C1continuity condition is much easier to handle in the VEM framework than in the traditional finite element methodology. Here we study the two most simple VEM elements suitable for KirchhoffLove plates as stated in (Brezzi and Marini (2013)). The formulation contains new ideas and different approaches for the stabilization needed in a virtual element, including classic and stabilization. An efficient stabilization is crucial in the case of C1continuous elements because the rank deficiency of the stiffness matrix associated to the projected part of the ansatz function is larger than for C0continuous elements. This project aims at providing engineering inside in how to construct simple and efficient virtual plate elements for isotropic and anisotropic materials and at comparing different possibilities for the stabilization. Different examples and convergence studies discuss and demonstrate the accuracy of the resulting VEM elements. Finally, reduction of virtual plate elements to triangular and quadrilateral elements with 3 and 4 nodes, respectively, yields finite element like plate elements. These C1continuous elements can be easily incorporated in legacy codes and demonstrate an efficiency and accuracy that is much higher than provided by traditional finite elements for thin plates.Leitung: P. Wriggers, B. HudobivnikTeam:Jahr: 2021

The neighbored element method for damage processes at large deformationsThe developed damage model was extended for the treatment of hyperelastic material subjected to large deformations. Along with the model derivation, a technique for element erosion in the case of severely damaged materials was also developed. Numerical results showed convergence for different mesh sizes and increasing regularization parameter. Efficiency and robustness of the approach is demonstrated by numerical examples including snapback and springback phenomena.Leitung: P. JunkerJahr: 2021

Thermodynamic topology optimizationFor the optimization of the topology, the local material density is defined as design variable within a given design space. The design space describes the geometrical bounds of the structure and to which the (mechanical) boundary value problem is applied. In each point of the design space, the density indicates whether material should be applied in that region or not. For mathematical relaxation, the density variable is continuous allowing intermediate densities during the optimization process, i.e. porous material. Intermediate densities are penalized so that the final topology contains approximately only full and void material (SIMPapproach). The underlying mathematical problem is illposed and according regularization techniques have to be applied. A gradientenhanced regularization is added for the density field and the evolution equation is formulated in its strong form. With the backward Euler scheme and an internal loop for numerical stability, no additional equation systems besides the FEM have to be solved within the optimization process. The second spacial derivatives in the strong form are computed via the neighbored element method. Herein, only the minimum number of neighboring points are used to calculate the required second spatial derivatives to reduce the calculation effort even further. The formulation is independent of the spacial discretization of the design variable: only data on the close neighborhood between points is required. Therefore, the method is suitable for meshbased as well as for meshfree methods. The minimum member size, i.e. the minimum cross section width of a structure feature, can be directly controlled by a usergiven parameter. Furthermore, the regularization technique can also be applied to regularization in other material models, as for example damage, wherein the width of the damaged zone can be controlled directly.Leitung: D. R. Jantos, P. JunkerJahr: 2021

Large deformationsWith only minor modifications to the optimization, the model is also capable to optimize structures under finite (large) deformations including buckling phenomena. The optimized topology is rather different than for small deformations and with large deformations, the direction of the applied forces influence the final topology (changing the sign of the forces considering small deformations does not change the result). The regularization and therefore the minimum member size are applied from perspective of production, i.e. the undeformed state, and do not require any recalculation of the operator matrices. The calculation effort of the optimization compared to the mechanical analysis is negligible.Leitung: P. JunkerJahr: 2021

PlasticityPlastic deformation or plastic zones can weaken the structure drastically or are also planned into the design of structure. Usual approaches for optimization with plastic material require the calculation of a full plasticity analysis with multiple load steps until convergence for each design optimization step, which results in a large number of mechanical analysis steps and therefore large calculation efforts. In the novel approach, a dissipationfree plasticity model is developed, whose evolution is pathindependent, so that only one mechanical analysis step is required for each optimization step. In combination with the operator split, the calculation effort for the optimization with plastic material is negligible higher than for an optimization with pure elastic material.Leitung: P. Junker, D. R. JantosTeam:Jahr: 2021

Anisotropic materialsHigh performance materials, as for example carbon fiber reinforced polymers but also structures produced with additive manufacturing inhere anisotropic material properties, which can be influenced during the production process, i.e. the applied direction of fibers or print path within 3D printing. Since the material orientation has a major influence on the structure performance, the local material orientation should also be considered as design variable for the optimization process. With the thermodynamic optimization approach, evolution equations for the optimal material direction described by Euler angles can be found and are combined with a simultaneous topology optimization, which results in significantly different varying optimal typologies in comparison to a topology optimization with isotropic material. For some production processes, as for example reinforcement with long fibers, or simply for a smoother fiber path design, the maximum fiber curvature can be constrained via a filtering technique with the filter radius R given by the user.Leitung: D. R. Jantos, P. JunkerJahr: 2021

Tension and compression affine materialsConcrete is economical but rather weak under tension load, whereas steel may bear tension and compression very well, but is much less economical. Therefore, an simplified approach for economical steelconcrete structures is to apply concrete only in regions predominant to compression loading and steel under tension loading. By introducing an energetic penalization, this approach can be implemented into an topology optimization with two elastic materials, in which one material is affine to compression (e.g. concrete) and one is affine to tension (e.g. steel). Due to different elastic properties of the both materials, i.e. Young's modulus an Poisson's ratio, the resulting optimization depends strongly on the load direction.Leitung: D. R. Jantos, P. JunkerJahr: 2021

Optimization and additve manufacturingThe results from the topology optimization are usually very difficult or even impossible to manufacture with conventional methods. However by use of additive manufacturing, as for example 3D printing, the production becomes not only feasible but most optimized structures can be directly produced without modification. However, the material characteristics and also bounds of the additive manufacturing processes, as for example material anisotropy, print directions, overhangs, thermomechanical properties should be considered as constraints for the optimization. Those effects strongly depend on the chosen additive manufacturing process and are considered in future projects.Leitung: D. R. Jantos, P. JunkerJahr: 2021

TSM for damage processesIn industrial applications the reliability of components with high cycle load is of interest. In addition to the TSM a damage model needs to be used. The combination of TSM with a damage model enables to predict the evolution of the reaction forces, which are influenced by the stochastic nature of the materials and the damage processes. The advantages of the TimeSeparated Stochastic Mechanics remain. The stochastic properties can be computed in advance of any concrete finite element simulation. This results in a low computational effort in comparison to Monte Carlo Simulations and enables to simulate industrially relevant problems with moderate computational resources.Leitung: P. Junker, J. NagelTeam:Jahr: 2021

PhysicsInformed DataDriven SimulationThis project investigates to what extent simulation with neural networks on the one hand and databased empirical modeling on the other hand can be combined in a symbiotic manner. The ultimate goal is the generation of reliable models for complex dynamical systems known as digital twins.Leitung: H. Wessels, P. WriggersTeam:Jahr: 2020

Waterinduced damage mechanisms of cyclic loaded highperformance concretesThe use of offshore wind energy is expanding and fatigueloaded concrete structures are built that are submerged in water. This currently already applies to socalled grouted joints, where highstrength finegrained concrete (grout) is used in the steel support structures of offshore wind turbines. Such constructions are subjected to several hundred million load cycles within their service life. An increased water content in the concrete results from the offshore exposure which is principally different to onshore constructions,. Comparatively few investigations of fatiguetested concrete specimens immersed in water are documented in the literature. Despite the fact, that considerably scatterings occur in these results a clear tendency can be observed. Specimens that are immersed in water have a significantly lower fatigue resistance compared with specimens tested in air. Some investigations also show that fatigueloaded concrete specimens immersed in water have a significant change in their fracture behaviour compared with specimens tested in air. This can be seen, in tests, for example, by ascending air bubbles, washouts of fine particles and premature crack initiation.Waterinduced damage mechanisms in fatigueloaded concrete have indeed been recognised in the past, but they were not identified and described with sufficient precision. Consequently, they cannot be quantified reliably. Based on the existing knowledge gap, the vast majority of these mechanisms have currently escaped numerical modelling and simulation.The aim of this research project is to understand, analyse and quantify macroscopically waterinduced damage mechanisms of fatigueloaded highperformance concretes in the ExperimentalVirtualLab (EVL) with complementary very latest stateoftheart experimental methods. At the same time, models will be created and numerically implemented on a micromechanical basis that enables proving of hypotheses that will be derived from the experimental investigations. The structural data serve for the validation of these models; the data will be determined by µCT scans, NMR measurements and mercury intrusion porosimetry.After a first clarification of the origin of mechanisms by the EVL, modelling at the macroscopic level will be attempted on the basis of the micromechanical investigations. In this way it will be verified, how the water influences the degradation behaviour of fatigueloaded highperformance concretes and which additional active, waterinduced damage mechanisms are decisively involved in the degradation process. It will be possible for the first time to carry out a prediction of the degradation behaviour of fatigueloaded highperformance concretes immersed in water based on microstructurally orientated parameters.Leitung: Fadi Aldakheel, Peter WriggersJahr: 2020Förderung: DFG SPP 2020, zweite FörderperiodeLaufzeit: 3 Jahre

Numerical simulation of pile installation in a hypoplastic framework using an SPH based MethodIn this project, a 3D computational tool using smoothed particle hydrodynamics (SPH) is developed which based on a hypoplastic constitutive approach for the mechanical behavior of the soil. The numerical code is firstly validated against a benchmark problem. Then several test cases are simulated including monotonic and vibratory penetration of piles into the soil. A good agreement with the experimental observation is found. Additionally, the impact of pile running in the presence of sheetpiles (retainers) are investigated to see how pile running can alter the applied forces on the sheet piles. The simulation of such complex geotechnical problems which involve large deformation, material nonlinearity and moving boundary conditions demonstrates the applicability and versatility of the proposed numerical tool in this field.Leitung: Peter WriggersTeam:Jahr: 2020

Virtual Element Method for 3D ContactThe computational modeling of contact has always been a challenging task, especially when the interface between two or more bodies, which will come into contact, has a nonconforming mesh. In this case, the virtual element method (VEM) can be used to modify the interface mesh, such that a conforming mesh arises. In this project, we employ the virtual element method in 3D to project the interface meshes between each other, such that new nodes can be inserted on both bodies, to obtain matching meshes at the interface. The insertion of new nodes does not change the Ansatz or total number of elements. These new nodes are either stemming from already existing vertices, or edgetoedge intersections (a). The later can be easily inserted in to the existing mesh, since this nodes are located at element edges. Nodes, which are getting projected from vertices will most probably lie in element faces. The insertion of these nodes needs an additional treatment. However, the projectionbased node insertion algorithm leads to matching meshes and allows to employ a simple nodetonode contact at the interface. The numerical results are showing that this way of modeling contact passes the patch test exactly (b)(c).Leitung: F. Aldakheel, B. Hudobivnik, P. WriggersTeam:Jahr: 2020

Peridynamic Galerkin MethodsSimulationdriven product development is nowadays an essential part in the industrial digitalization. Notably, there is an increasing interest in realistic highfidelity simulation methods in the fastgrowing field of additive and ablative manufacturing processes. Thanks to their flexibility, meshfree solution methods are particularly suitable for simulating the stated processes, often accompanied by large deformations, variable discontinuities, or phase changes. Furthermore, in the industrial domain, the meshing of complex geometries represents a significant workload, which is usually minor for meshfree methods. Over the years, several meshfree schemes have been developed. Nevertheless, along with their flexibility in discretization, meshfree methods often endure a decrease in accuracy, efficiency and stability or suffer from a significantly increased computation time. Peridynamics is an alternative theory to local continuum mechanics for describing partial differential equations in a nonlocal integrodifferential form. The combination of the socalled peridynamic correspondence formulation with a particle discretization yields a flexible meshfree simulation method, though does not lead to reliable results without further treatment. In order to develop a reliable, robust and still flexible meshfree simulation method, the classical correspondence formulation is generalized into the Peridynamic Galerkin (PG) methods in this project. On this basis, conditions on the meshfree shape functions of virtual and actual displacement are presented, which allow an accurate imposition of force and displacement boundary conditions and lead to stability and optimal convergence rates. Based on Taylor expansions moving with the evaluation point, special shape functions are introduced that satisfy all the previously mentioned requirements employing correction schemes. In addition to displacementbased formulations, a variety of stabilized, mixed and enriched variants are developed, which are tailored in their application to the nearly incompressible and elastoplastic finite deformation of solids, highlighting the broad design scope within the PG methods. Compared to related Finite Element formulations, the PG methods exhibit similar convergence properties. Furthermore, an increased computation time due to nonlocality is counterbalanced by a considerably improved robustness against poorly meshed discretizations.Leitung: Christian Weißenfels, Peter WriggersTeam:Jahr: 2019

Modelling and simulation of the joining zone during the tailored forming processIn this project, micromechanically motivated thermochemomechanical material models are developed on a microscopic length scale and transformed to an effective macroscopic material model. In order to achieve a high mechanical strength of the hybrid solid component, these material models are used to evaluate the sensitivity of different process parameters after joining and during forming and heat treatment. Moreover, with aid of the the evaluation results the material behaviour of the joining zone can be accurately adjusted during the Tailored Forming process.Leitung: F. Aldakheel, P. WriggersTeam:Jahr: 2019Förderung: DFG im Rahmen des SFB 1153

Virtual Element Method for Dynamic ApplicationsThe Virtual Element Method is a recent developed discretization method, which can be seen as an extension of the classical Galerkin finite element method. It has been applied to various engineering fields, such as elastoplasticity, multiphysics, damage and fracture mechanics. This project focuses on the extension of VEM towards dynamic applications. In the first part the appropriate computation of the Massmatrix regarding the vitual element ansatzspace will be done. In future works, VEM will be applied to engineering problems, considering the dynamic behavior.Leitung: F. Aldakheel, B. Hudobivnik, P. WriggersTeam:Jahr: 2019

Effective Characterization and Modelling of Elastomeric Materials for FEApplicationsFiniteElement simulations are in wide use for the development and design of industrial products. The calculation of rubber parts faces special problems due to the highly nonlinear and time dependent nature of the material. For good prediction of the final product these effects have to be captured by the underlying material models. Although there is a vast amount of different models, most of them do not offer a sufficient description of the materials behaviour or are numerically inefficient. The latter class, containing more advanced models, suffers from a large amount of parameters. Parameter identification is usually carried out by doing mechanical experiments dependent on the use case of the simulation. There is no guideline regarding the choice, parameters and amount of these experiments. In many cases there has to be a tradeoff between numerical cost, effort of characterization and accuracy of the resulting simulation, but the impact of each contribution is not precisely known. The proposed project aims to benchmark both established and emerging models for filled and unfilled elastomers in the context of usability. In more detail, the following indicators shall be investigated Numerical properties of the models. This includes numerical cost and speed, mesh size dependency and ease of implementation. Stability and robustness, especially in complex deformation states. Predictability and plausibility of the models response. Moreover, the relation between fitting parameters and aspects of the materials behaviour is investigated. This question is closely related to the effort of model parameterization. Physical basis and possibility of physical interpretation of fitting parameters. Quality of the model fit, which is related to the amount of effects (e.g. relaxation/creep, temperature, volume changes etc.), modelled. Modularity and extensibility. Based on the benchmarking a scheme for efficient parameter identification shall be drawn, dependent on the specific use case. This includes Choice of samples and measurement setup. Here, the effort for the different tests is taken into account for different materials. Measurement protocol including speed and relaxation/creep, if appropriate. Possibilities to characterize the temperature dependent response.Leitung: N.H. KrögerTeam:Jahr: 2019Förderung: Joint Industry ProjectLaufzeit: 3 years

TSM for viscoelastic structuresThe local TSM model for viscoelastic materials can also be employed for finite structures. To this end, it is evaluated for each integration point within a finite element routine. It is also possible to find analytic formulas for the expectation value and the standard deviation of each component of the reaction force. The numerical extra costs are less than 5% needed for a deterministic finite element simulation. Considering a minimum number of 400 finite element computations for a Monte Carlo simulation reveals that TSM provides a fast yet accurate procedure for the modeling of viscoelastic components with stochastic properties.Leitung: P. Junker, J. NagelJahr: 2019

The neighbored element method for damage processesDamage processes are modeled by a softening behavior in a stress/strain diagram. This reveals that the stiffness loses its ellipticity and the energy is thus not coercive. The underlying partial differental equation wouldn't have a unique solution and the numerical implementation of such an illposed problem yields results that are strongly dependent on the chosen spatial discretization. Consequently, regularization strategies have to be employed that render the problem wellposed. A prominent method for regularization is a gradient enhancement of the free energy. This, however, results in field equations that have to be solved in parallel to the EulerLagrange equation for the displacement field. Therefore the number of degrees of freedom (unknowns) would increase and the system solution using a finite element approach would be cumbersome and numerically demanding. A gradientenhanced material model for brittle damage using Hamilton’s principle for nonconservative continua was developed. The model is based on an improved algorithm, combining the finite element with strategies from meshless methods, for a fast update of the damage field function. This numerical treatment is referred to as neighbored element method (NEM). The model proves to be numerically stable and fast, with simulation times close to purely elastic problems. In addition, the model provides meshindependent results.Leitung: P. Junker, D. R. JantosJahr: 2018

2D VEM for crackpropagationLeitung: F. Aldakheel, B. Hudobivnik, P. WriggersTeam:Jahr: 2018Förderung: IRTG 1627

Virtual element method (VEM) for phasefield modeling of brittle and ductile fractureLeitung: F. Aldakheel, B. Hudobivnik, P. WriggersJahr: 2018Förderung: DFG SPP 1748

Instent restenosisLeitung: Michele Marino, Peter WriggersTeam:Jahr: 2018

Multiscale Modeling of Buckling of FiberReinforced PolymersThis project is about multiscale modeling of fiber kinking in unidirectional fiber reinforced composites.Leitung: S. Löhnert, P. WriggersTeam:Jahr: 2018Förderung: DFG (Graduiertenkolleg 1627)

Creep deformation of nickel based superalloysModeling of nickel based superalloys on two scales using crystal plasticity and XFEM methods.Leitung: P. WriggersTeam:Jahr: 2018

Using Machine Learning to Improve the Modelling of Machining and Cutting ProcessesMetal cutting is a fundamental process in industrial production. The fast and accurate online prediction of metal cutting processes is crucial for the Intelligent Manufacturing (IM). With the advent of highspeed computing, robust numerical algorithms and machine learning technology, computational modelling serves as a tool for not only accurate but also fast predicting the complex machining processes and understanding the complex physics. In this work, the machine learning based numerical model is developed for simulation of metal cutting processes.Leitung: C. Weißenfels, P. WriggersTeam:Jahr: 2018Förderung: China Scholarship Council (CSC)

The stress and fatigue analysis of the transportation lineThe conveyor of the production line in Salzgitter Flachstahl GmbH which carries the steel coils is going to be subjected to an extra load due to the bigger coil size. The objective is to do a structural analysis of the conveyor to see if the safety factor of structure is still in the allowable region. Since, the loading condition is naturally variable due to continuously feeding the moving conveyor with steel coils, a fatigue analysis is required in addition to an ordinary static analysis.Leitung: Peter WriggersTeam:Jahr: 2018

Charakterisierung sowie Modellbildung zur Beschreibung von Kompressionsmoduli technischer GummiwerkstoffeIn der Auslegung von Elastomerbauteilen steht zu Beginn ein aufwendiger Entwicklungsprozess. Dieser Prozess wird oftmals mit FiniteElementeAnalysen (FEA) zur Vorhersage der mechanischen und dynamischen Eigenschaften begleitet. Insbesondere für Dichtungsanwendungen sind vorab Aussagen über die Verformungen im Bauteil sowie Anpressdrücke, somit Aussagen zur Beständigkeit, von großem Interesse. Im Gegensatz zur Reifenindustrie, die fast ausschließlich sehr große Unternehmen umfasst, sind in der Herstellung von technischen Gummiwaren wie z.B. FederDämpferElementen, Dichtungen, Profilen und Schläuchen zahlreiche kleinere und mittlere Unternehmen tätig, für die die Projektergebnisse und deren Umsetzung auf Grund zu meist relativ geringer Entwicklungskapazitäten besonders wichtig sind. Zur Vorabberechnung per FEA sind Materialmodelle für die technischen Gummiwerkstoffe von Nöten. In Vereinfachung wird für die eingesetzten Elastomere Inkompressibilität angenommen. Diese Annahme ist korrekt für einfache Zugzustände. Überlagern sich einfache Zugzustände mit hydrostatischem Druck können deutliche Abweichungen zwischen der Annahme idealer Inkompressibilität sowie Kompressibilität vorkommen. In realen Bauteilbelastungen wird das Elastomer zudem zyklisch belastet und Teilbereiche im Bauteil erfahren unterschiedliche Belastungshistorien. Die aus der Belastung resultierende Inelastizität und Materialerweichung zum einem und Effekte eines nichtlinearen Kompressionsmoduls zum anderen führen in der Validierung bestehender Materialmodelle zu unbefriedigenden Resultaten. Im Rahmen dieses Projektes soll insbesondere ein Augenmerk auf die Quantifizierung des Kompressionsmoduls auf zyklische hydrostatischer Drücke, vgl. Dichtungen, gelegt werden. Diese Betrachtung findet bisher in der Literatur kaum Beachtung. Auf Grundlage der experimentellen Versuche wird ein geeignetes Materialmodell zur Beschreibung der Effekte erweitert und in der FEA validiert. In der Herstellung von technischen Gummiwaren wie z.B. FederDämpferElementen, Dichtungen, Profilen und Schläuchen sind zahlreiche KMU tätig, für die die Projektergebnisse und deren Umsetzung auf Grund zu meist relativ geringer Entwicklungskapazitäten besonders wichtig sind.Leitung: N.H. KrögerTeam:Jahr: 2018Laufzeit: 2 Jahre

TSM for viscoelastic materialsThe TSM has successfully been derived for viscoelastic materials. Here, two internal variables need to be computed which approximate the usual viscous part of the total strain. These internal variables are timedependent and thus also vary for varying loads; however, they are deterministic. The expectation and standard deviation for both the stochastic viscous part of the strains and the stresses is computed by means of the two internal variables and deterministic coefficients which depend on the stochastic behavior of the material. Once they are computed, they remain constant even if the external load is changing. This results in a computational effort which is doubled as compared to classical (deterministic) material models for viscoelasticity. However, for a Monte Carlo approach, at least 400 realizations need to be performed. This renders the TSM approach to be faster than Monte Carlo simulations by a factor of approximately 200.Leitung: P. Junker, J. NagelJahr: 2018

Smart hydrogels for drugdelivery and bioprinting applicationsLeitung: Peter WriggersTeam:Jahr: 2017

Waterinduced damage mechanisms of cyclic loaded highperformance concretesLeitung: P. WriggersTeam:Jahr: 2017Förderung: DFG SPP 2020, erste FörderperiodeLaufzeit: 3 Jahre

Environmentally best practices and optmisation in hydraulic fracturing for shale gas/oil developmentCollaborative Research Project funded in the "MSCARISE2016  Research and Innovation Staff Exchange" Program and the "Horizon2020EU.1.3.3.  Stimulating innovation by means of crossfertilisation of knowledge" Program.Leitung: Prof. Dr.Ing. Timon RabczukJahr: 2017Förderung: : H2020EU.1.3.3.  Stimulating innovation by means of crossfertilisation of knowledgeLaufzeit: 01.01.201731.12.2020

Computational modeling of instent restenosisThis project aims to develop a computational tool for the modeling of the longterm behaviour of stent deployment, with a special focus on both current and prospective approaches. A multiscale description of arterial constitutive behaviour will be employed, including possible damage due to the stenting procedure. Moreover, the chemobiological mechanisms underlying the growth and remodelling due to wound healing in tissues will be introduced. Therefore, a multiphysics computational framework will be developed and applied for the analysis of both metal and drugeluting stents. The project will allow to identify the dominant mechanisms driving instent restenosis, deciphering the role of the different molecular species in the pathological remodeling of arteries. The final target is to optimise the clinical outcome of current approaches and propose targeted therapeutic approaches.Leitung: M. MarinoJahr: 2017Förderung: Masterplan SmartBiotecs, MWK (Lower Saxony, Germany)

In silico morphogenesis of collagen tissues for targeted drugs and bioprintingThis project targets to understand the mechanisms behind the morphogenesis and the development of living tissues. To this aim, mechanical and biological actions that contribute to confer tissue desired topology and functionality will be modelled and analysed in silico. A computational framework for the modeling of tissue morphogenesis in natural and bioprinted systems will be developed. In particular, the project will address: the multiscale hierarchical and organized arrangement of tissue constituents; the chemomechanical interaction among tissue constituents and among cells; the chemomechanobiological mechanisms driving growth and remodeling; the extrusion and the curing of multicellular aggregates blended with bioinks. Obtained results will target to elucidate mechanisms behind tissue functional/dysfunctional structure; conceive targeted drug systems for stimulating optimal molecular pathways promoting tissue healing; develop novel or optimize existing 3D bioprinting technologies.Leitung: M. MarinoJahr: 2017Förderung: Masterplan SmartBiotecs, MWK (Lower Saxony, Germany)

ISPHbased Simulation of the Selective Laser Melting ProcessDevelopment of a thermomechanical model for the simulation of the SLM process.Leitung: Christian Weißenfels, Peter WriggersTeam:Jahr: 2017

Fatigue lifetime prediction using Wavelet transformation induced multitime scaling (WATMUS)A fast and accurate numerical method for fatigue lifetime prediction using eXtended Finite Element Method(XFEM) and WATMUSLeitung: S. Löhnert, P. WriggersTeam:Jahr: 2017

Red blood cell simulation using a coupled shellfluid analysis purely based on the SPH methodIf the rheological behavior of a RedBloodCell (RBC) changes, for example due to some infection, it is reflected in its deformability when it passes through the microvessels. It can severely affect its proper function which is providing the oxygen and nutrient to the living cells. In this research project, a novel 3D numerical method has been developed to simulate RBCs based on the interaction between a shelllike solid structure and a fluid. RBC is assumed to be a thin shell encapsulating an internal fluid (Cytoplasm) which is submerged in an external fluid (blood plasma). The approach is entirely based on the smoothed particle hydrodynamics (SPH) method for both fluid and the shell structure. The method was motivated by the goal to benefit from the Lagrangian and meshless features of SPH in order to handle several complexities in the problem due to the coupling between the RBC membrane as a deformable elastic shell and interior/exterior fluids.Leitung: Peter WriggersTeam:Jahr: 2017Laufzeit: 3 Jahre

Improved Frictional Models for Pile InstallationsTeam:Jahr: 2016

PatientSpecific FSI Analysis of the Blood Flow in the Thoracic AortaThe complexity of numerical modeling and simulation of blood flow in patientspecific thoracic aorta geometries leads to a number of major computational challenging issues. For instance, for an adequate simulation of the flow and pressure field, the incompressible NavierStokes equations have to be solved with the assumption that the relatively thin blood vessels suffer large displacements and undergo large elastic or viscoelastic deformations caused by the pulsatile blood flow. Subsequently, inaccurate predictions would be obtained for the hemodynamic quantities with the very simplifying rigidwall assumption (CFD modeling). Moreover, when applying only the CFD modeling approach the essential phenomena of pressure wave propagation in cardiovascular systems are disregarded, however these phenomena are of major relevance for clinical practice. Accordingly, strongly coupled FSI schemes are inevitable for comprehensive blood flow simulations in arterial systems, and as blood and vascular walls have comparable densities, monolithic or at least partitioned strongly coupled FSI schemes are required for solving the multiphysics problem with its inherent significant addedmass effects.Leitung: P. Wriggers, B. AvciTeam:Jahr: 2016

Process Simulation for Selective Laser MeltingA phase change model for solution with the meshfree Galerkin OTM method is developed.Leitung: Christian Weißenfels, Peter WriggersTeam:Jahr: 2016

A Novel Design Approach for Safety at Ship CollisionTeam:Jahr: 2016

3DPrinting of Curing Polymers3DPrinting simulations of curing polymers within the concept of Peridynamics are developed.Leitung: Christian Weißenfels, Peter WriggersTeam:Jahr: 2016Förderung: DFG (Graduiertenkolleg 1627)

High Performance Computing of Stereolithography ProcessesTeam:Jahr: 2016

MicroMechanically Based Modeling of Degradation of Composite Materials with Random MicrostructureHighperformance composite materials, such as carbonfiberreinforced polymers, serve as construction materials in various lightweight structures, subjected to high loads. Severe environmental conditions, such as oxidative atmosphere, affect the material microstructure and properties and thus induce material degradation which can lead to premature failure under mechanical loads. There is experimental evidence of a microstructure dependency of the material degradation. The goal of the work in progress is to develop a framework for analysis of the degradation of CFRP upon oxidation which accounts for the random distribution of the phases.Leitung: Prof. P. Wriggers, Dr. F. DaghiaTeam:Jahr: 2016Förderung: DFG (Graduiertenkolleg 1627)

Micro and mesoscale modeling of dental composite materialsHomogenization techniques can help to optimize composite materials. In this special PhD topic dental composite materials will be investigated. The main goal is, to optimize and improve the mechanical properties of these materials that consist of acrylate polymers and nanoparticles as fillers. One possibility is to change shape and geometric distribution of the fillers. This can be investigated at microscale by using homogenization to obtain the effective material parameters and direct computations to investigate material damage. The micro structure of the composite will be obtained by upscaling of results obtained by the group of P. Behrens and M.A. Schneider who investigate the molecular structure composite. The results are then validated by means of experiments performed in the group of Dr. L. Borchers/Prof. M Stiesch.Leitung: P. Wriggers, P. BehrensTeam:Jahr: 2016

Interfacial effects and ingrowing behaviour of magnesiumbased foams as bioresorbable bone substitute materialLeitung: P. WriggersTeam:Jahr: 2016Förderung: DFG

Topology optimization of nano piezo/flexoelectric structures for energy harvesting applicationsEnergy harvesters convert the ambient vibration into useful electrical energy. The energy harvesting ability of a structure is characterised by the energy conversion factor, which is the ratio of electrical energy and mechanical energy under external mechanical vibrations. The developments in nanotechnology has lead to the field of Nano Electro Mechanical Systems (NEMS). Nano scale energy harvesting devices with nano sized piezoelectric layers have also become a possibility, where the surface elastic and surface piezoelectric effects become dominant.Leitung: X. ZhuangTeam:Jahr: 2016

Nanoindentation for material property characterizationIn this work, techniques are developed for nanoindentation of soft polymers and brittle powdery materials and measurement of properties like modulus, hardness and fracture toughness.Leitung: P. Wriggers, S. LöhnertTeam:Jahr: 2016

Hypoplastic material models for soilstructure interaction problemsIn this work, a hypoplastic material model is implemented using AceGen with an eventual goal to model soilstructure interaction.Leitung: P. Wriggers, C. WeissenfelsTeam:Jahr: 2016

Thermal conductivity study of two – phase nano composite materialThis project focues on the thermal conductivity of polymermatrix nano composites accounting for the interface conductance. The influence of the scale effect and different fillers, i.e. spherical, cylindrical and platelike fillers (fullerene, carbon nanotubes and graphene sheets) with different ratios (plate diameter to plate thickness and length to diameter ratios for platelike and cylindrical fillers, respectively) on the thermal conductivity is studied. The representative volume elements (RVEs) possess periodical fillers. The computational homogenization is performed to extract the thermal conductivity of polymermatrix composites.Leitung: X. ZhuangTeam:Jahr: 2016

A 3D CAD/CAE integration using isogeometric symmetric Galerkin boundary element methodA seamless communication of computer aided design (CAD) and computer aided engineering (CAE) has always been the ultimate goal in product lifecycle management. The forward in tegration CAD/CAE, in which the simulation tasks are operated directly on CAD model, can be achieved by the isogeometric analysis (IGA) within the conventional finite element method (FEM). Despite of this successful implementation that covers many engineering aspects, the crucial challenge in this CAD/CAE integration is the incompatible geometric representation, namely the volumetric representation of CAE versus the boundary representation of CAD in threedimensional problems.Leitung: X. ZhuangTeam:Jahr: 2016

Microstructure Topology Optimization of Auxetic MaterialsAuxetic materials with negative Poisson’s ratio can lead to dramatic enhancements in mechanical properties of structures. Such materials are created by modifying periodic unit cells so that the micromechanical structure of the unit cells contain hingelike features. One of the implication of auxetic materials is their resistance to fracture since the lateral expand of material close up potential cracks. Auxetic materials flow toward the point of applied force in the impact problem and result in increase of dense at the impact zone. This show the indentation properties of auxetic materials and are adopted for various needs in military, automotive industries.Leitung: X. ZhuangTeam:Jahr: 2016

Higherorder stressbased gradientenhanced damage model using isogeometric analysis for shell delamination analysisThe microdamage associated with diffuse fracture processes in quasibrittle materials can be described by continuum damage mechanics. In order to overcome the mesh dependence of local damage formulations, nonlocal and gradientenhanced approaches are often employed.Leitung: X. ZhuangTeam:Jahr: 2016

Virtual Element Method for modeling crack propagationThe virtual element method (VEM) is a very recent numerical technique for solving partial differential equations. It can be seen as a generalization of the Finite Element Method to arbitrary polygons and polyhedra. What makes VEM become special is that the explicit calculation of integral shape functions is not required. It is possible through introduced polynomial functions and defined degrees of freedom. Due to the fact that VEM is able to generate flexible element mesh type even convex elements or concave elements, it allows us to arbitrarily add more nodes to the large stress concentration areas such as crack tips in crack simulation. In this study, we aim to develop an approach utilizing VEM to model crack growth with minimal remeshing or without remeshing. Nevertheless, the final formulation should fulfill the consistency and stability term in our approach to guarantee the accuracy and the convergence.Leitung: X. ZhuangTeam:Jahr: 2016

Durability analysis of composite materials by strong discontinuity embedded multifield frameworkComposite materials experience energy mass transport, potential phase change, chemical degradation and mechanical deformation when subjected to high temperature loading or long term chemical interaction with the surrounding environments, with is a coupled multiphysicalchemical process. Moreover, the evolving micro/macro cracks in the materials will cause extra mass transport and accelerate the degradation of materials, jeopardizing the durability of the structure.Leitung: X. ZhuangTeam:Jahr: 2016

Entropic approach to modeling Mullins effect in noncrystallizing filled elastomersThe work was done in collaboration with Mrs. Aarohi B. Shah and Dr. Julian J Rimoli of School of Aerospace Engineering, Georgia Tech, USA. In this work, we investigate noncrystallizing nanoparticlereinforced polymers. The effects of the interface rubber between elastomeric matrix and filler particles and its alteration are investigated as a primary cause of Mullins and Payne effect.Leitung: P. Wriggers, J. J. RimoliTeam:Jahr: 2016

Towards multiscale modeling of Abrasive wearThe work is motivated towards understanding wear as a multiscalemultiphysics approach. A 3D framework is developed to simulate cracks propagation in a microstructure due to contact loading to eventually predict wear trends in filled elastomeric compounds.Leitung: P. WriggersTeam:Jahr: 2015

Mesoscale constitutive modeling of filled elastomersIn this work, we develop a heterogeneous (or multiphase) constitutive model at the mesoscale model explicitly considering filler particle aggregates, elastomeric matrix and their mechanical interaction through an approximate interface layer. The developed constitutive model is used to demonstrate cluster breakage, also, as one of the possible sources for Mullins observed in noncrystallizing filled elastomers. This work considers the large deformation behavior of the filled elastomers.Leitung: P. WriggersTeam:Jahr: 2015

Numerical Simulation and Experimental Validation of Biofilm GrowthBiofilms are bacterial colonies growing on solidfluid interfaces, wherever enough dissolved nutrients are available. Their formation is a complex process in the sense that several Physical phenomena (ReactionDiffusionAdvection, Sedimentation, Erosion, FluidSolidInteraction) are coupled and consequently different timescales are involved. In this project, the focus is on the biofilm formation in a flow chamber which resembles the mouth cavity in the vicinity of dental implants. The goal is to develop a computational tool capable of simulating the biofilm growth. Numerical solution of the Navier–Stokes equation in domains with complex boundaries that dynamically change as a result of biological diffusionreaction, detachment and sedimentation in biofilm growth presents a very serious challenge to gridbased methods. In this project, a fully Lagrangian particle approach(meshless method) based on smoothed particle hydrodynamics (SPH) is developed.Leitung: P. Wriggers , M. StieschTeam:Jahr: 2015

Mesoscale modeling of large deformation behavior of nanoparticlereinforced elastomersElastomeric materials exhibit distinct fracture behavior compared to several other materials. The fracture process involves extensive chain scission (similar to crazing) in rubbery elastomers. Upon loading, the chains start to align along the direction of loading forming a zone just ahead of the crack tip. Upon further loading, more chains are drawn in from the bulk to eventually fail and leading to formation of crack front. Additionally, due to the viscoelastic nature of these polymers, there is a viscoelastic dissipation of energy just ahead of the crack tip leading to phenomena like crack tip blunting etc. A 3D finite thickness cohesive zone mode, alongside directional node release is used for modeling fracture in filled elastomeric materials.Leitung: P.. WriggersTeam:Jahr: 2015

Large Deformation CohesiveZone Element for Fracture in Rubbery PolymersIn this work, a 3D cohesive zone element is developed considering material and geometric nonlinearities and suitable for modeling large deformations and rotations.Leitung: P. WriggersTeam:Jahr: 2015

Experimental and Numerical investigation of collision of particlefilled double hull vesselA novel design approach for safety of double hull vessel is presently being investigated, which involves usage of granular materials between the hull of ship. This strategy provides a medium between the hull which can absorb impact energy and transfer the load to the inner hull. Therefore, impact energy is shared between two hulls, in contrast to localized impact on outer hull only.Leitung: P. Wriggers, C. WeißenfelsJahr: 2015

Simulation of atherosclerotic plaque impact on the red blood cells dynamics in arteriesAtherosclerosis, a coronary disease, is one of the main cause of mortality in the many countries. Atherosclerosis emerges as a results of hardening and narrowing of the blood vessels , caused by the gradual accumulation of deposits on the inside of arteries walls. This finally leads to atherosclerotic plaque. In this work, The impact of atherosclerotic plaque on red blood cells (RBC) dynamics in the blood vessels is studied. A fluidsolid interaction (FSI) analysis is developed. For the fluid phase, a meshless Lagrangian method is adopted which is called smoothed particle hydrodynamics (SPH). RBCs are considered to be the solid phase and are assumed to behave like deformable solid floated in the blood. A strong two way coupling is developed in the context of immersed boundary method (IBM) to capture the accurate fluidsolid interaction.Leitung: P. WriggersTeam:Jahr: 2015Förderung: DAAD

Gekoppelte Simulation von Aerosolströmungen in asthmatischen BronchienDas Ziel dieses Projektvorhabens ist es, auf Basis eines gekoppelten 3D Mehrfeldmodells die partikelbeladene Luftströmung in gesunden sowie in asthmatisch verengten Bronchien anhand von numerischen Simulationen zu studieren.Leitung: P. Wriggers, B. AvciTeam:Jahr: 2014Förderung: Leibniz Universität Hannover, Wege in die Forschung

In many cases, massive parallel largescale computations are indispensable for solving problems of practical interest. The numerical treatment of such class problems requires not only highly efficient scalable parallel solvers, moreover, efficient parallel algorithms covering the whole simulation pipeline – also including pre and postprocessing, mesh generation and design solvers considering uncertainties – are essential to model and to simulate largescale or exascale class problems. The specific goal of this project is therefore the development and implementation of new parallel algorithms and methods that will allow to solve largescale class problems with high efficiency.Leitung: P. Wriggers, B. AvciTeam:Jahr: 2014Förderung: FP7 of the EU

3D Dynamic Fracture in Heterogeneous MediaIn this project crack growth in brittle media is being investigated by means of the eXtended Finite Element Method (XFEM) and damage mechanics. XFEM is a numerical method, based on the Finite Element Method (FEM), which is especially designed for treating nonsmooth problems such as cracks. An essential advantage of the XFEM is that the finite element mesh does not require updating to be able to track the crack path. Enrichments added to classical FE models take into account the effects of a crack or discontinuity. In fiber reinforced materials a fracture process often starts with the delamination between the matrix material and the fibers. At some point these crack propagation processes may lead to an abrupt rupture of the entire structure. A gradient enhanced damage model is being utilized to evaluate degradation of the material at each point of the domain. In gradient enhanced damage models, a chosen length scale behaves as a localization limiter and describes the influence of the microstructure on the damage process. Moreover, such a model smoothes the deformation of the structure and avoids energy dissipation in a narrow band (surface). Damage values obtained based on this approach are used as the crack propagation criterion.Leitung: Principal Investigator: Dr.Ing. Stefan Löhnert  French CoAdvisor in Cachan: Prof. PierreAlain GuidaultTeam:Jahr: 2014Förderung: DFG (Graduiertenkolleg 1627)

Application of the Virtual Element Method to NonConforming Contact InterfacesWhen using standard Finite Elements the discretization is subject to limitations depending on the element geometry. In contrast to this the Virtual Element Method offers the possibility for elements with an arbitrary number of nodes and special geometries like nonconvex polygons or hanging nodes. In this Project the application of the Virtual Elements to different problems is investigated. Here it is used to create an efficient contact discretization.Leitung: P. WriggersTeam:Jahr: 2014

Modeling 3D crack coalescence and percolation with the XFEM and level setsIn three dimensions the accurate geometrical and mechanical modeling of crack coalescence, crack percolation and the splitting of cracks due to dynamic processes is a severe challenge. Using the XFEM in combination with level sets, new enrichment patterns as well as multiple level set functions need to be defined to account for the complex crack geometries and discontinuities within elements. In addition the definition of accurate fracture criteria for more complex material models remains a challenge. In this project crack coalescence and percolation in three dimensions is investigated in detail and accurate fracture criteria for elastoplastic material behavior within the fracture process zone are developed.Leitung: S. Löhnert, E. BudynTeam:Jahr: 2014

MultiFluid Simulations for High Density RatiosAlthough the contact between fluids or gases of different densities is a common event in nature, like the interaction of water and air, the simulation of multiple fluids often comes along with numerous problems. With the Lagrangian description of continuous fluids in terms of the Smoothed Particle Hydrodynamics (SPH) method multifluid interactions within the particle scale can simulated. Nevertheless with the standard SPH algorithms multifluid problems can not be solved because of the density jumps at the interfaces. Within the project the state of the art of current multifluid approaches are compared and evaluated to develop appropriate methods for the simulation of multifluid systems with high density ratios.Leitung: P. Wriggers, B. AvciTeam:Jahr: 2014

Nonkonvexe Partikel und parallelisierte BerechnungIn der Natur und technischen Prozessen sind viele Materialien Granulate. Als Beispiele sind Sand und Erze, Früchte und Getreibe oder auch (trockene) pharmazeutische und chemische Produkte zu nennen. Im Vergleich zu anderen Materialien, wie Stückgut, sind Granulate kompliziert in der Handhabung: Je nach Form und Oberflächenbeschaffenheit ergibt sich ein komplett anderes Materialverhalten. Um das Materialverhalten mit realitätsnahen Ergebnissen simulieren zu können, ist ein besseres Modell der Partikel notwendig. Die bisher häufig verwendeten rein konvexen Partikel (wie Kugeln oder Ellipsoide) reichen hierfür nicht aus, so dass eine komplexere Partikelbeschreibung und nichtkonvexe Formbeschreibung erforderlich ist. Die hierdurch verursachten höheren rechentechnischen Anforderungen können über Parallelisierung der Berechnung kompensiert werden.Leitung: P. WriggersTeam:Jahr: 2014Förderung: DFG (Graduiertenkolleg 1627)

Homogenization procedures for coupled thermochemomechanical problemsIn order to understand processes of continuum damage mechanics it is necessary to investigate thermochemomechanical coupled processes at micro scale. However for engineering purposes it is still necessary to be able to model these processes at macro scale, especially when large structures have to be designed. Thus a homogenization procedure or a FE^2 framework is necessary to transform the relation, describing the coupled thermochemomechanical response at micro scale to the macro scale. The related equations and procedures have to be developed and implemented in a finite element software system.Leitung: P. Wriggers, E. BarangerTeam:Jahr: 2013

Modelling the temperature development and crack propagation during sheetbulk metal formingn metal forming processes a large amount of mechanical work is dissipated due to large plastic deformations. The accompanying temperature rise leads to thermal strains and a change in the material behaviour which can influence the mechanical behaviour during the forming process and the final shape of the part. For this reason it is important to consider temperature effects and heat conduction in the material modelling of the polycrystalline microstructure. The resulting thermomechanical problem exhibits a strong coupling since on the one hand through mechanical deformation heat sources are introduced and on the other hand material parameters may depend on the temperature and also large thermal strains can emerge. Experimentally the temperature influence can be analysed by performing experiments at IW, IFUM, LFT or IUL with material specimens at different temperatures. The results can be used to develop a thermomechanical material model for the microstructure. By using homogenization techniques the macroscopic effective material model developed in period 1 of the SFB/TR73 will be extended by temperature effects. Another critical effect occurring during the forming process is the initiation and propagation of microcracks. This effect will lead to a stiffness reduction or even to failure of the entire structure. Therefore it is essential to study the degradation mechanisms of the crystallographic microstructure. A nonlocal damage model will be used to induce microcracks. For propagating the crack existing models have to be extended to nonlinear anisotropic and inelastic materials. Especially a criterion has to be found when cracks collide with grain boundaries. For the case of stable crack growth with a statistical simulation series a representative volume element can be found. This is used to produce a micromechanically motivated stress strain relationship by a homogenization procedure. With this material response the effective material model of period 1 of the SFB/TR73 will be extended. Here it is important to capture the softening effects with a nonlocal damage model which is for example used and developed at the IUL. In a last step the two approaches will be combined for the construction of a material model capturing thermomechanical effects and cracks on the microstructural level.Leitung: S. Löhnert, P. WriggersTeam:Jahr: 2013

Numerical simulation and experimental validation of biofilm formationIn this Reserch , a stateoftheart 3D computational model has been developed to investigate biofilms in a multiphysics framework using smoothed particle hydrodynamics (SPH) based on a continuum approach. Biofilms are in fact aggregation of microorganisms such as bacteria. Biofilm formation is a complex process in the sense that several physical phenomena are coupled and consequently different timescales are involved. On one hand, biofilm growth is driven by biological reaction and nutrient diffusion and on the other hand, it is influenced by the fluid flow causing biofilm deformation and interface erosion in the context of fluid and deformable solid interaction (FSI). The geometrical and numerical complexity arising from these phenomena poses serious complications and challenges in gridbased techniques such as finite element (FE). Such issues are generally referred to as mesh distortion. Here the solution is based on SPH as one of the powerful meshless methods. SPH based computational modeling is quite new in the biological community and the method is uniquely robust in capturing the interfacerelated processes of biofilm formation especially erosion. The fact is that SPH is a versatile tool owing to its adaptive Lagrangian nature in the problems whose geometry is temporarily varying (dynamic). Moreover, its meshless feature is considered to be favorable in interpreting the method as a particle based one. Hence, it is quite straight forward to incorporate complex interactions and adhoc rules at the particle level into the method. This is the case for the problems with coupled governing equations with different time and length scale. In this thesis all different physics which account for biofilm formation have been implemented in the framework of SPH and one can say that this tool is purely SPH based. Besides the numerical simulation, experiments were conducted by our partners in the medical school of Hannover. The obtained numerical results show a good agreement with experimental and published data which demonstrates that the model is capable of predicting overall spatial and temporal evolution of the biofilms. The developed tool can be employed in either controlling the detrimental biofilms or harnessing the beneficial ones.Leitung: Peter WriggersTeam:Jahr: 2013

Numerical simulations of delamination in FRP shell structures using XFEMWhen using Fiber Reinforced Plastics (FRP) delamination can occur leading to significant reduction of the load carrying capacity of a structure. Here the focus is on structural stability (buckling and snapthrough). Furthermore, the propagation of delamination in pre and postbuckling regime is of interest. A standard model for such simulations consists either of two shell elements with nodes at a given location of delamination or of a stack of shelllike solids, one per layer. The former has limits in its application while the latter leads to enormous computational effort. In this project eXtended FEM is applied to structural delamination problems. This allows the description of delamination at arbitrary throughthethickness locations by means of shape functions enriched for discontinuities. Criteria for starting and propagating delamination should be integrated, if applicable combined with cohesive zone models. Contact in a delaminated zone must be accounted for. The new element must be suitable for large rotations and buckling.Leitung: Prof. Wilhelm J.H. Rust, Prof. P. WriggersTeam:Jahr: 2013

Mehrskalenmodellierung von lokalisiertem duktilen VersagenEs existieren viele phänomenologische Materialmodelle, die duktile Schädigung vorhersagen. Um jedoch die Materialeigenschaften und Schädigungsmechanismen der vorliegenden Mikrostrukturen flexibel einzubinden, ist eine Mehrskalenformulierung notwendig. Die existierenden Multiskalenmodelle beschränken sich jedoch zumeist auf spröde Mikroschädigung. Aus diesem Grund soll in diesem Projekt eine Mehrskalenmethode entwickelt werden, die lokalisiertes plastisches Versagen aufgrund einer duktil schädigenden Mikrostruktur vorhersagen kann.Leitung: P. WriggersTeam:Jahr: 2012Förderung: DFG im Normalverfahren

Computational homogenisation of elasto plastic materialParticlematrix materials are commonly used in different fields(aerospace components, bicycle frames and racing car bodies) for its mechanical and economical advantages,such as high strength, low weight and less expense.However,Because of the microstructural complexities,it is very time and labor consuming to determin the mechanical properties of composite materials. Hence,in order to reduce laboratory expense, numerical simulations via Homogenized techniques are performed on RVE to predict mechanical behavior of composite material.Leitung: P.WriggersTeam:Jahr: 2012

Contact models for soil mechanicsThe installation of foundations influences strongly the load bearing capacity of the soil. The large discrepancy between experimental and numerical results, using Coulomb friction law for modeling the soil structure interaction, points out that new strategies to solve this kind of problems are necessary. Experimental observations show that for rough surfaces of the structure the friction angle at the contact zone corresponds to the friction angle of the soil. This leads to the conclusion that the contact zone lies completely within the soil. A way to improve the friction laws for soil structure interactions is to project the soil models onto the contact surface which is the motivation of this work. </a></p>Leitung: P. WriggersTeam:Jahr: 2012

Discrete Element MethodThis project is concerned with the development of a discrete element method (DEM) code for the simulation of large particle systems in 3D, where also complex moving boundary geometries can be taken into account. The DEM is a well established numerical method to simulate systems consisting of granular matter. Granular mixing, tumbling mills, transport of particles via conveyor belts or screw conveyors are just some examples of important particulate processes in industry sectors like mining, pharmaceutical and food industries. For such systems, the optimization of the design variables as well as the appropriate choice of the operating parameters is still a difficult and a challenging task.Leitung: P. WriggersTeam:Jahr: 2011

Multiscale Methods for Fracturing SolidsIn this project multiscale methods and homogenization techniques for the numerical simulation of three dimensional fracture processes are developed. These methods are important in aerospace and automotive industries and many other fields of mechanical and civil engineering as well as in biomechanics and material science. They will improve the prediction of the failure of structures.Leitung: P. Wriggers, S. LöhnertTeam:Jahr: 2011

Interaction between tire and vulcanizing mold during extractionOne substep of tire production is the vulcanization of a green tire under pressure inside a mold. Adherence of the rubber to this mold leads to problems during the subsequent extraction phase. Within this project the extraction of a vulcanized tire from a mold will be simulated, to obtain a better understanding of the mechanisms leading to the problems and to develop solution strategies.Leitung: P. WriggersTeam:Jahr: 2011

Crack propagation and crack coalescence in a multiscale frameworkIn this project a numerical framework for propagating and intersecting cracks on micro and macro scales is set up. Modeling cracks using the eXtended Finite Element Method (XFEM) provides an accurate and efficient numerical framework to model propagating and intersecting cracks. Since cracks of different length scales are assumed, a multiscale method is applied in order to be numerical efficient.Leitung: S. Löhnert, P. WriggersTeam:Jahr: 2010

Multiscale Method for HydroChemoThermoMechanics Coupling due to Alkali Silica Reaction in ConcreteAlkali Silica Reaction(ASR) is one of most determinant reasons leading to the deterioration of concrete structures, which can be ascribed to the expansion of gel produced by ASR in the microstructural level of concrete. The challenge in the modeling of ASR is due to the necessity to take into account the presence of heterogeneities and physical processes distributed over multiple length scales. With increasing computation power and the tomography scan technology, it can be implemented by numerical simulation . In this contribution, 3D multiscale hydrochemothermalmechanical coupling based on a staggered method is demonstrated, which explicitly describes the damage evolution originating from the chemical reaction in the microscale and the dependence on environmental factors.Leitung: P. WriggersTeam:Jahr: 2009

Multiskalenmodellierung und erweiterte finite Elmente Analyse von Bruchprozessen in KeramikDie erweiterte finite Elemente Methode (XFEM) ermöglicht die Modellierung von Rissen unabhängig von der Vernetzung. Dadurch hat sich die XFEM für Rissberechnungen durchgesetzt. Vor allem in der Nähe von Makrorissspitzen muss die Mikrostruktur des Materials berücksichtigt werden, da Mikrorisse das Risswachstum verstärken oder abschwächen können. Mikrorisse entstehen unter Belastung in der Nähe des fortschreitenden Makrorisses. Dies motiviert eine Mehrskalenmodellierung z.B. mit der Multiskalenprojektionsmethode, die in der Lage ist, Feinskaleneffekte dort genau aufzulösen, wo es notwendig ist. Auch wenn die Modellierung von Rissen mit der XFEM unabhängig von der Vernetzung ist, hat das Netz einen Einfluss auf die Genauigkeit der Spannungen. Spannungssingularitäten können mit feineren Netzen besser erfasst werden. Die Berechnung eines Diskretisierungsfehlers für den Mikrobereich ermöglicht eine adaptive Verfeinerung des Netzes, so dass genaue Ergebnisse erzielt werden können. Die verwendeten Modelle werden durch einen Vergleich mit experimentellen Daten validiert.Leitung: P. Wriggers, S. LöhnertTeam:Jahr: 2009

Direct Numerical Simulation of Multiphase FlowsMultiphase flows consisting of a continuous fluid phase and a dispersed phase of macroscopic particles are present in many engineering applications. In general, a main task in the study of the particleladen fluid flow of an application is to make predictions about the system's nature for various boundary conditions, since, depending on the volume fraction and mass concentration of the dispersed phase a fluidparticle system shows quite different flow properties. Unfortunately, often it is impossible to investigate such a system experimentally in detail or even at all. An option to capture and to predict its properties is performing a direct numerical simulation of the particulate fluid. For this purpose, an efficient approach is developed in this project by coupling the discrete element method and finite element method.Leitung: P. WriggersTeam:Jahr: 2009

MULTISCALE CONTACT HOMOGENIZATION OF GRANULAR INTERFACESDry granular third bodies are frequently encountered at multiple scales of contact interfaces in contexts that range from mechanical problems of tire traction and semiconductor manufacturing to biological problems of wear debris generation and mobility in implant joints. The investigations that are envisaged within this proposal will provide further insight into the modeling and simulation of third body effects in a fully nonlinear threedimensional virtual setting that accounts for inelastic phenomena.Leitung: P. Wriggers, I. TemizerTeam:Jahr: 2009

Micromechanics of NanoindentationViele moderne metallische Werkstoffe erhalten ihre Eigenschaften durch gezielte Beeinflussung ihrer Mikrostruktur. Die Korngröße eines Stahls bestimmt zum großen Teil sein makroskopisches Materialverhalten. Für die Untersuchung dieser Zusammenhänge auf der Mikroskala eignen sich beispielsweise Nanoindentierungsversuche. Ziel dieses Projekts ist die Simulation eines Nanoindentationsversuchs in eine polykristalline Metallprobe. Um die auftretenden Größeneffekte abbilden zu können, werden Gradientenkristallplastizitätsmodelle und ein Modell für das Korngrenzenverhalten benötigt.Leitung: P. Wriggers, C.B. HirschbergerTeam:Förderung: DFG IRTG 1627