bluuebunny/crossref_metadata_2025 huggingface dataset:
Continuum‐mechanical modelling of apoptosis
Authors: Schröder Patrick , Wagner Arndt , Stöhr Daniela , Rehm Markus , Ehlers Wolfgang
Published: November 2019

In cancer cells, the administration of drugs, such as TRAIL, can induce a mode of cell death (apoptosis). This applied reagent shifts the cell's internal inhibition and activation reactions towards the activation of caspases, triggering the cell death. In this contribution, a macroscopic model in the framework of the well‐known Theory of Porous Media is introduced to model the apoptosis reaction for lung‐cancer metastases located in brain tissue. Therein, the density‐production terms describe the apoptosis via a set of ordinary differential equations. The model is adapted to apoptosis experiments, measuring the survival rate of lung‐cancer cells in dependency of the TRAIL concentration. Thereby, the model is compared to a reduced model version using a constitutive logarithmic apoptosis function within the production terms.
On the analysis of crack‐closure behaviour using the phase‐field method together with the novel concept of Representative Crack Elements
Authors: Storm Johannes , Supriatna Dennie , Kaliske Michael
Published: November 2019

For the analysis of crack closure behaviour and the determination of forces transferred across the crack, several stress‐based splits are used for the phase‐field method so far. Steinke and Kaliske [1] proposed a kinematic analysis of the crack‐closure behaviour for isotropic linear‐elastic material behaviour, which overcomes some important issues of the previous splits (volumetric‐deviatoric and spectral split). The paper presents a novel approach for the phase‐field method, which adopts the idea of a kinematic crack analysis. Therefore, an underlying representative model of a discrete crack is coupled to the phase‐field model in order to determine the degraded and the crack‐closure behaviour. Finally, a closed form solution of the approach is presented for linear elasticity and results for thermo‐elasticity are shown. The model is validated by showing self‐consistency and the results are compared to those from the previously mentioned splits.
On higher‐order interface models
Authors: Heitbreder Tim , Mosler Jörn
Published: November 2019

Interface models are well established and frequently applied in material science. Classical non‐coherent interface models such as cohesive zone models are described by a Helmholtz energy depending on the displacement jump. The extension to thermodynamically consistent combination of classical non‐coherent cohesive zone models with surface elasticity is still relatively new, cf. [1] and [2]. These models depend on the displacement jump as well as on the surface deformation gradient. In this contribution the impact of higher‐order surface gradients is investigated.
A stochastic material model to describe continuous mode conversion
Authors: Zimmermann Eugen , Lammering Rolf , Eremin Artem
Published: November 2019

Deterministic material models are not able to comprehensively describe phenomena observed in experiments. The continuous mode conversion (CMC) of propagating waves in carbon fiber reinforced plastic (CFRP) plates is an example of this. The mechanism is similar to the conversion in the presence of defects. If a symmetrical mode while propagating through a plate‐like structure encounters a damage, which is non‐symmetric with respect to the waveguide thickness, the symmetrical mode converts into an asymmetric mode at the obstacle. The conversion is usually bounded to the location of the obstacle. In contrast, the CMC occurs even in damage free CFRP structures and manifests itself in conversion taking place permanently or continuously. The reason for this phenomenon is the irregular distribution of fiber and matrix material. With the extension to the stochastic context, it is possible to work out an enhanced material model which is able to reproduce the observed wave behaviour.
Efficient assembly of linearized equations in nonlinear homogenization
Authors: Kunc Oliver , Fritzen Felix
Published: November 2019

A novel deformation gradient‐based Reduced Basis homogenization method is compared to the well‐established displacement‐based approach in the geometrically nonlinear context. Algorithmic complexity, the intrusiveness, and the simplicity of the each approach are addressed. It is found that the novel method is advantageous in most respects, especially in returning good approximations of the macroscopic tangent stiffness.
Methods for Finding the Offset in Robust Subspace Fitting
Authors: Lellmann Jan , Neumayer Sebastian , Nimmer Max , Steidl Gabriele
Published: November 2019

We propose a method for finding the offset in robust PCA which differs from the often used geometric median and arises in a natural way from maximizing the log‐likelihood estimator of a heavy‐tailed Student's t‐distribution. Proof‐of‐concept numerical comparisons with other algorithms show the very good behavior of our approach.
Modeling the actuation and sensing behavior of an IPMC within the framework of the Theory of Porous Media
Authors: Bluhm Joachim , Serdas Serdar , Schröder Jörg
Published: November 2019

Electroactive polymers (EAPs) are considered as smart materials. Therein, a differentiation between an electric and an ionic EAP will be made. In this contribution, in particular the ionic polymer‐metal composites (IPMCs) are investigated which belong to the class of the ionic EAPs. These kind of materials act as an actuator and a sensor in variety of applications. The actuation application is given by applying an electrical voltage to the electrodes which instantaneously leads to the relocation of the mobile cations towards the cathode. The sensor application is performed by loading the IPMC mechanically which generates an electrical field. For the prediction of the behavior of this material, the theoretical framework of electrodynamics in combination with the Theory of Porous Media has been taken into account, see [1–3]. A numerical example for the 2D sensing behavior is investigated.
On the Dynamics of a Prestressed Sliding Wedge Damper
Authors: Aramendiz Jimmy , Fidlin Alexander , Baranowski Eugen
Published: November 2019

This paper presents a prestressed sliding wedge damper as an effective alternative for the reduction of vibration amplitudes. Due to the system's non‐smooth and non‐linear characteristics, it offers advantages over conventional linear dampers, e.g an amplitude adaptive behavior. First, the equations of motion which describe the system's characteristics are derived. Second, an analytical model based on a modal coordinate transformation and averaging methods is proposed. A numerical model, which uses an elasto‐plastic contact model is set up, in order to fully model the systems behavior. An analysis of the dampers characteristics shows that it is a pseudo‐viscous damper realized via dry friction. The analytical and numerical results are compared and show a reasonable agreement, as within asymptotic methods. This work presents the first investigations into prestress influence on such a damper and offers insight into future theoretical, numerical, and experimental analysis.
On different geometric approaches to the dynamics of finite‐dimensional mechanical systems
Authors: Eugster Simon R. , Capobianco Giuseppe , Winandy Tom
Published: November 2019

The language of differential geometry allows a coordinate‐free representation of physical quantities. This led to the development of several geometric theories for the description of finite‐dimensional mechanical systems. These approaches differ in the mathematical concepts they invoke and in the classes of mechanical systems they can describe. This short note aims to give an overview on the following three popular approaches, all of which are limited to time‐independent mechanical systems. While in the first approach, the motion of the mechanical system is considered as a curve in the system's configuration manifold, in the latter two, the corresponding motions are interpreted as curves in the tangent or the cotangent bundle of the configuration manifold.
Virtual testing of additively manufactured grid structures
Authors: Gebhardt Ulrike , Gärtner Roland , Berner Matthias , Holtzhausen Stefan , Hufenbach Julia Kristin , Kühn Uta , Kästner Markus
Published: November 2019

Additive manufacturing lifts the restrictions of classical manufacturing methods and enables us to produce lattice structures within otherwise massive bulk material to increase the lightweight potential of technical components. In this contribution we present a multiscale approach to characterise additively manufactured lattice structures. Tensile tests provide the properties of the bulk material and are input for a homogenisation scheme and a detailed numerical model to perform virtual experiments. The virtual experiments are compared to actual experiments on test specimen to validate the modelling approach.

Process parameters strongly influence the overall mechanical behaviour of additively manufactured lattice structures and are cause for macroscopic deviations of the geometry. Those deviations can be additional material at the struts or an inner porosity of the structure. They are identified, quantified and a first numerical analysis of their influence is presented.
Robust Feedback Control of Nonlinear PDEs by Polynomial Approximation of the Hamilton‐Jacobi‐Isaacs Equation
Authors: Kalise Dante , Kundu Sudeep , Kunisch Karl
Published: November 2019

We present a computational method for the synthesis of optimal robust feedback laws for nonlinear dynamics based on the solution of a nonlinear Hamilton‐Jacobi‐Isaacs equation. This equation is approximated with an iterative method involving the solution of high‐dimensional linear PDEs, for which we use of a Galerkin method with global polynomial ansatz functions. The method is applied for controlling dynamics arising from a pseudospectral discretization of nonlinear parabolic PDEs.
Influence of friction on the locomotion of soft robots
Authors: de Payrebrune Kristin M.
Published: November 2019

The recent interest in soft robots results from their adaptability, versatility and flexibility, which is very advantageous for new applications in human‐robot interaction, health care or field exploration. Many feasibility studies have already demonstrated the versatility of soft robots to grip irregular objects, walk on uneven surfaces, or interact with humans. Further research on mathematical models of these continuously deformable robots is ongoing to predict their performance in real life and operational situations. In particular, the models should be able to describe nonlinear material properties, contact situations and the dynamic behavior of the soft robot in action, which is a major challenge.

In this paper, basic measurements of the friction behavior of a fabricated pneu‐net bending actuator are performed in different actuation phases. In order to analyze the dependence on the momentary actuation, the coefficient of friction is related to the applied pressure, which shows a nonlinear characteristic. The results are used in the Euler's Elastica model of the soft bending actuator to describe the overall deformation according to the contact conditions more precisely.
Applying the FROSch Overlapping Schwarz Preconditioner to Dislocation Mechanics in Deal.II
Authors: Heinlein Alexander , Rheinbach Oliver , Röver Friederike , Sandfeld Stefan , Steinberger Dominik
Published: November 2019

Parallel computational results for problems in dislocation mechanics are presented using the deal.II adaptive finite element software and the Fast and Robust Overlapping Schwarz (FROSch) Preconditioner.
Parameter identification of strain rate dependent hardening for sheet metals
Authors: Söhngen Benjamin , Willner Kai
Published: November 2019

In this contribution we examine the influence of strain rate on the isotropic hardening of two sheet metals. The nominal strain rates vary between 0.0005 s−1 and 20 s−1 and the full field deformation is captured with the help of digital image correlation (DIC) technique. For modelling the strain rate dependent behaviour, we introduce a rate dependent part in the definition of the hardening stress, distinguishing between approaches that incorporate the rate dependency in an additive or multiplicative manner. The hardening laws are thereby embedded in a large strain plasticity framework based on the logarithmic strain space. The material parameters are identified both in a “direct” fashion, where the gap between constitutive equation and measured stress‐strain curve is minimized and inverse, by using the finite element method (FEM) to generate force‐displacement curves and the virtual fields method, which compares internal and external virtual work.
A New C0‐Continuous FE‐Formulation for Finite Gradient Elasticity
Authors: Riesselmann Johannes , Ketteler Jonas , Schedensack Mira , Balzani Daniel
Published: November 2019

Three field mixed C0‐continuous gradient elasticity finite element formulations contain both displacement and displacement gradients as solution variables. In this contribution a new formulation is proposed, in which the displacements are not part of the problem anymore, but only displacement gradients, leading to a reduced number of variables to be discretized. In numerical examples the proposed formulations are compared to finite strain adaptations of existing mixed three field approaches for small strains and unveil favorable computing time. For the 3D case a further reduction of variables through a penalty formulation is investigated.
SH wave generated Lamb wave in a plate with a localized region of material nonlinearity
Authors: Wang Yanzheng , Chen Weiqiu , Zhang Chuanzeng
Published: November 2019

Higher harmonics are sensitive to micro‐defects, which can be utilized in the development of nonlinear ultrasonic techniques (NLUTs). Thus, the higher harmonic generation by material nonlinearity has attracted considerable attention. However, few works have been done on the elastic wave propagation in a finite structure with a localized region of material nonlinearity. The propagation of the SH wave in a plate with a localized region of quadratic material nonlinearity is investigated in this paper. The nonlinear governing equations are reduced to a set of linear equations at different orders by using the perturbation method. The incident plane SH wave satisfies the zero‐order equations. The elastic waves generated by the nonlinear material region can be obtained by solving the first‐order equations, whose inhomogeneous terms can be regarded as the equivalent body forces and surface tractions. In the first‐order approximation, only the Lamb wave can be generated by the interaction of the SH wave with a region of quadratic material nonlinearity. In this paper, the analytical solution for the generated backward Lamb wave is obtained, whose amplitude varies with a material‐dependent constant linearly and with the length of the nonlinear region in the form of a sine function.
A study on nanoparticle transport in a micro blood vessel
Authors: Bavandi Mahrokh , Wünsch Olaf
Published: November 2019

This study focuses on the simulation of a nanoparticle loaded blood flow in a micro‐channel. The Euler‐Euler approach is used to describe the multi component behavior of blood. Nanoparticles are modeled by a concentration equation. The influence of the magnetic field gradient on particle transport is investigated for different Reynolds numbers.
On the influence of strain hardening on a rising bubble
Authors: Descher Stefan , Wünsch Olaf
Published: November 2019

This work deals deals with a constitutive approach that enables the independent modelling of shear and elongation behaviour. Studies are performed for a rising air bubble in a closed tank to investigate the influence of strain hardening on the shape of the bubble. It is shown that the occurrence of a cusp at the rear pole, which is well known to form in polymeric liquids, can be related to strain hardening only.
Effect of crystallographic orientation in modelling of anisotropic plasticity with an analytical yield function
Authors: Neuhaus Selina , Srivastava Kinshuk , Scholl Sebastian , Diebels Stefan
Published: November 2019

The mechanical properties of thermomechanical rolled low alloyed (TM) steels highly depend on their microstructure, which is formed during the production processes of the metal plate. Additionally, an elastic‐plastic anisotropy is encountered in these materials due to the texture of the ferritic grains. Hence, the material exhibits different stress‐strain curves in rolling direction (RD), normal direction (ND) and transverse direction (TD).

The aim of the present work is to include plastic anisotropy of the body‐centered cubic, ferritic phase in an already existing microstructure‐based model for the elasto‐plastic deformation of TM steels and thereby, to widen the scope of such a model to a broader range of materials. The following contribution discusses the results of simulations on single crystals and bicrystals by using an analytical yield function in order to accomplish a deeper understanding of the behaviour and applicability of an analytical, anisotropic yield function on grain level to describe anisotropically deforming metals.
A fuzzy uncertainty model for analytical and numerical homogenization of transversely fiber reinforced plastics
Authors: Caylak Ismail , Penner Eduard , Mahnken Rolf
Published: November 2019

This work is directed to aleatoric and epistemic uncertainties in the framework of mean‐field and numerical homogenization, in order to determine the overall effective properties of transversely linear elastic fiber reinforced composite (FRC) which are taken into account by stochastic and fuzzy analysis. The stochastic part of material parameters is expanded with the multivariate polynomial chaos expansion, where for epistemic uncertainties the polynomial chaos coefficients are defined as design variables modeled as fuzzy sets. In this work, the combination of both types of uncertainty are treated with fuzzy‐random variables. Then, the fuzzy response for each selected α‐level is obtained from the minimum and maximum values of the quantity of interest (QoI). However, the QoI becomes a fuzzy‐random variable and depends on the design variables as well as the random variables. In order to avoid stochastic optimizations, so‐called surrogate QoIs are used, which can be described by ordinary and central moments. The representative example deals with a fuzzy‐random analysis of a unidirectional boron/aluminum FRC to demonstrate the versatility of the proposed formulation.
Reconstruction of Non‐Stationary Signals by the Generalized Prony Method
Authors: Keller Ingeborg , Plonka Gerlind , Stampfer Kilian
Published: November 2019

We derive a method for the reconstruction of non‐stationary signals with structured phase functions using only a small number of signal measurements. Our approach employs generalized shift operators as well as the generalized Prony method. Our goal is to reconstruct a variety of sparse signal models using a small number of signal measurements.
Variational Integrators and Fluid‐Structure‐Interaction at Low Reynolds‐Number
Authors: Kern Dominik , Groß Michael
Published: November 2019

For the special case of incompressible and highly viscous fluids, the interaction with a rigid body can be collected in a damping matrix, relating the velocities and angular velocities of the body with the fluid force and torque. This damping matrix (a.k.a. viscous resistance matrix) depends exclusively on the geometry and needs to be computed only once. We consider a rigid body moving in an unbound fluid. The generalized dissipative forces from the fluid onto the body enter the time discretization via the discrete D'Alembert Principle. As generally large rotations may occur, we chose quaternions for a singularity‐free description of the body orientation. The corresponding holonomic constraint of a unit quaternion is enforced on the position and momentum level by the RATTLE algorithm. The problem of Stokes drag on a sedimenting particle serves as an example.
Detailed simulations for flamelet modelling of SOx formation from coal
Authors: Wen Xu , Stein Oliver T. , Debiagi Paulo , Scholtissek Arne , Kronenburg Andreas , Kempf Andreas M. , Hasse Christian
Published: November 2019

This paper reports on recent progress in the modelling of pulverised coal flames. A brief review of current research on fully‐resolved and Euler‐Lagrange simulations in the context of flamelet modelling of pulverised coal combustion is given first. This is followed by more recent results from the flamelet modelling of SOx formation due to fuel‐S in pulverised coal flames.
On the approximation of surface elasticity theory by means of phase‐field theory
Authors: Lammen Henning , Mosler Jörn
Published: November 2019

Within surface elasticity theory originally proposed by Gurtin and co‐workers ( [1]), effects associated with surface tension are naturally captured. In this paper, surface elasticity theory is approximated by means of phase field theory, cf. [4] and [5]. The resulting approximation is employed in order to analyze the size effects induced by the coupling of bulk and surface energies. For that purpose, the phase field framework is compared to the underlying sharp interface model proposed in [2].
Low rank surrogates for fuzzy‐stochastic partial differential equations
Authors: Gruhlke Robert , Eigel Martin , Moser Dieter , Grasedyck Lars
Published: November 2019

We consider a particular fuzzy‐stochastic PDE depending on the interaction of probabilistic and non‐probabilistic (via fuzzy arithmetic in terms of possibility theory) influences. Such a combination is beneficial in an engineering context, where aleatoric and epistemic uncertainties appear simultaneously. The fuzzy‐stochastic dependence is described in a high‐dimensional parameter space, thus easily leading to an exponential complexity in practical computations. To alleviate this severe obstacle, a compressed low‐rank approximation in form of Hierarchical Tucker representation of the desired parametric quantity of interest is derived. The performance of the proposed model order reduction approach is demonstrated.
Automatic generation of material laws based on rheological models using a genetic algorithm
Authors: Wulf Hans , Kießling Robert , Gypstuhl Richard , Ihlemann Jörn
Published: November 2019

Developing material laws based on rheological models is an established method in the field of material modelling. Here, the identification of an appropriate rheological model fitting a given set of experimental data is often a challenging task. This contribution presents an automated method for searching such rheological models. To this end, a tree representation for rheological models is defined first. Then, a generic material law, that can implement any rheological model given by a model tree, is introduced. Based on this, a genetic algorithm is used to generate rheological models, which are subsequently evaluated by fitting to measurements. This methods allows to search for a global optimum in the space of material models. Successful applications to both synthetic and actual experimental data are demonstrated.
Application of Artificial Neural Network accelerating a porous media FE2 homogenization scheme
Authors: Bartel Florian , Ricken Tim , Schröder Jörg , Bluhm Joachim
Published: November 2019

Multiscale techniques, which include information of discrete lower level substructures of real material, are state of the art methods of current researches. This technology has the advantage of achieving more accurate results, by imaging the real geometry information from the microscopic level. In addition, it provides the opportunity to design a certain microstructure which fulfills the specific requirements at a macroscopic level. The drawback lies on the increasing computational effort. Simulation of a 3‐dimensional, nonlinear, time‐dependent, coupled, two‐scale problem with industrial relevance, could cause unacceptable runtimes. There are several strategies to overcome this disadvantage, such as parallelization, analytical derivatives and various surrogate models. This contribution shows the feasibility of storing microstructural information in an Artificial Neural Network, in order to reduce computational runtime.
Reduced‐order FFT‐based homogenisation by tensor approximation
Authors: Liu Dishi , Vondřejc Jaroslav , Ladecký Martin , Matthies Hermann
Published: November 2019

We enhanced the efficiency of Fast Fourier transform (FFT) based Galerkin methods on numerical homogenisation problems by exploiting low‐rank tensor approximations in canonical, Tucker, and tensor train formats. This leads to a significant reduction in computational complexity and memory requirement. The advantages of the approach are demonstrated in a numerical example of a model homogenisation problem with stochastic heterogeneous material coefficients.
On VOIGT and KELVIN Matrix Notations of Second‐Order Tensors
Authors: Schlebusch Rainer
Published: November 2019

The implementation of constitutive models into a computer software necessitates the conversion of abstract tensors into real numbers that can be processed by a computer. This is accomplished (1) by introducing a basis, and (2) by arranging the scalar tensor components into matrices. In literature, such conversion processes are often used ad hoc without any rigorous mathematical derivation or justification. Probably most prominent are the VOIGT and KELVIN matrix notations. These matrix notations use existing symmetries of the tensors and allow to remove any redundant information from the matrix representations. Thus, in this special but very common case, the effective size of the matrices are significantly reduced and with this the computational effort.

In this contribution, the mathematical background for the two mentioned conversion processes is explained. It is shown that VOIGT and KELVIN matrix representations are not restricted to orthonormal bases, and with this not to Cartesian tensors. Moreover, it is demonstrated that the value of a duality pairing is invariant with respect to the conversion process.
Differences and similarities between reinforcement learning and the classical optimal control framework
Authors: Gottschalk Simon , Burger Michael
Published: November 2019

In this contribution , we discuss Reinforcement Learning as an alternative way to solve optimal control problems. Especially for biomechanical models, well‐established classical techniques can become complex and time‐consuming, because biomechanical models have often much more actuators than degrees of freedom. Furthermore, the solution of such a technique is normally only applicable to this specific setting. This means, that a slightly change of the initial value of the model or the desired end position does make the computed solution useless. We give a short overview to Reinforcement Learning and apply it to an optimal control problem containing the above mentioned challenges. We use an algorithm, which updates the weights and biases of a neural network, which takes the role of a controller, using simulated trajectories of the model generated by the current neural network.
On the application of a greedy reduced basis scheme to the multi‐frequency solution of acoustic boundary element equations
Authors: Jelich Christopher , Baydoun Suhaib Koji , Marburg Steffen
Published: November 2019

In this work, a greedy reduced basis scheme for the multi‐frequency solution of linear time‐harmonic acoustic problems is investigated. The scheme allows to express the approximate solution within a frequency range of interest as a linear combination of a few basis vectors. These basis vectors are given by the solutions of the underlying frequency dependent linear system at iteratively chosen frequency samples within the frequency band. In each step of the algorithm, the next basis vector is evaluated at a frequency point for which the solution is worst approximated by the current reduced basis. In order to approximate the solution between the frequency points, a least square solver is used and an a posteriori error estimator is applied for assessing the quality of the approximation. The boundary element method is used for discretizing the underlying Helmholtz problem and an iterative solver is applied for the solution of the high‐fidelity system. In view of medium to large‐scale problems, a data sparse representation of the system matrix based on the ℋ2‐format is introduced. This reduces both the memory requirements of the scheme as well as the computational effort of the matrix‐vector products. The performance of the proposed scheme is shown based on interior and exterior acoustic problems. Comparisons to conventional multi‐frequency strategies verify the efficiency of the method.
Comparison of different Excitation Strategies in Operational Modal Analysis (OMA)
Authors: Gille Max , Berninger Tobias F. C. , Rixen Daniel J.
Published: November 2019

Different ways of exciting a structure for the use in Operational Modal Analyisis (OMA) are compared and evaluated on a simple structure. As in OMA the exact excitation is unknown, some assumptions about the excitation have to be made and it is very hard or even impossible to meet all theoretical requirements, such as randomness of the excitation in time and space. As a result, compromises have to be made. Therefore, multiple techniques are evaluated to give a recommendation for those who want to perform OMA measurements themselves.

Classical Experimental Modal Analysis (EMA) is performed as a reference, and we compare these results with those of OMA with different types of excitation. These are: tipping with fingers on the structure, brushing, and acoustic excitation with noise and different styles of music through a loudspeaker. The experimental results are evaluated using the Polymax algorithm for both EMA and OMA.
Comparison of MRI measurements and CFD simulations of hemodynamics in intracranial aneurysms using a 3D printed model ‐ A benchmark problem
Authors: Giese Daniel , Heinlein Alexander , Klawonn Axel , Knepper Jascha , Sonnabend Kristina
Published: November 2019

A benchmark for the comparison of MRI (Magnetic Resonance Imaging) measurements and CFD (Computational Fluid Dynamics) simulations for blood flow in intracranial aneurysms is presented. The benchmark setting is designed to allow for CFD simulations that are completely independent of the MRI measurements. This facilitates a fair comparison of both methods. Furthermore, results showing the good agreement of MRI and CFD are presented.
Locating the extremal entries of the Fiedler vector for rose trees
Authors: Gernandt Hannes
Published: November 2019

In this note we locate the extremal entries of the Fiedler vector for the class of rose trees, which consists of paths with a star graph attached to it. We derive directly from the eigenvector equation conditions to characterize in which cases the extremal values are located either at the end points of the path or on the pendant vertices of the star graph.
Computational Modeling of Drying Shrinkage in Early‐Age Concrete
Authors: Ghasabeh Mehran , Göktepe Serdar
Published: November 2019

This contribution is concerned with the computational modeling of durability problems related to drying shrinkage. The associated formulations are conducted by developing a coupled constitutive modeling approach, which is furnished by the robust computational tools within the framework of poroviscoelasticity. In contrast to the existing studies, we employ a physically motivated technique where the pore pressure is obtained as a function of the water content that is determined using sorption‐desorption equations for a given value of the local relative humidity. Therefore, the proposed model accounts for the hygro‐chemo‐mechanical cross coupling effects between the shrinkage‐induced strain development due to the pressure evolution through humidity variations and the stress concentrations in hardening and hardened viscoelastic concrete. The comparison of the numerical examples with experiments demonstrates excellent predictive capacity of the proposed model.
Parameter identification for constitutive models of innovative textile composite materials using digital image correlation
Authors: Hofmann Justin Felix , von Boyneburgk Claudia , Tunger Sophie , Heim Hans-Peter , Kuhl Detlef
Published: November 2019

This contribution focuses on an innovative composite material consisting of textile layers made from continuous wooden fibers embedded in a thermoplastic matrix. A finite element simulation of potential use‐cases is planned to support the development process and to study the suitability of the material in an architectural context. The simulation is based on a constitutive model assuming homogenous orthotropic elastic behavior and will be expanded to include multiscale modeling in future research. The material parameters used in such models can often be determined based on a small number of local measurements during experiments like tensile tests, which assume classical one dimensional load scenaria at least in parts of the specimen. However, this is not sufficient for non‐homogeneous materials, especially when dealing with non‐isotropic materials in off‐axis configurations and the need for full‐field measurements like digital image correlation (DIC) arises. Experimental results of uniaxial on‐ and off‐axis tensile tests using DIC are presented and used in the identification of the material parameters of the given model. Results of simulations and experiments are compared and the suitability of the material model is discussed.
Adaptive isogeometric discretizations for diffuse modeling of discontinuities
Authors: Hennig Paul , Maier Roland , Peterseim Daniel , Kästner Markus
Published: November 2019

In this contribution, we discuss the modeling of discontinuities using non‐conforming meshes. For weak discontinuities we propose to regularize the sharp material interface over a characteristic length scale. To define the material properties in the transition region, homogenization assumptions are used that fulfill the kinematic compatibility across the interface and the static equilibrium at the interface. For strong discontinuities we use a phase‐field model that is able to account for failure of adhesive interfaces and extend it to general heterogeneous materials. To improve the efficiency of the approach, adaptive isogeometric analysis is used to discretize the computational domain.
On Aerodynamic Load Transfer to the Flexible Car‐Body of a High Speed Train
Authors: Dou Weiyuan , Zhang Lele , Stichel Sebastian
Published: November 2019

Investigating the influence of aerodynamic loads on the flexible car‐body of high speed trains (HST) , a method to investigate the elastic vibrations of the car‐body modeled as a dynamic system, induced by aerodynamic‐loads during operation, was developed based on an equivalent force system. A reduced degree of freedom model was developed by considering master nodes in the full‐scale model. The results demonstrate the feasibility of our proposed method which introduces aerodynamic‐loads as input to analyze the aerodynamic performance of a HST with a flexible car‐body. The new method can also reduce the time consumption in the multi‐body dynamics calculation and provide more information of the elastic vibration of a car‐body.
Soil modeling with a DEM Lookup approach
Authors: Jahnke Jonathan , Steidel Stefan , Burger Michael
Published: November 2019

We consider an efficient, data‐driven approximation approach for the prediction of soil‐tool interaction forces. In a time‐consuming offline phase, we perform a set of Discrete Element Method basis simulations. In each simulation, we consider a different tool state, process the acquired data and save it into a data structure, which we call a Lookup Table. In an online phase, when performing arbitrary tool maneuvers, we obtain tool forces and moments from the Lookup Table, based on the current tool state. In other words, we generate a data base of tool maneuver forces and access it efficiently.
Incorrect Estimates by the Four Wave Interaction(FWI) system for the Fermi‐Pasta‐Ulam(FPU) System
Authors: Sunny Danish Ali , Farooq Sarfraz
Published: November 2019

Recently it was proved in [9] that the nonlinear Schrödinger equation fails to predict accurately the dynamics of an original system because of unstable resonances. By extending the ideas in [9], we prove a similar result for the Four Wave Interaction System.
Model order reduction for space‐adaptive simulations of Navier‐Stokes
Authors: Gräßle Carmen , Hinze Michael , Lang Jens , Ullmann Sebastian
Published: November 2019

We consider model order reduction with proper orthogonal decomposition (POD) for simulations of incompressible, laminar flow governed by the Navier‐Stokes equations. The major goal in reduced‐order modeling is to replace expensive high‐fidelity systems by low‐order approximations while ensuring a good approximation quality. In this work, the reduced‐order model is constructed from snapshots which are space‐adapted finite element solutions. In order to guarantee stability of the POD surrogate model, we either use a projection onto a common divergence‐free space or utilize a supremizer enrichment of the reduced velocity space. In a numerical experiment, we compare the accuracy of the resulting reduced solution with the standard approach using a static, uniform snapshot discretization.
Global proper orthogonal decomposition for parametric model reduction of geometrically nonlinear structures
Authors: Meyer Christian H. , Rixen Daniel
Published: November 2019

Finite element simulations of structures that undergo large deformations can imply long simulation times due to the nonlinearity of the resulting equations of motion and a high number of degrees of freedom. Especially for design studies, where the equations of motion must be solved several times, it is highly desired to reduce the simulation time.

The simulation time can be reduced by nonlinear model reduction. Nonlinear model reduction is carried out in two steps: First, the dimension of the problem is reduced by projecting the equations of motion onto a low‐order subspace that is defined by a reduction basis. Second, the evaluation of the nonlinear restoring force term, that originates from large deflections, is accelerated through hyperreduction.

The first step can be challenging for design studies spanning large parameter intervals. For those studies, the calculated reduction basis either must be updated several times or must provide a subspace that captures the solution vectors for the whole parameter space. The latter option can be performed by sampling the parameter space, building local reduction bases at these sampling points and then applying a proper orthogonal decomposition on their concatenation.

This contribution shows how this procedure is used for parametric model reduction of geometrically nonlinear structures. It demonstrates its accuracy and computation time on a shape‐parameterized beam structure that undergoes large deflections. It turns out that the success of the proposed method is highly dependent on the implementation of the shape parameterization.
Wear mechanisms of hard phase containing materials
Authors: Röttger Arne
Published: November 2019

Wear affects the service life of tools and counteracts an economic operation of a tunneling project. Because of wear, tools must be replaced to ensure adequate penetration, which means downtime. Targeted planning of replacement intervals requires knowledge of precise wear prediction models. In these predictive models the abrasiveness of the soil has to be regarded, which can be evaluated by experimental experiments such as the LCPC test for soil and the CAI test for solid rock. However, the forecast models developed provide only a rough guide value and often do not correlate with the real wear conditions of the tools during a tunneling project. The main reason here is to mention the disadvantage that in the previous work not the overall tribological system has been considered sufficiently. Thus, the wear occurring on the tool is not only dependent on the abrasiveness of the soil to be penetrated, but is also determined by the material properties of the tool, the loads acting on it and the presence of any intermediate and surrounding media. From this simple consideration, it can be seen that wear is not a sole property of the soil or of the tool material, but a system property. The motivation of this short report is to show the basics of tool wear of tools used for tunneling applications as well as to show basic boundary conditions for future experimental work and simulations in the field of tool wear. First, the tribological system and the four main wear mechanisms will be presented. In a further step, the damage mechanisms are focused on the dominant wear mechanisms abrasion and surface disruption of tunneling tools. Thereby, interaction of abrasive particles or crack propagation in hard phase materials at the microstructure level will be discussed.
Phase field modelling of stress assisted corrosion of biodegradable magnesium alloys
Authors: Ma Songyun , Zhang Dawei , Markert Bernd
Published: November 2019

Biodegradable magnesium alloys are regarded as promising biomaterials for orthopaedic fixation devices due to obvious advantages over conventional permanent implants. Experimental studies have shown that the stress state has a significant impact on the corrosion rate of biodegradable magnesium alloys. In the present work, the phase field modelling approach is used to simulate the stress assisted corrosion of biodegradable magnesium alloys with porous microstructures. The simulation results demonstrates effects of the porous microstructure on the degradation behaviour of biodegradable magnesium implants.
DIC‐measurement during tensile testing and its approach for the FEM‐simulation of "Die‐Less‐Hydroforming"
Authors: Metzger Andreas , Ruff Daniel C. , Ummenhofer Thomas
Published: November 2019

Digital Image Correlation (DIC)‐measurement is an optical measurement method which enables contactless and area‐wide continuous acquisition of 3D‐geometry, deformation and surface strain during experimental investigations. Within Die‐Less‐Hydroforming, an increasing innovative forming technology, see [1] and [2], the DIC‐measurement may be used for two tasks at once: The forming process of Die‐Less‐Hydroforming can be investigated continuously within the scope of the classical application of DIC in terms of geometry and deformation acquisition. However, this paper focuses on the use of DIC during the uniaxial tensile test of sheet metal used for manufacturing the double‐layered Die‐Less‐Hydroforming‐blank. Using DIC during the tensile test facilitates to measure the current cross‐section area continuously which allows the determination of a true stress‐true plastic strain‐curve. This curve is required as input for FEM‐forming‐simulation to achieve significant results. But with conventional testing methods, for the case of flat tensile test specimens, it cannot be determined beyond uniform strain Ag. Therefore, the “true” values beyond Ag are often estimated by mathematical approximations.
Investigation of a centrifugal exciter with two coaxial unbalances on a carrier performing planar motion
Authors: Yüzbasioglu Tunc , Drozdetskaya Olga , Fidlin Alexander
Published: November 2019

Passing through and capturing into the resonance of a centrifugal exciter is investigated. The current work is the continuation of [1], which considered a minimal model of a centrifugal exciter consisting of a carrier with one degree of freedom. The analysis is conducted using an averaging method for partially strongly damped systems. Additional stationary and periodic solutions in vicinity of the resonances of the carrier system have been found, which don't exist in the simpler system investigated previously.
A Model Problem for Optimal Control of a Parabolic PDE Fully Coupled to ODEs
Authors: Kimmerle Sven-Joachim
Published: November 2019

In many applications we encounter fully coupled systems involving a partial differential equation (PDE) and an ordinary differential equation (ODE). A particular class is the case in which the PDE is parabolic. This coupled optimal control problem is considered in theory in [1]. Here we consider a toy example with the heat equation and a second order ODE given by Newton dynamics. The acceleration in the ODE may be controlled and is subject to box constraints. We present numerical optimal control results for this toy example.
Kino‐Geometric Modeling: Insights into Protein Molecular Mechanisms
Authors: Budday Dominik , Leyendecker Sigrid , van den Bedem Henry
Published: November 2019

Proteins are dynamic macromolecules that perform an immense variety of biological functions on a broad range of spatio‐temporal scales. Their conformational ensemble is a fundamental determinant of functionality in health and disease. While computational advances have increasingly enabled the computation of atomically detailed trajectories from Molecular Dynamics (MD) simulations, there remain considerable drawbacks when aiming for fast, yet elaborate insights into the molecular mechanisms of function. Here, we explore the potential of kinematics and geometry based methods, inspired from traditional robotics, to study protein conformational dynamics. Using geometric tools, we demonstrate insights into molecular mobility from instantaneous rigidity and flexibility analysis on selected example systems. Resulting motions from kinematically sampling along collective degrees of freedom show qualitative and quantitative agreement with motions from MD simulations. Coupled to sophisticated motion planning strategies, our approach is capable of providing structural ensemble representations from sparse experimental data such as double electron‐electron resonance (DEER) that remain difficult to interpret otherwise. Overall, we establish our Kino‐Geometric Sampling tool KGS as an efficient alternative to obtain high‐level insights into molecular mechanisms across scales, with ample applications in protein design and human health.
Heat Transfer Modeling of Confined Bubble Evaporation in a Microchannel
Authors: Sadir Sahba , Talebi Mohammadmahdi , Woias Peter , Dittmeyer Roland , Frohnapfel Bettina , Stroh Alexander
Published: November 2019

In this study, we model the heat transfer mechanism for a single nucleate vapor bubble which then expands to an elongated bubble during evaporation in a microchannel. The model is a logical mix of empirical correlations and analytical models and is defined for the two steps of bubble growth including: (a) partially confined growth, in which the bubble expands from nucleation site until it fills the entire cross‐section of the channel, and (b) fully confined growth, in which the bubble reaches the side walls and begins to elongate axially in downstream direction. To estimate the heat transfer characteristics of vapor bubble growth during evaporation in the microchannel, the time variation of liquid film thickness and bubble nose position are evaluated. Finally, a time‐averaged value of local heat transfer coefficient is obtained for a period of time using available heat transfer correlations for each heat transfer process separately.