bluuebunny/crossref_metadata_2025 huggingface dataset:
Coordinate‐Invariant Linear Quadratic Control
Authors: Burnett Ethan R. , Sinclair Andrew J. , Butcher Eric A.
Published: November 2019

This paper shows how the linear quadratic regulator (LQR) designs in different coordinate choices are related. Given the LQR design in one coordinate choice, it is shown that the LQR design for an alternate coordinate choice can be recovered through use of the nonlinear and linearized coordinate transformations. This provides the analyst a method of comparing coordinate choices that is more straightforward than previously suggested methods involving nonlinearity indices.
A closed‐form analytical approach for stress concentrations at elliptical holes in moderately thick plates
Authors: Felger Julian , Becker Wilfried
Published: November 2019

In this work, a modified plate model situated in‐between the classical Kirchhoff‐Love and first‐order shear deformation plate theory (FSDT) is proposed. The modified plate model includes transverse shear deformation and the governing system of partial differential equations can be tackled employing a complex potential approach. This allows for using the powerful tool of conformal mapping enabling closed‐form analytical solutions on complex domains. Based on the established complex potential methodology, the distribution of bending moments at an elliptical hole in an infinite plate under bending loading is derived. Solutions of the modified plate model are compared against numerical reference data employing FSDT.
On the Lubricant Flow and the Friction Coefficient in Partially Filled Gaps
Authors: Stahl Lukas , Müller Michael , Ostermeyer Georg-Peter
Published: November 2019

Starved lubrication is a friction regime in which the gap between the contact partners is not fully filled with fluid. It can serve as an important strategy for minimizing the amount of lubricant needed, and also inevitably occurs during idling and fail‐safe lubrication. In this regime, however, the flow of the lubricant and the related friction coefficients are yet to be fully understood. Strong non‐linear behaviour, transient influences and experimental limitations exist and hamper the creation of a comprehensive theory. This paper aims to make a fundamental contribution to the understanding of contact mechanics of partially lubricated contacts. A unique experimental setup with macroscopic asperities has been used to study the lubricant flow, the coefficient of friction (COF), and other variables over a wide range of parameters. Distinct friction behaviours were observed, for example the typical characteristic of the Stribeck curve. In addition to this well documented behaviour the experiments show a similar Stribeck‐like behaviour regarding the lubricant filling level in the gap. This proves and quantifies the expected fact that the friction regime can also be controlled by the fluid volume in the gap. To investigate this behaviour the fluid was evaluated with still images from the experiments. This study exhibits distinct flow patterns for different friction regimes of starved lubrication.
Investigating the Effect of Complex Particle Shapes in Partially Liquid‐Filled Particle Dampers using Coupled DEM‐SPH Methods
Authors: Gnanasambandham Chandramouli , Eberhard Peter
Published: November 2019

The process of energy dissipation in particle dampers (PDs) occurs mainly due to relative motion between solid particles within the damper container. The degree of relative motion between solid particles is especially sensitive to vibration amplitude changes. As the vibration amplitude decreases, less relative motion between solid particles is observed, leading to a drastic decrease in the damping performance of PDs. In this work a new approach is investigated, in which the damper contains a combination of both solid and liquid fillings, to overcome the shortcomings of a conventional PD. In order to better understand the underlying energy dissipation mechanisms a simulation model of a partially liquid‐filled particle damper with complex non‐convex shapes is set up. The liquid motion is modeled using the Smoothed Particle Hydrodynamics (SPH) method and the Discrete Element Method (DEM) is used to model the motion of solid particles. A numerical experiment is set up, where a particle damper is attached to a one degree of freedom spring‐mass‐damper system. By analysing the free response behavior of this system, the energy dissipated in various PD configurations is compared. Simulation results show more relative motion, hence more energy dissipation, in the liquid‐filled PD case than in the purely solid filled and purely liquid PD case, especially under low vibration amplitudes. Moreover, numerical studies were performed using a coupled SPH‐DEM approach to study the effect of the particle shape on the energy dissipation in liquid‐filled particle dampers.
Evaluation of source signature during Full Waveform Inversion for seismic reconnaissance in tunneling
Authors: Riedel Christopher , Musayev Khayal , Baitsch Matthias , Hackl Klaus
Published: November 2019

By transmitting seismic waves in the ground the spread, reflected and refracted waves can be recorded at different positions. The arising seismograms contain information of the geology, which can be evaluated with the Full Waveform Inversion (FWI). For the application of FWI for reconnaissance in tunneling extensive information has to be provided to achieve an appropriate model of the geology in front of the tunnel face. Such information are the position and geometry of reflecting boundaries, exact position of sources and receivers, a proper initial model of the distribution of the material parameters. The signal, which is transmitted by the senders, has also an influence on the inversion. Even if the intended source function is known, the effective signal depends on the transfer functions between sender‐soil and soil‐receiver and its identification is challenging. To avoid cumbersome investigations on the source function in advance we applied a simultaneous identification of the source signature during the FWI in the frequency domain. For synthetic models of a 2D tunnel configuration with disturbances, we will show how the calculated source signature of a frequency converges to the real source signature during the iterations of the FWI. The influence of different sender and receiver configurations will be analyzed. Furthermore, the influence of the simultaneous evaluation of the source signature on the results of the FWI will be evaluated. In a post‐processing step of the FWI, the source signature of the whole frequency spectrum will be determined.
A Navier‐Stokes‐Korteweg Model for Dynamic Wetting based on the PeTS Equation of State
Authors: Diewald Felix , Heier Michaela , Lautenschläger Martin , Horsch Martin , Kuhn Charlotte , Langenbach Kai , Hasse Hans , Müller Ralf
Published: November 2019

Dynamic wetting of component surfaces can be investigated by finite element phase field simulations. Often these models use a double‐well potential or the van der Waals equation to define the local part of the free energy density at a point of the computational domain. In order to give the present model a stronger physical background the molecular dynamics based perturbed Lennard‐Jones truncated and shifted (PeTS) equation of state is used instead. This results in phase field liquid‐vapor interfaces that agree with the physical density gradient between the two phases. In order to investigate dynamic scenarios, the phase field description is coupled to the compressible Navier‐Stokes equations. This coupling requires a constitutive equation that complies with the surface tension of the liquid‐vapor interface resulting from the PeTS equation of state and is comparable to the so‐called Korteweg tensor.
Simulation of vibrational sources and vibroacoustic transfer in wind turbine drivetrains
Authors: Ihlenburg Frank , Zarnekow Marc , Grätsch Thomas
Published: November 2019

Tonal effects in the noise radiation from wind turbines can be traced back to mechanical sources within the drivetrain. A hybrid analytical‐numerical model for the gear transmission error is used to generate the vibrational source for a large‐scale vibroacoustic FE model of a wind turbine drivetrain, and a case study of transfer path analysis is presented.
On the energetics of dynamic cohesive crack formation
Authors: Laschütza Tobias , Seelig Thomas
Published: November 2019

Dynamic fracture under static loading, as it takes place in the absence of a perfect pre‐crack, is studied from simple 1D and 2D examples. Special emphasis is placed on the cohesive fracture energy which gives rise to a finite duration of the fracture process and – in conjunction with the material's tensile strength – introduces a material specific length scale.

In case of the 2D problem (plate with hole under remote tension/compression), a (quasi‐)spontaneous formation of the finite crack increment, as predicted by FFM, can only be identified for compressive loading (stable crack growth). For tensile loading (unstable crack growth), a non‐monotonic dependence of the crack velocity on the hole radius was observed, attributed to a competition between the effects of crack initiation under higher overall stress for smaller holes and a comparatively larger process zone w.r.t. the hole radius.
Numerical Analysis of Fluid‐Film‐Cavitation on Rotordynamic Vibration and Stability Behavior
Authors: Dong Huaxin , Nowald Gerrit , Lu Daixing , Schweizer Bernhard
Published: November 2019

The dynamic vibration and stability behavior of a rotor supported in journal bearings is investigated. In the lubricating film of a hydrodynamic bearing, different cavitation phenomena may occur. Cavitation in hydrodynamic bearings is most commonly caused by surrounding air, which is sucked into the bearing gap and also by outgassing of dissolved gases. Cavitation effects have to be considered in order to precisely analyze the performance of rotor/bearing systems. Numerous approaches have been proposed to treat cavitation using appropriate boundary conditions in the REYNOLDS fluid film equation, which is applied to calculate the hydrodynamic pressure distribution in the bearing gap. These approaches are generally divided into two types: non mass‐conserving and mass‐conserving cavitation models. In this paper, a mass‐conserving cavitation model based on a 2‐phase approach (lubricant/air mixture) is applied. For the 2‐phase model, a relationship has to be defined that describes the dependency between density of the oil/gas‐mixture and the pressure. Different density/pressure models are presented and discussed. Numerical run‐up simulations are performed to study the stability of rotor/bearing systems incorporating different cavitation models. The numerical model for the rotor/bearing system consists of a multibody model for the rotor and a finite element model for the fluid film. Both models are coupled by a co‐simulation approach. The different cavitation models are compared. The influence of the cavitation model and the cavitation parameters on the stability behavior of the rotor/bearing system are analyzed. The cavitation approaches are also compared with respect to accuracy and efficiency.
From cybernetics to mechatronics: Seven decades of interdisciplinary engineering
Authors: Schiehlen Werner
Published: November 2019

Cybernetics is a transdisciplinary approach for exploring controlled systems. Norbert Wiener defined cybernetics in 1948 as “the scientific study of control and communication in the animal and the machine”. Mechatronics unites the principles of mechanics, electronics and computing to generate simpler, more economical and reliable systems. An industrial robot is a prime example of a mechatronic system, it includes aspects of mechanics, electronics, and computing to do its day‐to‐day jobs. The high reputation of mechatronics as a science was recently underlined by a mark of distinction for Kurt Magnus with a commemorative plaque erected by the foundation Stiftung‐Werner‐von‐Siemens‐Ring and unveiled 2018 at the Technical University of Munich. The Stiftung Werner‐von‐Siemens‐Ring honored the scientific work of Kurt Magnus with respect to “gyroscopes and vibrations as well as co‐founder of mechatronics” including nonlinear oscillations, too.
A Brief Historical Tour of Glacier Ice on Earth and its Role in Climate Dynamics
Authors: Gross Dietmar , Hutter Kolumban
Published: November 2019

This paper provides short excerpts of the beginnings of glacier ice research. It is restricted to the period from the beginnings in the 17th century up to the formulation of a flow law in the fifties of the forgoing century. Its role in climate research is not touched; it will be discussed in another publication.
Soil Mechanical Influence on Numerical Foundation Design of Tower Cranes
Authors: Müllner Herbert W. , Meister Herbert R.
Published: November 2019

The static design of foundations for tower cranes is mostly based on calculations of structural safety. Nevertheless further investigations considering the interaction between soil and structure including settlement calculations for evaluating the inclination of the crane are essential for safe and economic foundation solutions. Based on the experience of more than 150 tower crane positions throughout Europe a method has been developed satisfying the normative and crane specifically requirements and meeting the standards of one of the biggest building contractors in Europe.
Filtering and Model Reduction of PDAEs with Stochastic Boundary Data
Authors: Stahl Nadine , Marheineke Nicole
Published: November 2019

In this paper we investigate state reconstruction for gas pipeline networks using model hierarchies derived from model order reduction techniques. The pipeline network is described by partial differential algebraic equations (PDAEs), for which model order reduction was extensively studied in [1]. We use and extend upon the aforementioned results to estimate the system state, when the boundary data is perturbated by an Ornstein‐Uhlenbeck process. We study the performance of state reconstruction based on the derived model hierarchy. Of special interest, hereby, is the relationship between the quality of the state estimation and the underlying reduced order model.
CANFIS‐Based Semi‐active Vibration Control of Stochastically Excited High‐Rise Civil Engineering Structures with Nonlinearities and Uncertainties
Authors: Altay Okyay , Klinkel Sven
Published: November 2019

This study introduces a co‐active neuro‐fuzzy inference system (CANFIS) based vibration control strategy for high‐rise civil engineering structures, such as buildings, wind turbines and towers. The proposed approach uses semi‐active dampers, which are distributed in the structure. Attached to the structural members, semi‐active dampers generate adaptive restoring forces to reduce the structural vibrations by autonomously tuning their parameters. The nonlinear behavior and the uncertainties involved in the mathematical models of both the semi‐active dampers and the structures require sophisticated control strategies. Previous studies have shown that fuzzy logic controllers (FLCs) can overcome these challenges and perform effectively with semi‐active dampers to mitigate the structural vibrations. Nevertheless, FLCs require a predefined parameter tuning of their fuzzy rules and membership functions, which must be performed based on the knowledge of a human expert. Combining FLCs with artificial neural networks (ANNs), hybrid systems are proposed, which can determine the parameters of FLCs by using learning based training and adaptation strategies of ANNs. However, there is only limited research investigating the performance of these adaptive systems in the field of vibration control of civil engineering structures. The present work is concerned with a numerical formulation of such an adaptive system, in particular the CANFIS, and its implementation on a non‐linear seismically excited three‐story steel benchmark building with semi‐active dampers. To determine the premise parameters of the membership functions and the consequent parameters of the fuzzy rules a hybrid training method is performed using the recursive least‐square algorithm and the steepest descent method. Investigations with historic earthquakes show a significant reduction of the roof displacements of the building. For instance, during the Hachinohe earthquake the peak value of the displacement is reduced by 87 %.
An anisotropic brittle damage model with a damage tensor of second order using a micromorphic approach
Authors: Fassin Marek , Eggersmann Robert , Wulfinghoff Stephan , Reese Stefanie
Published: November 2019

The work presents a gradient‐extended ansisotropic damage model for brittle materials utilizing a second order damage tensor. In order to take into account tension compression asymmetry (TCA), the strain tensor is split into a tension and a compression related part by means of a spectral decomposition. The formulation is based on a global incremental potential allowing for large time/load steps. The gradient extension is accomplished using the micromorphic approach. Although using a damage tensor of second order, only one scalar additional degree of freedom (micromorphic variable) is introduced. First, the effects of TCA are illustrated with a simple uniaxial loading case at integration point level. Afterwards, the effect of the additionally introduced artificial viscosity, used in order to circumvent snapback situations, is shown for a structural example (without TCA). Finally, a structural example considering TCA is presented for which spurious failure in compression can be avoided.
Water‐induced failure mechanics for concrete
Authors: Aldakheel Fadi , Tomann Christoph , Lohaus Ludger , Wriggers Peter
Published: November 2019

This work outlines a micro‐mechanical framework for modeling water‐induced damage mechanism of concrete. Concrete has a highly heterogeneous micro‐structure and its composite behavior is very complex. Due to that various effects must be considered for analyzing failure response at micro scale, e.g. modeling the solid skeleton, fluid bulk phases and their interaction. For obtaining a deeper understanding of the influence of water on the concrete at the micro‐level, a micro‐computed‐tomography (micro‐CT) scan has been conducted at IfB to illustrate the micro‐structure geometry and concrete content. These data are required to build the constitutive model and the design of the numerical simulations, in line with [1]. Then a micro‐mechanical model is developed for the coupled problem of fluid‐saturated heterogeneous porous media at fracture. The modeling of microscopic cracks in porous heterogeneous media can be achieved in a convenient way by a continuum phase‐field approach, which is based on the regularization of sharp crack discontinuities [2,3]. This avoids the use of complex discretization methods for crack discontinuities, and can account for complex crack patterns. The numerical examples proposed in this contribution stem out from the DFG Priority Program SPP 2020 “Cyclic Damage Processes in High‐Performance Concretes in the Experimental Virtual Lab”.
A new domain‐based implicit‐explicit time stepping scheme based on the class of exponential integrators called sEPIRK
Authors: Straub Veronika , Ortleb Sigrun , Birken Philipp , Meister Andreas
Published: November 2019

Reliable simulations of flows in real applications involve the task of discretizing both space and time in an accurate and efficient way. To cope with the large semidiscrete systems resulting from a space discretization on appropriate grids, which often include comparatively few very small cells near solid walls for boundary layer resolution, an implicit‐explicit time stepping scheme can be the most efficient variant. We present such a type of scheme utilizing recent exponential integrators called sEPIRK and show its computational advantages opposed to IMEX‐Runge‐Kutta schemes.
On predictive modelling of yield stress increase in fresh cement paste
Authors: Huang Haiqin , Zilian Andreas
Published: November 2019

Freshly mixed concrete is composed of cement paste as fluid‐like component and aggregates as solid particulate component. Development of yield stress in fresh mortar is significant for reliable and high‐quality concrete operation as too low or too high yield stress causes process‐ability challenges like the multi‐layer problem, aggregate flocculation or blockage. Traditional experimental tests on the evolution of yield stress are costly since a wide spectrum of different material and environmental conditions needs to be studied. Progressing hydration, thermal effects and mechanical loading/unloading may influence spatial distribution of the apparent yield stress. However, this local information is very difficult to obtain using traditional laboratory tests and virtual fresh concrete testing is therefore promising.

In the context of a single‐component flow approach to homogenized modelling of the cement paste composition at the macro‐scale, the microstructural evolution affecting the development and distribution of apparent yield stress is taken into account by a thermo‐chemo‐mechanical phase‐field model bridging the micro‐macro length scales by using a Ginzburg‐Landau‐type free energy function. The phase‐field, that describes the smooth spatial transition between fluid‐like and solid‐like behaviour of cement paste in the setting phase, is governed by bond‐building chemical processes (hydration) and reversely‐acting mechanical effects (bond breakup). The resulting set of coupled nonlinear advection‐reaction‐diffusion equations are formulated in the Eulerian framework and discretized in space using the weighted residuals method and finite differences in time. Implementation of the predictive model is demonstrated using the FEniCS framework, together with numerical examples supporting model validation.
Mechanical properties assessments of as‐cast light alloys predicted by a new size‐sensitive variant of Differential Effective Medium theory
Authors: Parashkevova Ludmila , Drenchev Ludmil
Published: November 2019

The presented analytical approach is aimed to evaluate the mechanical properties of multiphase alloys regarded as “in situ” multiphase composites. The materials of interest are composites with high volume fraction of phases embedded into the micropolar matrix. According to the two‐steps homogenization procedure adopted, the multiphase Representative Volume Element (RVE) is equivalent to a RVE containing several pseudo grains. Each pseudo‐grain is a two‐phase composite with predominant non‐matrix phase. The new size‐ sensitive variant of Differential Effective Medium (DEM) homogenization scheme for a two‐phase composite is described in close form for sphere‐like inclusions. The particular case when the inclusions and the matrix have one and the same bulk modulus is applied to model the elastic behaviour of cast Mg alloys with discontinuous precipitations. The analytical solutions obtained for a composite with zero bulk modulus of inclusions are appropriate for modelling of high porosity materials with closed cells.
Multi‐Fidelity Optimization using Reduced Order Models
Authors: Tolle Kevin , Marheineke Nicole
Published: November 2019

Optimal control problems constrained to nonlinear partial differential equations appear in many applications. Because the discretization of these problems leads to large‐scale systems, a direct approach is not always viable. We consider the aggressive space‐mapping approach using surrogate models derived with the help of model order reduction techniques in order to efficiently solve such problems, while maintaining an acceptable accuracy. Numerical results based on a medical application (laser‐induced thermotherapy) are used to evaluate the effectiveness of the proposed approach.
Efficient reliability analysis coupling importance sampling using adaptive subset simulation and PGD model reduction
Authors: Robens-Radermacher Annika , Unger Jörg F.
Published: November 2019

One of the most important goals in civil engineering is to guaranty the safety of constructions. National standards prescribe a required failure probability in the order of 10−6 (e.g. DIN EN 199:2010‐12). The estimation of these failure probabilities is the key point of structural reliability analysis. Generally, it is not possible to compute the failure probability analytically. Therefore, simulation‐based methods as well as methods based on surrogate modeling or response surface methods have been developed. Nevertheless, these methods still require a few thousand evaluations of the structure, usually with finite element (FE) simulations, making reliability analysis computationally expensive for relevant applications.

The aim of this contribution is to increase the efficiency of structural reliability analysis by using the advantages of model reduction techniques. Model reduction is a popular concept to decrease the computational effort of complex numerical simulations while maintaining a reasonable accuracy. Coupling a reduced model with an efficient variance reducing sampling algorithm significantly reduces the computational cost of the reliability analysis without a relevant loss of accuracy.
The explicit jump discretization with Lippmann‐Schwinger solvers for thermal computational homogenization problems
Authors: Dorn Christian , Schneider Matti
Published: November 2019

We present a Lippmann‐Schwinger equation for the explicit jump discretization of thermal computational homogenization. Our solution scheme is based on the fast Fourier transform and thus fast and memory‐efficient. We reformulate the explicit jump discretization using harmonically averaged thermal conductivities and obtain a symmetric positive definite system. Thus, a Lippmann‐Schwinger formulation is possible. In contrast to Fourier and finite difference based discretization methods the explicit jump discretization does not exhibit ringing and checkerboarding artifacts.
Investigation of elastic grinding pins
Authors: Lamping Frederik , de Payrebrune Kristin
Published: November 2019

In order to develop a grinding tool for shape adaptive grinding, elastic grinding pins are used as an example to investigate the behaviour of those tools. In the following, we describe the results for test tubes machined with elastic grinding pins. Therefore, the surface profile of the test tubes is analysed for different parameter sets. The varied parameters are the size of the grinding particles and the stiffness of the base material.

The interdependencies between the parameters are as expected: larger particles and stiffer material lead to a rougher surface. This is the case for both acrylic glass and steel tubes. However, irregularities in the uniformity of the specimens surface indicate that the manufacturing process has still to be improved at different points.
A first order homogenization approach for structural elements: Beam kinematics
Authors: Klarmann Simon , Gruttmann Friedrich , Klinkel Sven
Published: November 2019

This contribution deals with a first order homogenization approach for structural elements with the focus on shear deformable beam elements. The homogenization theory itself is based on the well‐known Hill‐Mandel condition. Therefore, the numerical treatment leads to a coupled multiscale approach whose calculation can be performed with the so‐called FE2 scheme. As a result, not only cross‐sectional properties in the linear elastic case can be evaluated but also geometrical and physical nonlinearities can be considered. Since the mesoscale, which will be homogenized, is modelled by 3D brick elements, the considered global structure only needs to be periodic to allow a definition of a representative volume element (RVE). Thus, the procedure is not limited to pure cross‐sectional modelling, but is also able to consider inhomogeneities in the longitudinal direction of the system.

As the beam kinematics do not describe the complete deformation gradient or strain tensor, the equilibrium condition introduces a length dependency of the homogenized shear stiffnesses and the stiffnesses which depend on them due to eccentricities. This is due to the fact that the averaged shear deformation of the RVE does not linearly depend on its length multiplied by the beam shear deformation. To overcome this problem, additional constraints are introduced which ensure this linear connection. They are chosen in a way that they do not contribute to the virtual internal work. Therefore, the Hill‐Mandel condition is not affected by them. With these assumptions, the length dependency is eliminated and the averaged shear deformation of the RVE equals the shear deformation of the beam kinematics. As a result, the method is able to reproduce well‐known cross‐sectional values known from the literature and is also capable to evaluate complex nonlinear systems. For the latter, the agreement of the results with those of continuum models is very satisfying.
An optimal design of an elastic plate in a dynamic contact with a rigid obstacle
Authors: Bock Igor , Kečkemétyová Mária
Published: November 2019

We deal with an optimal design problem governed by an initial‐boundary value problem for a hyperbolic variational inequality describing the perpendicular vibrations of a simply supported anisotropic elastic plate against a rigid obstacle. A variable thickness of a plate plays the role of a control variable. The set of admissible thicknesses for the design problem consists of solutions of a state problem gained as limits of the sequences of functions solving penalized problems.
Geometry Processing Problems Using the Total Variation of the Normal Vector Field
Authors: Bergmann Ronny , Herrmann Marc , Herzog Roland , Schmidt Stephan , Vidal-Núñez José
Published: November 2019

This paper presents a novel approach to the formulation and solution of discrete geometry processing problems including mesh denoising. The main quantity of interest is the piecewise constant unit normal vector field, which we consider on piecewise flat, triangulated surfaces. In a similar fashion as one does for images defined on ‘flat’ domains, our goal is to remove noise while preserving shape features such as sharp edges. To this end, we model a denoising problem via a quadratic vertex tracking term and a regularizer based on the total variation of the normal vector field. Since the latter has values on the unit sphere, its total variation reduces to a finite sum of the geodesic distances of neighboring normals. We solve the model numerically by applying split‐Bregmann iterations and provide results for the ‘fandisk’ benchmark.
Characterization of fiber matrix interface of continuous‐discontinuous fiber reinforced polymers on the microscale
Authors: Rohrmüller Benedikt , Schober Michael , Dittmann Kerstin , Gumbsch Peter , Hohe Jörg
Published: November 2019

In lightweight constructions fiber reinforced polymers are an important material group. They combine low density with high strength and stiffness. The characterization of fiber reinforced polymers includes the characterization of the fibers, the matrix and the intermediate interface. The fibers and the matrix can be characterized on the neat materials. Single fiber tests are typically used to characterize the interface. However, the interaction between different fibers inside a composite is not taken into account in a single fiber test. The investigated sheet molding compound (SMC) has a bundle arrangement of the fibers, where the contact of different fibers is very close and therefore also the fiber‐fiber interaction has a high influence. Here we investigate the micromechanical behavior of hourglass shaped micro specimens with several hundreds of fibers with quasi‐static tensile tests. For the interface characterization the microstructure of the specimens is rebuilt in a simulation. The glass fibers are modeled as linear elastic, the matrix as hyperelastic and the interface by means of a cohesive zone model.
Two novel Kirchhoff plate finite elements for the modified strain gradient theory
Authors: Kandaz Murat , Dal Hüsnü
Published: November 2019

Microplates are vastly used in MEMS and NEMS devices. Due to size effect, classical theories of continuum mechanics can not be used to model mechanical behaviour of them. Instead, higher order continuum theories should be implemented. Modified Strain Gradient Theory (MSGT) is considered to be one of the most accurate methods for this, considering both theoretical compatibility and numerical accuracy. In this study, two sets of Kirchhoff and twist‐Kirchhoff bending rectangular plate finite elements for MSGT are developed as novel aspects. This is done by first obtaining the weak forms by using variational methods and then deriving the set of algebraic equations for the finite element formulation starting with shape functions. Although non‐conforming, the finite elements are in alignment with the existing models with the given length scale parameters. The plate finite elements are then implemented to existing models. The length scale parameters for MSGT are also identified for gold using the existing experimental results in literature. This study proposes the use of higher order theories for gold microplates for thicknesses less than 40 µm.
A comparison of numerical methods for conservative and positive advection‐diffusion‐production‐destruction systems
Authors: Kopecz Stefan , Meister Andreas
Published: November 2019

In many simulations it is important to guarantee positivity of the numerical approximations. For standard ODE solvers positivity is usually achieved by restrictions of the time step size, in contrast, MPRK schemes are unconditionally positive, which allows for much faster computations. We compare MPRK schemes and standard ODE solvers applied to an advection‐diffusion‐produ system for which it is essential to avoid negative approximations .
A numerical approach for dynamic analysis of solids in boundary representation
Authors: Méndez Salas Arturo , Chasapi Margarita , Klinkel Sven
Published: November 2019

This contribution is concerned with a numerical approach for dynamic analysis of solids in boundary representation. The aim of this investigation is to provide accurate results for the dynamic analysis in cases where only the boundary of a solid is available, whether this is defined for an open or closed domain. In CAD solids are defined through their bounded surfaces. Hence, the present method is perfectly suited to analyse such kind of geometries. The proposed approach is, therefore, based on the principle to represent a computational domain by scaling its boundary with respect to a scaling center. NURBS basis functions are used to depict the geometry of a domain and to approximate the unknowns of the problem. The core of this study is formally supported, firstly by high continuity generated by the selected interpolation functions, that provide a superior approximation for the dynamic properties of a domain, and secondly, by the adopted parametrization in boundary representation. In the entire domain, which is an elastic, homogeneous and isotropic medium under plain‐strain motion, the weak form is enforced to solve the equation of motion of the problem. An implicit method is employed for time integration. The robustness and stability of this approach are studied considering higher order NURBS basis functions to calculate superior eigenvalues of an open domain. The proposed approach is compared with the standard isogeometric analysis, which differs from the parametrization in this study, in order to show the performance of this formulation.
An interface model to account for damage and plasticity at grain boundaries
Authors: Rezaei Shahed , Rezaei Mianroodi Jaber , Brepols Tim , Wulfinghoff Stephan , Reese Stefanie
Published: November 2019

Grain boundary (GB) characteristics play a major role in the understanding and prediction of polycrystalline behavior [1]. GB roles become more important when it comes to nanocrystalline metals and ceramics. To gain a deeper insight into the behavior of the grain boundary, molecular dynamics (MD) simulations are utilized. The Mode I, mode II and mixed mode loading behavior is investigated using different MD simulations. By adding the unloading path to the MD simulations it was possible to differentiate between different active mechanisms at the GB. An interface model is introduced based on our understanding from the atomistic simulation of the grain boundaries. When it comes to the grain boundary (GB) behavior, the current model is able to capture the competition between the intergranular fracture and the grain boundary sliding. The interface model is thermodynamically consistent and is able to capture the complex behavior of the GB under different loading conditions.
Optimal Bounds for the Probability of Failure of Sheet Metal Forming Processes of DP Steel
Authors: Miska Niklas , Balzani Daniel
Published: November 2019

In this contribution, the Optimal Uncertainty Quantification framework is extended to account for aleatory uncertainties, such that both epistemic and aleatory uncertainties can be quantified. The extended framework is demonstrated for an example of a forming process of a Dual‐Phase steel sheet, for which optimal bounds on the probability of failure are computed under polymorphic uncertainties.
Controlling Sliding Droplets with Optimal Contact Angle Distributions and a Phase Field Model
Authors: Bonart Henning , Kahle Christian , Repke Jens-Uwe
Published: November 2019

We consider the optimal control of a droplet on a solid by means of the static contact angle between the contact line and the solid. The droplet is described by a thermodynamically consistent phase field model from [Abels et al., Math. Mod. Meth. Appl. Sc., 22(3), 2012] together with boundary data for the moving contact line from [Qian et al., J. Fluid Mech., 564, 2006]. We state an energy stable time discrete scheme for the forward problem based on known results, and pose an optimal control problem with tracking type objective.
Solid‐fluid coupling in a fully Lagrangian framework
Authors: Bender Jens , Kuhnert Jörg
Published: November 2019

The simulation of multiphase flows consisting of granular and fluid phases is of great interest in a wide variety of industrial applications, such as chemical process engineering, design of conveyor systems and abrasion modeling. In this context, the granular phase is often described by the discrete element method, which calculates the trajectory of each individual solid particle in a Lagrangian manner while resolving inter‐particle and geometry collisions. While the models behind individual interactions are generally not very complex, the necessary data structures and neighbor search algorithms often have a major impact on performance. Here, we present the coupling of this approach to a Lagrangian generalized finite difference method for the fluid phase which has been successfully used in a wide variety of practical applications. Coupling these two approaches enables us to treat all phases in a common framework and to use efficient and scalable data structures and algorithms. At the same time we retain the advantages of meshfree fluid solvers in free surface problems or rapidly changing flow geometries.
Optimal inflow control in transport systems with uncertain demands ‐ A comparison of undersupply penalties
Authors: Lux Kerstin , Göttlich Simone
Published: November 2019

We address the challenging task of setting up an optimal production plan taking into account uncertain demand. The transport process is represented by the linear advection equation and the uncertain demand stream is captured by an Ornstein‐Uhlenbeck process (OUP). With a model predictive control approach, we determine the optimal inflow. We use two types of undersupply penalties and compare the average undersupply as well as the number of undersupply cases in a numerical simulation.
Elasto‐plastic phase‐field model for pullout tests of steel fiber embedded in high‐performance concrete: numerical calibration and experimental validation
Authors: Pise Mangesh , Brands Dominik , Gebuhr Gregor , Sarhil Mohammad , Schröder Jörg , Anders Steffen
Published: November 2019

In this paper, the pullout behavior of steel fiber embedded in high‐performance concrete (HPC) is investigated. First, a constitutive framework of elasto‐plastic phase‐field model of fracture is constructed and applied to simulation of pullout tests for different embedded lengths of steel fibers. Thereby, the description of the mechanical behavior the Drucker‐Prager plasticity model is used. The numerical calibration of the above mentioned model is performed by simulating pullout tests and validated by data obtained from experiments. Therefore, the mechanical behavior of high‐performance concrete is studied in experiments.
Orthotropic Hyperelastic Energy Functions for the Geometrically Nonlinear Simulation of Textile Membrane Structures
Authors: Motevalli Mehran , Balzani Daniel , Uhlemann Jörg , Stranghöner Natalie
Published: November 2019

In this contribution new orthotropic hyperelastic energy functions are proposed for the geometrically nonlinear simulation of woven textile membranes. The new models are investigated and compared with a competitive formulation with respect to mathematical characteristics, accuracy in representation of experimental data and their robustness in numerical simulations. Part of the models is polyconvex and thus, a physically meaningful and mathematically sound formulation is obtained. The models are adjusted to stress‐strain paths of a glass‐PTFE fabric under cyclic uniaxial and biaxial tension tests. Moreover, a new large scale experimental setup is presented which enables the study of the material behavior in real structural problems.
Free Material Optimization of Multilayer Composite Materials
Authors: Loske Simon , Barthold Franz-Joseph
Published: November 2019

The use of composite materials in various types of devices has increased steadily in the past decades. Hence, it is worth investigating into the structural behaviour of these materials. The optimization of stacking sequences in multilayer composite materials opens a large field of improvements in industrial applications of composite materials. The center of investigation is set on fiber reinforced laminate plies, which are examined in the case of linear anisotropic theory of elasticity. One very auspicious way for optimization of these laminates is the implementation of Free Material Optimization (FMO). In these optimization procedures arbitrary values of parameters of the elasticity matrix are obtained under constraints which only claim the elasticity matrix to be symmetric and positive semidefinite. Also the trace of the elasticity matrix is restricted to avoid the total stiffness of the material to get unnaturally large. The sensitivity information are received by the variational approach for sensitivity analysis [1] which represents the most efficient known way of computing sensitivity information.
Application of higher‐order strain gradient theories in the phase‐field modelling of fracture mechanics
Authors: Juhre Daniel , Makvandi Resam
Published: November 2019

The simulation of crack propagation has always been a challenging task from a computational point of view. In the past, many mathematical and mechanical assumptions had to be taken into account to successfully simulate this process. The problem of tracking the sharp crack surface was among the first issues which was alleviated by the introduction of phase‐field models. The appearance of stress singularities near the crack tip in the classical continuum mechanics theory is considered to be another source of problem which makes the selection of proper mesh sizes for numerical models very cumbersome, and leads to unphysical results. In the presence of a singularity, the crack propagation starts earlier in problems with a finer discretization which is only natural considering that the strain energy density is higher and increases faster for smaller mesh sizes. Likewise, a loading which normally could not cause a crack to nucleate or propagate inside a structure, will do so in the numerical simulation due to over‐estimated stresses. Therefore, it stands to reason that removing this singular field from the results is a very crucial step in achieving physically meaningful results. The goal of the current contribution is twofold: first, existing models are shown to exhibit a singular stress behavior, and second, a possible remedy is proposed based on the application of higher‐order strain gradients.
Nonlinear bilateral caloric–electromechanical couplings in polycrystalline ferroelectrics
Authors: Warkentin Andreas , Lange Stephan , Wingen Marius , Ricoeur Andreas
Published: November 2019

This research is about irreversible domain wall motion leading to a temperature change of the material. The materials are mostly subjected to high frequencies and large electrical loads, which is why insufficient heat dissipation can lead to undesirable temperature developments, so–called self heating. Predictions concerning polycrystalline material behavior are made by the condensed method.
Development of a Macro‐Model for Magnetorheological Elastomers based on Microscopic Simulations
Authors: Kalina Karl A. , Metsch Philipp , Brummund Jörg , Kästner Markus
Published: November 2019

Herein, the parametrization of a macro‐model for magneto‐rheological elastomers based on microscopic simulations is presented. Within a computational homogenization, the effective response of the composite system is calculated and the data are used for parameter identification. The merit of this strategy is the adjustment of the model independent of any macroscopic sample geometry. With the developed model, the magnetostrictive behavior of a macroscopic sample is simulated.
Adaptive space‐time finite element solvers for parabolic initial‐boundary value problems with non‐smooth solutions
Authors: Langer Ulrich , Schafelner Andreas
Published: November 2019

We consider conforming finite element schemes on completely unstructured simplicial space‐time meshes for the numerical solution of non‐autonomous parabolic problems with coefficients that may discontinuously depend on the space and time variables. We present a priori estimates for low‐regularity solutions. We compare two adaptive procedures that are based on residual and functional a posteriori error indicators.
Parameter Identification of Brake Pad Shims for Complex Eigenvalue Analysis
Authors: Schmid Dominik , Sessner Vincent , Gräbner Nils , von Wagner Utz , Weidenmann Kay André
Published: November 2019

Composite structures called shims are bonded to brake pad backplates to increase the damping in brake systems. The aim of this measure is to avoid squeal which is a high‐frequency audible brake vibration disturbing customers and the environment. This NVH problem originates from self‐excited vibrations resulting from the friction contact between pad and disk. Multi‐layer shim compounds consisting of steel and elastomer layers use the shear deformation of the viscoelastic core obtaining a high energy dissipation potential.

In this contribution parameter identification for Finite Element brake simulations, so called complex eigenvalue analyses is focused. Therefore dynamic mechanical analyses on constrained layer damping structures are carried out receiving loss factors for a broad temperature and therefore frequency band. The results are compared with experimental modal analyses and possible differences between the two procedures are pointed out. The main goal is to identify input parameters for a subsequent implementation of damping characteristics for complex eigenvalue analysis.