
H1: Realtime diagnostics of complex mechanical systems
Realtime damage diagnostics of complex mechanical systems, such as aircraft engines or gas turbines in power plants, is one of the greatest current challenges in maintenance industry to control cost and time. In the project we focus on a combination of compressive sensing and machine learning in order to extract critical damage indicators from the complex information of key vibration sensors. A wavelet basis will allow for addressing nonlinear behavior, tracking frequency changes in time. The retrieved signal characteristics are then evaluated against small, partial mechanical models, data sets representing characteristic damage patterns from previous cases, data from healthy systems, and expert assessments. Uncertainty will be considered in the partial mechanical models, in the data, as well as in the expert assessments. Hence, the aspired damage identification will be developed as a statistical test assessing the distance between distribution functions, prospectively with the Bhattacharyya distance expanded to epistemic uncertainties from expert assessments. A selfgenerating mechanism for consecutive performance improvement of the algorithm will be implemented through a machine learning approach in form of Bayesian compressive sensing. In this regard, the general and fundamental algorithms can achieve optimal performance in a broad range of application areas.
Literature
 Bi, S.F.; Broggi, M.; Beer, M. (2019) The role of the Bhattacharyya distance in stochastic model updating. Mechanical Systems and Signal Processing, 117, 437–452
 Wang, Y.; Zhao, T.Y.; Phoon, K.K. (2019) Statistical inference of random field autocorrelation structure from multiple sets of incomplete and sparse measurements using Bayesian compressive samplingbased bootstrapping. Mechanical Systems and Signal Processing, 124, 217236

H2: Efficient timedependent reliability analysis of dynamical systems
Time dependent reliability analysis and life time predictions solving the first passage problem for complex structures and systems is one of the most demanding challenge in engineering. In the project we envisage to attack this problem by combining the fundamental concepts of probability density evolution and statistical emulation of limit states in time. Probability density evolution being based directly on the fundamental physical principle of preservation of probability will be used to achieve a trajectorybased formulation of the reliability problem in time, which reduces the dimensionality of the sample space drastically for efficient identification of the failure trajectories. Targeted stochastic sampling, using subset simulation, will identify these failure trajectories at some specific points in time. The resulting support points in space and time are used to establish a temporal and spatial kriging model in form of a stochastic field, which describes the stochastic evolution of the limit states with high efficiency and low dimensionality. This approach will not only allow for efficient identification of failure probabilities and, potentially rare but critical, failure events, but it will also enable a transparent and structured analysis of how these failure events evolve in order to implement most effective design measure for risk mitigation.
Literature
 Chen, J.B.; Yang, J.S.; Jensen, H. (2020) Structural optimization considering dynamic reliability constraints via probability density evolution method and change of probability measure. Structural and Multidisciplinary Optimization, 62(5), DOI: 10.1007/s00158020026214
 Au, S.K; Beck, J.L. 2001 Estimation of small failure probabilities in high dimensions by subset simulation. Probabilistic Engineering Mechanics, 16(4), 263277

H3: Error models for nonresolved structure or processes in simplified geothermal reservoir models
Predicting stresses or water and heat fluxes in geothermal reservoirs is challenging due to the lack of knowledge about the subsurface structure, but also due to the extensive computational costs for the models that describe complex flow processes in complex 3d structures. Model parameters are often obtained from model calibration using different indirect observations. Addressing also model uncertainty often requires a large number of forward runs of the model, which is mostly unfeasible due to the computational costs. It can be practical to represent the system in a simplified way. This may mean that specific structural details are not resolved, but it may also mean that processes are neglected or that the reservoir model is set up in 2d. To avoid biased parameter estimations, it can be beneficial to compensate the mismatch due to nonresolved structure by error models, which express the mismatch due to the simplification of the real system. It is a challenge to derive appropriate error models, in particular if processes are slow and quasisteady state reactions cannot be expected, as this requires timedependent error models. A model of a geothermal reservoir will be set up and the potential of error models for different types of simplifications (coarsening, fracture representation, spatial dimensionality) will be investigated in a setting where well pressure data are used for parameter identification. An Iterative Ensemble Kalman Filter will be used for parameter estimation. It will be tested if machine learning algorithms can be useful for derivation of appropriate error models. It will also be tested how the impact of using an error model is on prediction uncertainty.
Literature
 Cabarello, E., F. A. Rochinha, M. Borges and M. A. Murad, An enhanced ensemble Kalman filter scheme incorporating model error in sequential coupling between flow and geomechanics. Int J Numer Anal Methods Geomech. 43, 482500 (2019). doi.org/10.1002/nag.2872
 Xu, T., A. J. Valocchi, M. Ye, and F. Liang, Quantifying model structural error: Efficient Bayesian calibration of a regional groundwater flow model using surrogates and a datadriven error model, Water Resour. Res. 53, 40844105 (2017). doi:10.1002/2016WR019831.
 Erdal, D., I. Neuweiler and J. A. Huisman, Estimating effective model parameters for heterogeneous unsaturated flow using error models for bias correction, Water Resour. Res. 48, W06530 (2012). doi:10.1029/2011WR011062

H4: Estimating unknown exchange fluxes in heterogeneous aquifers using a reduced order model
The unknown boundary conditions are one of the big challenges when modeling aquifer systems. Often there is exchange with other hydrosystems, which should be represented as flux boundaries. These exchange fluxes are mostly not known and need either to be calculated by modeling a larger system, including the neighboring hydrosystems, or the fluxes need to be treated as unknown boundary conditions. An example is the exchange between subsurface water in hydraulic contact with a river. Often, such fluxes have to be estimated together with unknown model parameters. This problem can become computationally very expensive, as the number of unknown fluxes and parameters is large and there are strong dependencies. In recent years, model reduction methods have been applied successfully to reduce the burden of searching the parameter space. Principal component decomposition will be used to optimize pumping schemes under uncertain boundary fluxes, given different sets of pressure observations.
Literature
 Asher, M.J., B.F. Croke, A.J. Jakeman and L.J.M Peeters, A review of surrogate models and their application to groundwater modeling, Water Resour. Res. 51, 59575973 (2016). doi:10.1002/2015WR016967
 Erdal, D. and O. A. Cirpka, Joint inference of groundwaterrecharge and hydraulicconductivity field from head data using the ensemble Kalman filter, Hydrol. Earth Syst. Sci. 20, 555569 (2016). doi:10.5194/hess205552016

H5: Fast parametric investigations for boneimplant surgery planning
Stress adaptive bone remodeling simulations have been well developed in the past. However, for clinical application a framework for parametric investigations is needed, where the parameter space is defined by patient individual constitution. In this project it is planned to derive a reduced order model for fast evaluation of the whole parameter space and visualization. For that, the full highfidelity simulation scheme (starting from model generation based on image data, positioning of implants and remodeling simulation will be parametrized). A sophisticated snapshot technique, e.g. adaptive greedy sampling, will be used to generate a reduced order model (e.g. adaptive grid, response surface). Results will be postprocessed for major quantities of interest, e.g. priorimplant stability, boneloss in Gruen zones, and visualized on the fly. 3d virtual reality approaches will be utilized to augment the visualization.
Literature
 Nackenhorst U. (2020) Modeling of Bone Adaption Processes. In: Altenbach H., Öchsner A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. doi.org/10.1007/9783662557716_33
 Quarteroni, A., Rozza, G. & Manzoni, A. Certified reduced basis approximation for parametrized partial differential equations and applications. J.Math.Industry 1, 3 (2011). doi.org/10.1186/2190598313

H6: Stochastic twoscale approach on fatigue simulation of concrete specimen
Fatigue tests of concrete specimen in the laboratory typically scatter because of variations on the microscale composition and random microcrack generation. A computational model for that scenario will be set up in order to understand the mechanism in detail. At the mesoscale a detailed finite element model consisting of cement matrix, aggregates and interface transition zones a model will be studied (typical laboratory specimen). Aggregates and initial defects will be randomly distributed in the model, which is loaded under uniaxial and triaxial conditions. An efficient stochastic collocation scheme will be applied to obtain the homogenized mechanical properties. On the macroscopic lengthscale a homogenized continuum model is assumed where the material properties are described as randomfields based on the statistical information obtained from the mesomodel. Again, efficient stochastic schemes will be applied to obtain the statistical information about the damage evolution and fatigue limit. Model parameter will be calibrated to existing labexperiments which also serve for validation purpose.
Literature
 Wang, X., Zhang, M. and Jivkov, A.P. (2016): Computational technology for analysis of 3D mesostructure effects on damage and failure of concrete, International Journal of Solids and Structures, 80: 310333, doi.org/10.1016/j.ijsolstr.2015.11.018.
 Zhang, W. and Fau, A. and Nackenhorst, U. and Desmorat, R. (2020): Stochastic Material Modeling for Fatigue Damage Analysis, in Wriggers, P. and Allix, O. and Weißenfels, C. (eds.): Virtual Design and Validation, Springer, 329 – 347. doi: 10.1007/9783030381561_17

H7: Efficient compressive strength uncertainty quantification for composite structures
Microbuckling is a strain localization phenomenon which can be observed in fiber reinforced composites loaded under compression. As a strength limiting mode of failure in carbon or glass fiber reinforced polymer matrix composites, it is of significant economic importance. Moreover, it poses an interesting scientific challenge and has attracted significant attention by the research community. These efforts led to a good understanding of the basic mechanisms behind the microbuckling phenomenon, however, existing computational models are either lacking in predictive capability or are unsuitable for practical application. Major obstacles in the development of computational models for microbuckling are the uncertainty regarding the local microstructure, and the need for computational efficiency. Mesoscale approaches in combination with proper stochastic modelling of the local fiber orientation are well suited to address these aspects.
Literature
 B. Daum, N. Feld, O. Allix, and R. Rolfes. A review of computational modelling approaches to compressive failure in laminates. Composites Science and Technology, 181:107663, 2019. URL:www.sciencedirect.com/science/article/pii/S0266353818329063, DOI:doi.org/10.1016/j.compscitech.2019.05.020.
 D. Liu, N.A. Fleck, M.P.F. Sutcliffe, Compressive strength of fibre composites with random fibre waviness, J. Mech. Phys. Solids 52 (7) (2004) 1481–1505.

H8: Multiscale spacetime modeling of multiphysics problems
Multiscale methods in space have been investigated in great detail over the last years. However, the treatment of temporal scales is equally important – but only a few publications exist to date. Examples of such problems are multiphysics simulations of reactive flow interacting with arteriel walls and fracture processes embedded in larger domains. In this project, we take multiscale modeling in space and formulate corresponding methods for temporal multiscale problems. To get started, stationary problems are considered first. Then, nonstationary configurations within spacetime settings such as nonlinear, nonstationary fluidstructure interaction are treated. The methodology is first developed and tested for 2D problems in space and later extended to 3 spatial dimensions.
Literature
 K. Takizawa, T.E. Tezduyar; Multiscale spacetime fluidstructrure interaction techniques, Comp. Mech. (2011), 48: 247267
 L. Failer, T. Wick; Adaptive TimeStep Control for Nonlinear FluidStructure Interaction,
Journal of Computational Physics (JCP), Vol. 366, 2018, pp. 448  477

H9: Modelorder reduction in fluidstructure interaction and coupling to phasefield fracture
Fluidstructure interaction is a classical example of a multiphysics problem, which is still hard to be solved in an efficient computational way. In this project, a monolithic formulation of fluidstructure interaction is adopted first. Then, a reduced order model (ROM) is designed with the help of the variational multiscale method. To this end, a basis of the lowdimensional space is constructed with the help of proper orthogonal decomposition (POD). This basis is a collection of high fidelity snapshots. These developments are substantiated with a classical fluidstructure interaction benchmark problem. In the second part of this project, we then assume that the solid is damage and formulate a fluidstructure problem coupled to a phasefield formulation to treat damage. We then extend the model order reduction techniques to this larger system. Applications can be found in blood flow (aortic dissection) and porous media application in subsurface modeling for instance.
Literature
 Tello, A, Codina, R, Baiges, J. Fluid structure interaction by means of variational multiscale reduced order models. Int J Numer Methods Eng. 2020; 121: 2601– 2625.
 Wick, T; Multiphysics PhaseField Fracture: Modeling, Adaptive Discretizations, and Solvers, Radon Series on Computational and Applied Mathematics, Band 28, de Gruyter, October 2020

H10: A 3D parallel solver of FSI including goaloriented a posteriori error estimation for discretisation, iteration, and model errors
Goaloriented a posteriori error estimation for discretisation, iteration, and model errors has been well developed for simple model problems in recent years. In this project we plan to extend these methods to parallel solution techniques. Secondly, we then apply them to multiphysics simulations and realworld applications. Here we expect typical, not foreseen, difficulties when as it is wellknown when well tested solution technqiues are applied to practical 3D applications. There is an urgent need to further reduce the computational cost for full problems of direct numerical simulations since these are still necessary as the snapshots in reduced order modeling. Applications of fluidstructure interaction are widerange in mechanical engineering, biomedical engineering, and so forth.
Literature
 B. Endtmayer, U. Langer, T. Wick; MultigoalOriented Error Estimates for Nonlinear Problems, Journal of Numerical Mathematics (JNUM), Vol. 27(4), 2019, pp. 215236
 D. Jodlbauer, U. Langer, T. Wick; Parallel BlockPreconditioned Monolithic Solvers for FluidStructureInteraction Problems, International Journal for Numerical Methods in Engineering, Vol. 117 (6), 2019, pp. 623643
 T. Richter; FluidStructure Interaction, Springer, 2017

H11: Highly efficient fatigue prediction in composites in the VHCF regime
The potential of laminated Fibre Reinforced Polymers (FRPs) composites is especially utilised for components for which besides the structural weight the fatigue resistance is a decisive criterion. In structures, such as rotor blades in wind turbines, an extremely large number of load cycles is to expect over the lifespan of the blade, potentially causing socalled very high cycle fatigue (VHCF). When a composite laminate is subjected to cyclic loadings in the VHCF regime, multiple damage mechanisms, such as interfibre failure, delamination and fibre failure, are to expect.
To numerically predict the initiation and evolution of fatigue damage in composites, an energy approach has been developed at ISD, which allows to quantify the loss of the laminate’s stiffness and strength under cyclic loading in a physical manner. Although the validity of this approach has been demonstrated for various usecases (e.g. bending beam, open hole tension, bolted joints) in the past years, the approach lacks the numerical efficiency required to perform fatigue analyses in the VHCF regime for complex finite element models in an appropriate time span. To address this issue, the current version of the ISD’s fatigue damage model should be extended by an efficient cyclejump technique, as well as homogenization techniques for the analysis of larger structures. The hereby extended fatigue damage model will be calibrated and validated based on experimental results.
Literature
 P. Shabani, F. TaheriBehrooz, S. S. SamarehMousavi, M. M. Shokrieh: Very high cycle and gigacycle fatigue of fiberreinforced composites: A review on experimental approaches and fatigue damage mechanisms. Progress in Material Science, 100762, 2020. URL:www.sciencedirect.com/science/article/abs/pii/S0079642520301262 DOI:doi.org/10.1016/j.pmatsci.2020.100762
 C. Gerendt, A. Dean, T. Mahrholz, N. Englisch, S. Krause, R. Rolfes: On the progressive fatigue failure of mechanical composite joints: Numerical simulation and experimental validation. Composite Structures, 248, 112488, 2020. URL:www.sciencedirect.com/science/article/abs/pii/S0263822320310552, DOI:doi.org/10.1016/j.compstruct.2020.112488

H12: Concurrent material and structure optimization of multiphase hierarchical systems for microplasticity driven stability failure
Lodging is the bending over of plant stems near ground level, which can dramatically reduce yield. Therefore, the improvement of lodging strength of crops such as oat or wheat constitutes a major goal of agricultural research. Conventional breeding methods are based on identifying single traits that strongly correlate with lodging, mainly through visual inspections on a large number of genetic lines in the field. To enable the detection of combinations of traits that correlate with lodging, we plan to establish a novel computational framework that combines multistep homogenizationbased engineering analysis [1] with material and structure optimization methods [2].
A major mechanism behind lodging is macroscopic stability failure initiated by the plasticization of constituent materials at microscales. From the analysis viewpoint, this mechanism is essentially a coupling of inelastic effects that originate from the microscale, and the macroscopic stability failure mechanisms. In the context of concurrent material and structure optimization, we will address the following three objectives:
 introducing a pathdependent optimization strategy that leverages inelastic multistep homogenization schemes to tackle the highdimensional design variables across hierarchical scales;
 developing robust sensitivity analysis and optimization methods at the macroscale, including linearized buckling constraints; and
 setting up an efficient highperformance computing framework with proper parallelization and memory usage to tackle the computing challenge of optimizing multiphase hierarchical plant systems.
The eventual goal of this research is to identify relevant combinations of physiological and morphological parameters and associated genetic trait loci that support collaborators in the plant sciences in their efforts to breed more lodgingresilient crop varieties.
Literature
[1] T. Gangwar, J. Heuschele, G. Annor, A. Fok, K. Smith, D. Schillinger: Multiscale characterization and micromechanical modeling of crop stem materials. Biomechanics and Modeling in Mechanobiology, doi.org/10.1007/s10237020013696, 2021.
[2] T. Gangwar, D. Schillinger: Concurrent material and structure optimization of multiphase hierarchical systems within a continuum micromechanics framework. Structural and Multidisciplinary Optimization, 2021.

H13: Imagingdriven reduced order modeling of hierarchical multiscale flow systems
Hierarchical multiscale flow systems such as the human liver are characterized by the interaction of different flow regimes across varying length scales. At the macroscale, the arteries and veins that supply and drain blood from the organ are a centimeter wide. At the microscale, blood is driven through small capillaries with a diameter of ten micrometers. The overarching goal is to transfer a computationally expensive highfidelity liver model, see e.g. [1], into a patientspecific reduced order model that is computationally tractable and accurately predicts the overall perfusion characteristics of the system.
A highfidelity liver perfusion model requires the coupling of different flow regimes. As illustrated in Fig. 1, they are represented by a discrete pipe network at the larger scales and porous media flow at the small scales. To effectively adjust the multiscale perfusion model to diagnostic imaging of an individual patient, we require reduced order representations of all system components.
At the pipe network scale, we will obtain a reduced order model by limiting the recursion depth of the vessel tree, replacing the effect of all the removed scales by a homogenized flow resistance. To efficiently perform this homogenization, we require a reduced order model of the porous media flow computation, which operates at the leaves of the fullscale vessel tree. At that continuum level, the application of reducedbasis methods using snapshots and appropriate sampling methods can significantly decrease the required number of degrees of freedom. The parametrized reduced order model is implemented on a local highperformance cluster, leveraging the parallelization and data handling opportunities of modern heterogeneous compute systems. Validated against perfusion profiles extracted from CT perfusion imaging data from different patients, it can be used in combination with a CutFEM strategy to simulate liver resection scenarios, exploring the potential of the parametrized patientspecific reduced model in collaboration with liver surgeons.
Literature
[1] S.K.F. Stoter, P. Müller, L. Cicalese, M. Tuveri, D. Schillinger, T.J.R. Hughes: ''A diffuse interface method for the NavierStokes/Darcy equations: Perfusion profile for a patientspecific human liver based on MRI scans.'' Computer Methods in Applied Mechanics and Engineering, 321:70102, 2017.

H14: Multiscale thermodynamic topology optimization
Thermodynamic extremal principles constitute an important method for the development of material models. Here, the constructions of extended Hamilton functionals and their stationarity for all physical state variables have proven beneficial for the derivation of field equations for various applications. Appropriate formulations of the extended Hamilton function allow to “invert” the process of damage: instead of reducing the stiffness at spatial positions with locally high loading in terms of the free energy density, stiffness is increased in these very places. An important side aspect is that this thermodynamic topology optimization (TTO) offers the inclusion of materialnonlinearities in a holistic manner while simultaneously transforming the optimization problem into an evolutionary problem. However, during the course of material development, the optimization at the microscale has not yet been considered in TTO such that the aim of this project is the derivation of the multiscale thermodynamic topology optimization. To reduce complexity, machine learning algorithms will be employed at the microscale to account for the impact of substructures on the topology optimization at the macroscale. The model will be used to optimize the microstructure, e.g. the shape and distribution of inclusions, for various materials such that construction parts with local materials design are computed. The topologies of the optimized construction parts will consequently differ from those obtained for optimizing homogeneous materials.
Literature
 Jantos, D. R., Junker, P., & Hackl, K. Optimized growth and reorientation of anisotropic material based on evolution equations. Comput. Mech., 62(1), 4766 (2018); doi: 10.1007/s0046601714833.
 Gaganelis, G., Jantos, D. R., Mark, P., & Junker, P. Tension/compression anisotropy enhanced topology design. Struct. Multidisc. Optimization, 59(6), 22272255 (2019); doi: 10.1007/s00158018021890.

H15: Timeseparated stochastic mechanics for damage processes
A fundamental assumption in engineering is that the properties of a specific material can be quantified by means of experiments for simple specimens. Then, the related parameters, e.g. Young’s modulus, can be used for computing the behavior of construction parts made of the same material but having a different topology. These material parameters, however, are often subject to stochastic fluctuations from one sample to the next. It is therefore expected that the different realizations of the same construction part during serial production show a stochastic behavior. The exact quantification of the stochastic fluctuations can be determined by Monte Carlo simulations (MCS). Unfortunately, these computations consume massive amount of computational power, especially in the case of nonlinear materials and when applying finite element simulations. Therefore, this project aims at applying the socalled timeseparated stochastic mechanics (TSM) to the modeling of damage processes. TSM makes use of decomposition of the state variables into timeindependent stochastic terms and timedependent deterministic terms. This decomposition provides a huge saving of computational power for viscoelastic materials and yielding the same results as MCS. While being direct applicable at the material point level, TMS for damage needs to be further developed for finite element simulations. To this end, machine learning will be employed to obtain a numerically efficient model that allows to quantify the expectation and variance of the stress distribution and reaction forces for damaging materials when the material parameters fluctuate stochastically.
Literature
 Junker, P., & Nagel, J. An analytical approach to modeling the stochastic behavior of visco‐elastic materials. ZAMM‐J. Appl. Math. Mech., 98(7), 12491260 (2018); doi: 10.1002/zamm.201700257.
 Junker, P., & Nagel, J. Modeling of viscoelastic structures with random material properties using time‐separated stochastic mechanics. Int. J. Num. Meth. Eng., 121(2), 308333 (2020); doi: 10.1002/nme.6210.