bluuebunny/crossref_metadata_2025 huggingface dataset:
A thermomechanical‐phase‐field approach for modeling of residual stresses in fusion welding
Authors: Ali Baharin Rahim Ali , Heider Yousef , Markert Bernd
Published: January 2021

The welding process of metallic components, such as using gas tungsten arc welding (GTAW), is often accompanied by detrimental deformations and residual stresses, which affect the strength and functionality of these welded components. In this work, a phase‐field model, usually used to track the state of the phase‐change materials, is embedded in a thermo‐elasto‐plastic finite element model in order to simulate the welding process and the residual stresses. The phase‐field method (PFM) enables us to track the melting front of the metal, due to the welding heat source, and to split the analysis domain into soft and solid regions. In this way, temperature and phase‐field‐dependent material properties can properly be assigned to different regions in the domain. The phase‐field evolution is governed by Allen‐Cahn equation and relies on specification of the free energy density function as the main driving force for the phase change. Having a coupled thermomechanical process during the welding heating‐cooling cycle, the onset of residual stresses is associated with plastic deformations and can be observed after cooling to the ambient temperature. The plasticity model considers J2 plasticity with isotropic hardening. The coupled nonlinear system of equations is solved in the open‐source FE package, FEniCS, with time discretization based on the finite difference method.
A transfer operator based computational study of mixing processes in open flow systems
Authors: Klünker Anna , Padberg-Gehle Kathrin
Published: January 2021

We study mixing by chaotic advection in open flow systems, where the corresponding small‐scale structures are created by means of the stretching and folding property of chaotic flows. The systems we consider contain an inlet and an outlet flow region as well as a mixing region and are characterized by constant in‐ and outflow of fluid particles. The evolution of a mass distribution in the open system is described via a transfer operator. The spatially discretized approximation of the transfer operator defines the transition matrix of an absorbing Markov chain restricted to finite transient states. We study the underlying mixing processes via this substochastic transition matrix. We conduct parameter studies for example systems with two differently colored fluids. We quantify the mixing of the resulting patterns by several mixing measures. In case of chaotic advection the transport processes in the open system are organized by the chaotic saddle and its stable and unstable manifolds. We extract these structures directly from leading eigenvectors of the transition matrix.
A lattice Boltzmann study on the effect of fluid viscosity contrast on the retention behavior of two‐fluid flow in porous media
Authors: Chaaban Mohamad , Heider Yousef , Markert Bernd
Published: January 2021

In this contribution, the Shan‐Chen (SC) two‐phase flow model of the lattice Boltzmann method (LBM) is numerically implemented to simulate multiphase fluid flow on microtomography (µ‐CT) data of a sphere packing. From the model, the saturation degrees of the fluid phases, i.e. invading and displaced fluids, are extracted from the computed lattice density distribution functions. Several simulations are run with different degrees of kinetic viscosity contrast between the fluid phases within increasing increments of capillary pressure. At each increment, the relative permeability regarding each fluid phase is computed as a function of the saturation degree. The motivation of this study is to (1) investigate the effect of the kinetic viscosity contrast between the fluid phases on the retention behavior, (2) analyze the range of validity of the van Genuchten relation according to the computed retention data and (3) propose an extension towards an upscaling micro‐to‐macroscopic hierarchic scheme for the simulation of multiphasic fluid flow in unsaturated porous media.
On the non‐uniqueness of marginally separated boundary layer flows
Authors: Stojanovic Ivo , Braun Stefan
Published: January 2021

A stationary or time dependent, laminar flow with a locally separated boundary layer is considered. The Navier‐Stokes equations are analysed with the method of matched asymptotic expansions. The resulting integro‐differential equation, known as the fundamental equation of marginal separation, is solved numerically by means of a spectral method based on Chebyshev polynomials. The critical value of the parameter controlling the magnitude of the adverse pressure gradient is associated with a bifurcation of the stability characteristics of the locally separated shear layer. The solution behaviour of the integro‐differential equation in the corresponding parameter space is investigated. Special emphasis is placed on the observed non‐uniqueness of solutions and the associated branch points.
Orthogonal projections for image quality analyses applied to MRI
Authors: Breger Anna , Ramos Llorden Gabriel , Vegas Sanchez-Ferrero Gonzalo , Hoge W. Scott , Ehler Martin , Westin Carl-Fredrik
Published: January 2021

Measuring digital image quality is of importance in numerous applied research fields, such as image acquisition, image processing or image reconstruction. Subjective evaluation, i.e. assessment by human beings, is often too time‐consuming, expensive and inconsistent in complicated tasks such as medical imaging. In order to better understand the relation between objective image quality assessment measures, we compare a selection in an experimental setup. It is well known that L2 error estimation, i.e. computing the mean squared error (MSE) between two images, does not correspond well to the perceptual evaluation by the human visual system. Here, we illustrate on the example of MRI data the interaction of the MSE with the signal to noise ratio (SNR), the variance and subjective evaluation. We use random coverings of the space of orthogonal projections for coil combination to enable a comprehensive correlation analysis.
Efficient Solution of Distributed MIP in Control of Networked Systems
Authors: Liu Zonglin , Stursberg Olaf
Published: January 2021

Certain classes of optimization‐based control problems stated for networked systems involving hybrid dynamics and logical constraints can be cast into Mixed‐Integer Programming (MIP) problems. Since these belong to the complexity class NP‐hard, the motivation arises to find approximations of the optimal solution by distributed solution efficiently. For the cases that the cost functional is linear or quadratic and the constraints are linear, this paper proposes an alternative to the standard centralized schemes, by employing dual decomposition into a set of local problems of moderate size which can be solved in parallel. Numerical examples demonstrate that the scheme can efficiently approximate the global solution.
Formal Calculation of Positive Invariant Sets for the Lorenz Family Combining Lyapunov Approaches and Quantifier Elimination
Authors: Röbenack Klaus
Published: January 2021

The Lorenz family is a class of dynamic systems which is parameterized in one variable and includes both the classic Lorenz system and the Chen system. Both systems (and therefore the Lorenz family) can show chaotic behaviour. For different questions of system analysis, e.g. for the estimation of various types of dimensions, it is helpful to be able to determine bounds on the attractor. One typical approach ist the usage of Lyapunov functions to describe positive invariant sets. However, this approach usually requires a good knowledge of the system to perform the necessary calculations. For polynomial systems, these calculations can be carried out using a computation technique known as quantifier elimination. In this contribution we describe this approach and employ it to calculate bounds on the Lorenz family.
An Overset Grid (Chimera) Method for a Discontinuous Galerkin Discretization of the Navier‐Stokes Equations
Authors: Genuit Fabian , Keßler Manuel , Krämer Ewald
Published: January 2021

The discontinuous Galerkin (DG) method, a high‐order method in space, is applied to discretize the compressible Navier‐Stokes (NS) equations. The temporal discretization is realized using an implicit backward differentiation formula. Furthermore, an overset grid method is employed to enable rigid relative movements of flow bodies in the numerical setup. The Magnus effect serves as a test case and reveals promising results compared to reference values in literature.
Damage and fracture of the optimized X0‐specimen
Authors: Gerke Steffen , Liedmann Jan , Brünig Michael , Barthold Franz-Joseph
Published: January 2021

The paper deals with numerical and experimental results of the gradient based optimized biaxial X0‐specimen. The original, engineering based design has been optimized under producibility restrictions for two different loading conditions to gain a distinct (high or low) stress triaxiality maintaining a sufficiently homogeneous distribution in the notched regions of the specimen. Specimens with the initial and the two load case dependent optimized geometries have been fabricated of aluminum alloy sheets and biaxially tested. Here the corresponding results with respect to biaxial tension loading are presented and the numerical results clearly indicate the higher stress triaxialities and the experimental results demonstrate elevated void growth as leading damage mechanism.
Consideration of accelerations within the Theory of Porous Media
Authors: Bergmann Julia Nicolina , Bluhm Joachim , Schröder Jörg
Published: January 2021

This report deals with Theory of Porous Media (TPM) calculations, which take the accelerations into account. Two concepts for a simplified binary model considering accelerations as well as the question when to include accelerations are discussed with the help of two numerical one dimensional examples. After a brief description of the basic equations, an infinite half space, presenting porous soil filled with water, with two distinct spatially constant load cases is simulated, showing the advantages and disadvantages of the approaches.
A polyhedral element formulation based on the scaled boundary method for the analysis of nonlinear problems in solid mechanics
Authors: Reichel Rainer , Klarmann Simon , Klinkel Sven
Published: January 2021

In this contribution a numerical element formulation for the nonlinear analysis of solids is proposed. The element is defined by a polyhedron with an arbitrary number of polygonal faces. It is based on the scaling concept, which is adopted from the so‐called scaled boundary finite element method (SBFEM). The SBFEM is a semi‐analytical formulation to analyze problems in linear elasticity. Within this method the fundamental concept is to scale the domain's boundary with respect to a scaling center in order to describe the interior domain. The present element formulation employs the scaling concept twice and in contrast to SBFEM, uses a numerical approximation for the displacement response in both scaling directions. This makes it suitable for the analysis of geometrically and physically nonlinear problems. The advantages of the proposed element formulation is its high flexibility in mesh generation. It avoids the hanging node problems as arbitrary element geometries are possible. For example, using Octree algorithms, a fast and reliable mesh generation can be achieved. In case of curved boundaries the element formulation allows a precise representation of the geometry even with coarse meshes. Some numerical examples are presented to evaluate the accuracy of the proposed numerical method against analytical solutions, and a comparison to standard element formulations is given as well.
An uncertainty model for the curing process of transversely fiber reinforced plastics
Authors: Penner Eduard , Caylak Ismail , Mahnken Rolf
Published: January 2021

Lightweight structures, such as fiber reinforced plastics (FRPs), become increasingly important due to their excellent mechanical and lightweight properties. During the manufacturing process, curing of the matrix is a dominant effect as it is highly temperature dependent and influences strongly the mechanical, thermal and chemical properties of FRPs. Variations in the manufacturing process, measurement errors and missing or incomplete information are typical causes of uncertainties. This contribution presents a framework for an uncertainty model for the curing process of transversely fiber reinforced plastics. As a key idea the overall effective properties of the cured matrix during the manufacturing process are calculated by uncertainty homogenization models.
Numerical simulation of cyclic deformation behavior of SLM‐manufactured aluminum alloys
Authors: Wiegold Tillmann , Klinge Sandra
Published: January 2021

The selective laser melting process has already been developed for many metallic materials, including steel, aluminum, and titanium. The quasi‐static properties of these materials have been found to be comparable or even better than their conventionally manufactured counterparts. However, for their reliable application in operational components, their fatigue behavior plays a critical role. This phenomenon is dominated by several process‐related features, such as surface roughness, remnant porosity, microstructure and residual stresses. The present contribution shows a model which relies on an assumption for the Helmholtz free energy and the dissipation potential. To be more precise: the phase‐field method is applied to simulate the damage evolution, whereas plastic effects are modeled in terms of the isotropic hardening. It is assumed that the damage evolution only occurs in the tension mode of a cyclic load, which is achieved by the decomposition of the stored energy. The numerical results give insight into the evolution of plastic deformations and of damage at a material point and for a chosen mesoscopic sample.
The influence of magnetic field on nanoparticle transport in a micro channel
Authors: Bavandi Mahrokh , Wünsch Olaf
Published: January 2021

The present study focuses on a new solver considering the effect of magnetic field on nanoparticles concentration in a micro size channel. To describe the multi component behavior of blood, the Euler‐Euler method is used. Particles are modeled by a concentration equation considering a magnetic drift. The influence of a realistic magnetic field on nanoparticles is investigated. A result for a test case is presented. It shows that the magnetic body force resulting from nanoparticles also influence the hematocrit distribution in the channel.
Mixed/Hybrid finite elements for finite deformations of quasi‐incompressible materials with non‐constant bulk moduli
Authors: Schneider Patrick , Schönherr Josef Arthur , Mittelstedt Christian
Published: January 2021

Technical elastomers are usually quasi‐incompressible. For simulations they are, therefore, often modeled as ideal incompressible or a linear relation between the hydrostatic pressure and the (volumetric) dilation is assumed, i.e., a constant bulk modulus. However, for strongly compressed structural components, like sealings or damper elements, a nonlinear material model for the compression behavior is required in order to achieve accurate results.

In general, the numerical ill‐posedness of irreducible (purely displacement‐based) finite element (FE) formulations for quasi‐incompressible materials demands for a hybrid/mixed finite element implementation. State of the art hybrid/mixed elements still suffer from numerical stability issues that can be greatly amplified by the usage of nonlinear compression models. In the talk, a versatile mixed/hybrid finite element family for finite deformations is introduced that can readily be used in combination with any invariant‐based hyperelastic material model. The numerical stability is assessed by a benchmark test and compared to other established hybrid elements. The presented finite element family is way robuster than comparable hybrid elements implemented in the commercial FE‐code Abaqus Standard, Simulia (Dassault Systèmes).
Prediction of changes in local quantities of interest due to structural modifications
Authors: Materna Daniel
Published: January 2021

In this contribution a method for the prediction of the change in a quantity of interest due to structural modifications is considered. The approach is based on a goal‐oriented method by using the primal and dual problems. The method can be used in order to reduce the overall computational cost in the numerical simulation. Furthermore, the proposed method is easily to implement in existing finite element programs, because no derivatives with respect to the design variables are necessary.
Modeling of Single‐Slip Finite Strain Crystal Plasticity via the Virtual Element Method
Authors: Böhm Christoph , Hudobivnik Blaž , Aldakheel Fadi , Wriggers Peter
Published: January 2021

This work addresses an efficient low order virtual element method (VEM) for the modeling of single‐slip crystal plasticity system undergoing finite deformations. VEM has been attracting attention as a novel scheme within the field of computational mechanics. A key advantage of VEM is the ability of constructing an arbitrary element shapes that can be non‐convex [1]. Another important aspect is that VEM fits the grain shapes of crystal plasticity within polycrystalline aggregates perfectly. Contrary, classical finite element (FE) approaches request a fine mesh‐size at possibly sharp geometric regions, i.e. complex shaped grain boundaries.
A thermomechanical simulation method for fused deposition modeling
Authors: Oelsch Erik , Landgraf Ralf , Ihlemann Jörn
Published: January 2021

3D printing is a complex manufacturing method with completely new challenges. One of them is the simulation of the whole process. In this contribution the building process of the 3D printed part is thermomechanically coupled simulated with step by step element activation along a path from a slicer program. Thereby a hyperelastic material model and material parameters from literature are used. Simulation results of an exemplifying building process are in good agreement with corresponding experiments.
Phase‐Field Simulation of Crack Propagation at Adhesive Interfaces in Brittle Materials
Authors: Dammaß Franz , Hansen-Dörr Arne Claus , Kästner Markus
Published: January 2021

When it comes to failure of a heterogeneous material, the adhesive interfaces linking the different constituents can crucially influence its mechanical behavior. In this contribution, a diffuse description of interfaces in the context of the phase‐field approach to brittle fracture is outlined. Two‐ and three‐dimensional simulations of crack phenomena are presented and serve for validation of the model against LEFM.
Preconditioning of a FETI‐solver for a nonlinear asynchronous time‐integrator applied to structural dynamics
Authors: Seibold Andreas S. , Rixen Daniel J.
Published: January 2021

In this work we construct a Dirichlet‐type preconditioner for a FETI‐solver in a nonlinear version of the BGC‐macro asynchronous time‐integrator. This preconditioner is then tested on a simple beam‐model with six substructures and an impact load.
A computational framework for gradient‐enhanced damage – implementation and applications
Authors: Schulte Robin , Ostwald Richard , Menzel Andreas
Published: January 2021

A gradient‐enhanced damage model is combined with finite viscoelasticity and implemented in an Abaqus user subroutine, exploiting the heat equation solution capabilities for the damage regularisation, in order to simulate soft polymers. This regularised damage approach provides the advantage of mesh independent results and avoids localisation effects. In this work, a self‐diagnostic poly(dimethylsiloxane) (PDMS) elastomer is chosen as an example. To this end, an efficient two‐step parameter identification framework is developed to calibrate the corresponding model parameters.
Practical Economic MPC
Authors: Zanon Mario , Faulwasser Timm , Gros Sébastien
Published: January 2021

As opposed to tracking Model Predictive Control (MPC), economic MPC directly optimizes a given performance objective rather than penalizing the distance from a reference. On the one hand this typically improves performance. On the other hand, however, this also poses challenges in terms of stability and computational burden. In order to make economic MPC implementable in practice, we recently proposed some techniques that address both issues. In this contribution, we give a brief overview on economic MPC and the related literature and discuss how to exploit existing results in order to apply economic MPC in practice. Finally, we present a new promising research direction towards data‐driven economic MPC: the use of reinforcement learning to obtain optimality for the real system, rather than for the (unavoidably inaccurate) model used by MPC.
Aerodynamic‐thermal/structural design optimization of missile fin configuration during supersonic flight condition
Authors: Rašuo Boško , Vidanović Nenad , Kastratović Gordana , Mirkov Nikola
Published: January 2021

The main goal of this paper is to expand previously conducted study and consequently to upgrade the proposed multi‐modular numerical environment developed for fluid‐structure interaction simulation (FSI) and multi‐disciplinary design optimisation (MDO) purposes, in a manner that thermally induced structural responses in a current study are taken into consideration. The present study concerns with a broader observation of critical multi‐point flight conditions and represents a more realistic scenario which presents one contribution more in a scope of fluid‐thermal‐structure interaction (FTSI) numerical modelling and optimisation. This means that thermo‐mechanical effects of the missile fin structure are observed and implemented into established numerical environment. Numerical modelling of FSI/FTSI and MDO within an industry‐accepted design tool was resulted in powerful monolithic environment which with adopted multi‐point regimes and multi‐criteria settings is used for aerodynamic‐thermal/structural optimisation. The multi‐disciplinary shape optimisation, with respect to predefined objectives and constrains, was carried out in order to achieve global improvement of missile initial aerodynamic and to prevent aerothermally‐induced critical responses of the fin configuration.
Actuation of an elastic membrane by the use of an electrorheological valve
Authors: Schomberg Thomas , Gerland Florian , Wünsch Olaf , Rütten Markus
Published: January 2021

The dynamic response of a fluidic actuator is investigated on the basis of numerical simulations. With this actuator a membrane is excited to oscillate by means of an electrorheological valve. For this purpose the solid and fluid domains are coupled. Furthermore, the constitutive equation of the fluid is coupled to the electric field. The dynamic response is discussed on the example of a variable stiffness of the membrane. Actuators of this type offer the potential to delay the transition of a boundary layer.
Modeling inelastic‐anisotropic damage behavior of concrete considering lateral deformation
Authors: Stein Timo , Gafoor Ajmal , Dinkler Dieter
Published: January 2021

Although isotropic damage models are considered for a first approximation to simulate the deformation behavior of concrete, micro‐cracking of concrete occurring due to the sequential and multi‐directional loads necessitates an anisotropic description of damage for a reliable representation of damage in concrete. The present paper discusses modeling aspects of mechanical degradation behavior of concrete based on continuum damage theory. The model characterizes the distinct behavior of concrete in tension and compression using using multi‐loading surfaces. The principal strains govern the growth of damages in principal directions. The damage effect tensors are based on the principal tensile or compressive damages. Crack‐opening/closure effects and permanent strains are described through inelastic crack strains under tension and compression. The effect of tensile/compressive damage evolution on the Poisson's ratio is incorporated to capture large strains in the lateral directions during tension‐compression loadings. The numerical results of several test cases exhibit good agreement with experimental results.
Contribution of Large and Very Large Scale Motions to the Turbulent Kinetic energy in Turbulent Pipe Flow
Authors: Hallol Zeinab , Merbold Sebastian , Egbers Christoph
Published: January 2021

In the present investigation in turbulent pipe flow we study the contribution of turbulent structures, such as Large scale motion (LSM) and very large scale motion (VLSM) to the turbulent kinetic energy. Hence, the streamwise velocity fluctuation is measured using a single hot wire anemometer in the Cottbus Large Pipe Facility test facility (CoLaPipe) at Brandenburg University of Technology Cottbus‐Senftenberg (BTU) for Reynolds numbers Reτ = 1.3 × 104 and 1.9 × 104, where Reτ is the Reynolds number based on the friction velocity (Uτ) and the pipe diameter (D). By the use of pre‐multiplied power spectra of the streamwise velocity, we aim to understand the influence of the LSM and VLSM onto the turbulent momentum budget at different wall normal locations.
A potential‐based formulation of the classical and relativistic Navier‐Stokes equations
Authors: Scholle Markus , Marner Florian , Gaskell Philip H.
Published: January 2021

Analogies drawn to Maxwell's equations in tandem with complementary viscous flow theory, involving the introduction of a tensor potential, has been used to achieve exact integration of the Navier‐Stokes equations. The same methodology facilitates the derivation of an elegant four‐dimensional Lorentz‐invariant first‐integral formulation of the energy‐momentum equations for viscous flow assuming a flat space‐time, consisting of a single tensor equation. It represents a generalisation of corresponding Galilei‐invariant theory associated with the classical incompressible Navier‐Stokes equations, with the key features that it: (i) takes the same form as its two‐ and three‐dimensional incompressible counterparts; (ii) applies to any physical model, in that it does not depend at outset on the constitutive fluid relationship forming the energy‐momentum tensor, other than that the latter is taken as being symmetric. The new general theory is applied to the problem of propagating acoustic waves, with and without viscous damping, and shown to recover the well‐known classical expressions for sound speed and damping rate consistent with those available in the open literature.
Simulation of guided waves in cylinders subject to arbitrary boundary conditions for applications in material characterization
Authors: Itner Dominik , Gravenkamp Hauke , Dreiling Dmitrij , Feldmann Nadine , Henning Bernd
Published: January 2021

Material characterization of viscous polymers is typically carried out as quasi‐static or in the low‐frequency range. However, some applications require excitation in the high‐frequency range, and subsequently adequate elastic properties capable of describing such specific behavior. The FEM may be used to solve the elastic wave equations, however three‐dimensional simulations in the ultrasound regime require considerable computational resources. The computational time can be reduced by combining the scaled boundary finite element method with the Fourier finite element method for cylindrical domains: then, only the radial direction is discretized. We present such an axisymmetric formulation, which is extended to allow the definition of circumferential as well as arbitrarily shaped dynamic boundary conditions. It is shown that the results are in good agreement with standard FEM procedures, while greatly reducing computational time.
Fourier Analysis of DG Schemes for Advection‐Diffusion
Authors: Ortleb Sigrun
Published: January 2021

This work compares the wave propagation properties of discontinuous Galerkin (DG) schemes for advection‐diffusion problems in particular with respect to the discretization of diffusion terms. Extending previous investigations, the advection discretization now additionally varies between the choices of central or upwind fluxes. The results show that a previously recognized better performance of central schemes for well‐resolved problems only hold for even polynomial degrees and that upwind‐type discretizations also perform better on Gauss‐Lobatto nodes.
A priori reduced order model of steady Navier‐Stokes equations for low Reynolds number
Authors: Hoareau Christophe , Shang Lan , Zilian Andreas
Published: January 2021

This work focuses on a priori reduced order model of the parameterised steady Navier‐Stokes equations for a Reynolds number lower than 100. The approach is based on the Proper Generalized Decomposition [1, 2] where the velocity and the pressure are expressed as series of separated function variables. Each term of the off‐line basis is computed progressively contrary to classical reduced order model techniques which necessitate snapshots of the problem before the reduction [3]. The curse of dimensionality could be overcome if the number of parameters increases. The approximation of the solution can be computed in real‐time once the terms of the reduced basis are known. Here, the Reynolds number µ and the position coordinate vector X are taken as parameters in the classical 2D lid‐driven cavity problem. The key points of the approach, which involve a succession of nonlinear problems expressed in a weak form, are briefly illustrated. Preliminary results, obtained with the use of the open source FEniCS software are presented. The velocity approximation is finally compared to a high fidelity solution. The results show that a small number of modes (fewer than 8) are necessary to obtain a velocity approximation with a global error lower than 1%.
Automatic model order reduction for vibro‐acoustic problems
Authors: Aumann Quirin , Müller Gerhard
Published: January 2021

Numerical models of vibro‐acoustic systems require a fine spatial discretization to be valid also for high frequent vibrations. This results in large models with high memory consumption and a large computational cost. Model order reduction (MOR) methods reduce the size of such problems, allowing an efficient design process. However, the assumptions made prior to the reduction process, e.g. desired size of the reduced model or distribution of expansion points, heavily influence the quality of the reduced models. In this contribution, we investigate interpolation based MOR methods to automatically generate reduced order models of vibro‐acoustic systems valid in a limited frequency range not starting at zero.
A comparative study of numerical approaches for the computation of effective properties of micro‐heterogeneous materials
Authors: Assaf Rama , Scheunemann Lisa , Birk Carolin , Schröder Jörg , Ooi Ean Tat
Published: January 2021

The paper presents a comparative study of the finite element method (FEM) and the scaled boundary finite element method (SBFEM) for the numerical evaluation of the volume‐averaged stress of composites. Two‐dimensional meso‐scale models of concrete represented by digital images and discretized using an automatic mesh generation algorithm are considered. The different computational approaches are discussed and compared with respect to accuracy and efficiency for both scenarios.
Parameter estimation for orthogonal polynomial moments
Authors: Lorenz Dirk , Schneppe Felix
Published: January 2021

Prony's method recovers a Dirac ensemble μ = Σi=1M aiδxi with given sparsity level by separating the reconstruction of the unknown coefficients and positions. While it recovers the positions by examing the so called Prony polynomial, its reconstruction is heavily based on solving linear systems, which can be constructed by given monomial moments.

The intention of this article is to propose a Prony‐like method to recover the Dirac ensemble with an upper bounded sparsity level from orthogonal polynomial moments.
Superstructures in turbulent boundary layers with pressure gradients
Authors: Bross M. , Eich F. , Schanz D. , Novara M. , Schröder A. , Kähler C. J.
Published: January 2021

Large‐scale coherent structures have been observed in various wall‐bounded turbulent flows. In turbulent boundary layers, streamwise elongated regions of high‐ and low‐momentum in the log‐law layer that can extent up to several boundary layer thicknesses are often referred to as superstructures. These structures contain a relatively large portion of the layer's turbulent kinetic energy and have been shown to interact with the near‐wall features. In the last few decades extensive research on zero‐pressure gradient turbulent boundary layers has been done, however by comparison, the structural characteristics for adverse pressure gradient turbulent boundary layer flows are much less studied. Therefore, the three‐dimensional dynamics of turbulent superstructures in a turbulent boundary layer flow is investigated in the Atmospheric Wind Tunnel Munich (AWM) measurement using a novel multi‐camera 3D time‐resolved Lagrangian particle tracking approach. In this study, the structural properties and dynamics of turbulent superstructures within a zero pressure gradient (ZPG) turbulent boundary layer at Reτ = 5000 or Reθ = 14000 that then flows over a curved plate subjected to a favorable (FGP) and strong adverse (APG) pressure gradient, which eventually separates, is considered. It was found that while the average superstructure topology is modulated by decelerating flow in the APG when compared to the ZPG region the basic shape and pattern is preserved.
A discrete element model for reinforced concrete
Authors: Kaschube Jan , Dinkler Dieter
Published: January 2021

Reinforced concrete structures are built all over the world. The development of cracks is an unavoidable appearance, based on the interaction of the concrete and the reinforcement. The crack pattern can have an significant influence at the ageing of the structure. The presented modelling concept describes the reinforced concrete on the mesoscale. For the description of the concrete the Discrete Element Method (DEM) is used. The plain concrete is discretised by spherical particles. Spherical particles, surrounded by an rigid hull, are also used to describe the reinforcement. For an interaction between concrete and reinforcement massless virtual particles are added inside the reinforcement. With this concept a resilient bond behaviour without sliding can be described.
Damage simulation of thermo‐chemo‐elasto‐plastic fibre reinforced composites using mean‐field homogenization methods
Authors: Lenz Peter , Mahnken Rolf
Published: January 2021

This work presents a three‐scale mean‐field homogenization framework for constitutive multiscale (micro‐meso‐macro) modelling of fibre reinforced composites (FRC) considering a curing process and damage. An FRC is decomposed into unidirectional fibres surrounded by an interface, which in turn is surrounded by a matrix material. Based on the Mori‐Tanaka mean‐field homogenization method effective properties are determined. In each material phase damage is considered, namely matrix damage, fibre damage and interface damage. Based on a curing process effective elastic, thermal, chemical and plastic properties of the matrix and the interface are determined in terms of a degree of cure.
Two applications of the asymptotic homogenization method
Authors: Sheshenin Sergey , Artamonova Nina , Klementyev Petr
Published: January 2021

The first part of the paper presents the application of the asymptotic averaging method for determining the effective moduli and stress concentrations in the B4C/2024Al composite using 2D and 3D x‐ray images of the internal structure. The second study concerns an application of asymptotic homogenization to metamaterials. Metamaterials may have unusual bahaviour such as tension–bending coupling or tension–torsion coupling. Most metamaterials have a periodic structure in Cartesian coordinates. Here it is important to formulate the question regarding the number of periodicity cells, which determines whether the metamaterial is really a material or it is just a structure. If some property remains to be true for infinite number of cells, then such a metamaterial is treated as real material. On contrary, the metamaterial must be treated just as a structure, if the same property is valid only for finite number of cells and vanishes when the number of cells increases.
A simple success check for delay differential‐algebraic equations
Authors: Ahrens Ines , Unger Benjamin
Published: January 2021

Solutions of delay differential‐algebraic equations (DDAEs) may depend on derivatives and future evaluations of some of its equations. Structural analysis can be used to determine how often each equation needs to be differentiated and shifted. Unfortunately, these numbers are not always correct, such that a post‐processing step is required to validate the result. In this contribution, we present the first step towards a success check for DDAEs.
3D thermo‐mechanical dynamic crack propagation with the XFEM and gradient enhanced damage
Authors: Sun Jian , Löhnert Stefan
Published: January 2021

This work presents the application of the extended finite element method (XFEM) to dynamic crack propagation with thermo‐mechanical coupling. A gradient‐enhanced damage model is coupled that allows for a damage‐based propagation criterion. The transient thermal and dynamic mechanical fields, along with a gradient enhanced damage, are solved simultaneously for each time step by utilizing the Newmark‐beta method. The level set method enables the crack front to be implicitly tracked during crack propagation. The global crack tracking method is used to solve the extension of the propagation velocity more efficiently. The accuracy and robustness of the employed approach is assessed by means of some linear elastic fracture mechanics examples.
Benchmarking pre‐trained Encoders for real‐time Semantic Road Scene Segmentation
Authors: Evers Lennart
Published: January 2021

Semantic segmentation, i.e. assigning each pixel in an image a class to which it belongs, can be a part of the implementation for the perception model of autonomous vehicles. Over the last years multiple powerful neural network architectures for solving this task have been developed. In this work, a simple lightweight but modular, fully convolutional encoder‐decoder network has been implemented and multiple, publicly available pre‐trained classification networks are evaluated on their encoder performance on the Cityscapes [8] benchmark dataset with respect to their accuracy and their inference speed.
Finite element simulation of multi‐component vesicle morphologies undergoing phase separation
Authors: Savitha Eshwar J. , Mandadapu Kranthi K. , Sauer Roger A.
Published: January 2021

Morphological changes in lipid bilayer vesicles are due to phase transitions and surface deformations occurring in unison. We present a dynamic chemo‐mechanical finite element model to study such changes. This is achieved by coupling two fourth order partial differential equations (PDEs): The Cahn‐Hilliard [2] mass balance equation based on irreversible thermodynamics, and the Kirchhoff‐Love [1] rotation free thin shell equation. The Helmholtz free energy consists of Helfrich energy to model elastic bending, and also includes in‐plane elastic energy with a finite shear modulus for the purpose of regularization. The geometry is discretized by C1‐continuous NURBS shape functions. An implicit second order accurate generalized‐α scheme is used for time integration. Newton‐Raphson iterations are utilized to solve the resulting linearized weak form monolithically. The proposed formulation is illustrated by a numerical example.
Particle Interactions in Magneto‐Active Elastomers: Experiments and Simulations
Authors: Metsch Philipp , Schmidt Henrik , Kalina Karl A. , Brummund Jörg , Auernhammer Günter K. , Kästner Markus
Published: January 2021

In this contribution, particle‐matrix interactions in magneto‐active elastomers are analyzed with regard to the resulting mechanical deformations. By comparing experimental observations with the results of finite element simulations, a fully coupled continuum model for magneto‐active elastomers is validated with the help of real data. The model under consideration permits the investigation of magneto‐active elastomers with arbitrary particle distances, shapes and volume fractions as well as magnetic and mechanical properties of the individual constituents. Our results show a very good agreement of experiments and numerical simulations ‐ the deformation behavior of the system under consideration is captured by the model qualitatively as well as quantitatively.
Development of a macroscale constitutive model for porous magneto‐ active polymers using a computational homogenization approach
Authors: Gebhart Philipp , Wallmersperger Thomas
Published: January 2021

Over the last years there has been a growing interest in the study of the behavior of field‐responsive or so called smart materials. Porous magnetoactive polymers (MAPs) are a special class of these materials, where micron‐sized ferromagnetic particles are embedded into a porous crosslinked polymer matrix. Due to the mutual interaction of the particles upon magnetic stimulation, MAPs are able to deform and alter their effective material characteristics reversibly if subjected to a magnetic field. This strong magneto‐mechanical coupling makes them attractive for engineering applications e.g. in the field of sensors and actuators. The magneto‐mechanical behavior of porous MAPs is a complex phenomenon that spans over multiple length‐scales and essentially depends on (i) the constitutive behavior of the individual components, (ii) their morphology and microstructural arrangement and (iii) the macroscopic shape of the specimen. The strong shape effects pose a crucial challenge in the precise parameter identification of macroscopic models for MAPs based on experiments, see Keip & Rambausek [6] and Gebhart et al. [2, 3]. In order to circumvent these inherent problem, we propose a microscopic continuum‐based framework embedded into a suitable computational homogenization scheme to bridge between the micro‐ and macroscale, see Chatzigeorgiou et al. [1]. This modeling approach allows us to use much simpler constitutive models on the microscopic scale for which detailed and precise material parameters are available, see Kalina et al. [4, 5]. The proposed framework is then used to predict the effective macroscopic behavior of porous MAPs with random monodisperse microstructures. Based on the generated data set a thermodynamically consistent macroscale model for isotropic porous MAPs in an energy‐based constitutive setting is developed.
Data‐based models of drive technology for automation in automotive production
Authors: Dierkes Eva , Jung Francesca , Büskens Christof
Published: January 2021

The digital revolution, especially in the field of manufacturing, has great potential to change the economy sustainably. In this work, the development of methods for predictive maintenance and condition monitoring is a central focus. Data‐based models for drive technology in automotive production are investigated in order to generate adequate models, to make statements about the life cycle of the drives, or to suggest system modifications, such as the adjustment of weights. One task in this field is to detect anomalies or disturbances in given engine data. Since this collected data is variable and noisy, the detection of faults is non‐trivial. In this context two different methods for anomaly detection are studied. First, a model based on statistical analyses and second, a machine learning model is evaluated.
Real‐time parameter estimation for sensitivity‐based LQ regulator adaptation
Authors: Runge Margareta , Flaßkamp Kathrin , Büskens Christof
Published: January 2021

In this contribution we consider linear quadratic regulator problems subject to parameter perturbations within the system dynamics. Due to the perturbations, optimality of the regulator would be lost. Iteratively recomputing the optimal feedback matrix is likely to be too costly for real‐time applications, but approximated updates using parametric sensitivities can be efficiently derived. Online parameter identification is applied in order to obtain current parameter perturbations to which the controller shall be adapted. Numerical results for the benchmark example of the inverted pendulum on a cart are discussed.
Simulating 3D crack propagation with XFEM to investigate failure mechanism in high strength concrete
Authors: Patel Rohan , Scheiden Tim , Hüpgen Markus , Rozanski Corinna , Loehnert Stefan , Oneschkow Nadja
Published: January 2021

High strength concrete compared to normal strength concrete has a denser micro‐structure, i.e. tight packaging or bonding between glued aggregates and cement paste, which increases strength and durability. The disproportionate ratio in ingredients of concrete, water to cement ratio and binding agents to form cement paste are subjected to self‐desiccation during the hydration process which leads to shrinkage, that has potential to form micro‐cracks and delamination within the ITZ (Interfacial Transition Zone), which ultimately causes deterioration in health of the structure. In order to investigate this phenomenon, a computational model to simulate the formation and propagation of cracks within the micro‐structure is developed. The geometrical model for the computation and simulation of the micro‐structure is extracted by means of computer tomography (CT) scans of concrete samples. The eXtended Finite Element Method (XFEM) in combination with level set techniques is employed to simulate discrete cracks and their advancement within the micro‐structure. The criterion for the crack propagation is obtained from a gradient enhanced damage model and once it is fulfilled, the crack geometry is updated using an advance algorithm for level sets.
In Silico Modeling of Coupled Physical‐Biogeochemical (P‐BGC) Processes in Antarctic Sea Ice
Authors: Thom Andrea , Ricken Tim
Published: January 2021

Antarctic sea ice formation in the Marginal Ice Zone (MIZ) and its mutual effects on ocean biology and chemistry is very sensitive to climate change. The formation of ’pancake’ ice floes and the coupled physical‐biogeochemical (P‐BGC) processes can be modeled by using the continuum mechanical multi‐phase description of the extended Theory of Porous Media (eTPM), and simulated with the Finite Element Method (FEM). The ice formation is described via a salinity‐temperature equilibrium of the enclosed ocean water. The growth of the thriving ice algae, enclosed and attached to the pancake ice floes, is modeled with a phenomenological approach given with an ordinary differential equation.
Extension of the local strain approach to transient material behavior and residual stresses
Authors: Kühne David , Fiedler Melanie , Kästner Markus
Published: January 2021

In engineering practice generally empirical durability concepts, such as the Local Strain Approach (LSA) [1], are used for the fatigue life estimation of components. The LSA calculation is based on a given series of reversal points of the elastic stress history, e.g. computed in terms of a finite element model of the component. The fatigue life of components is subject to various factors. During the forming processes of steel‐alloy components, residual stresses are induced into components. In addition, steel‐alloys exhibit a cyclic transient material behavior, for example cyclic strain hardening with different characteristics under tensile and compressive loadings. While the state‐of‐the‐art LSA assumes stabilized cyclic material behaviour throughout the entire fatigue life of the component, this assumption is not adequate for residual stress‐afflicted components.