bluuebunny/crossref_metadata_2025 huggingface dataset:
On the Construction of Diagonal Mass Matrices for Serendipity Elements
Authors: Duczek Sascha , Gravenkamp Hauke
Published: December 2018

The diagonalization of the mass matrix is an important prerequisite for the implementation of explicit time integration schemes. However, in the context of higher order serendipity finite elements (p ≥ 2) established mass lumping approaches, such as the row‐sum method or the nodal quadrature technique cannot be applied. Due to the existence of negative/zero lumped masses explicit time integrators might diverge and therefore different methods are needed. In this communication, we investigate the performance of the newly introduced manifold based mass lumping technique in comparison to the standard formulation using a consistent mass matrix. By means of a modal analysis of a slender rod it is shown that only sub‐optimal rates of convergence are achieved if a lumped mass matrix is employed, whereas the conventional formulation yields optimal convergence. That is to say, when using diagonal mass matrices we observe a significant gain in computational efficiency by sacrificing the accuracy of the approach to a certain extent.
Parametric model order reduction for district heating networks
Authors: Rein Markus , Mohring Jan , Damm Tobias , Klar Axel
Published: December 2018

This contribution focuses on the model order reduction of index 1 hyperbolic differential algebraic equations which are quadratic in state, at the example of district heating networks. We demonstrate that an appropriate splitting of the state space variables in the two categories massflow and temperature leads to a linear parameter varying system, allowing the use of tools from linear model order reduction. We measure a significant decrease of computational effort to simulate the underlying network dynamics while preserving stability.
Similarity of Field Quantities in Scaled Radiation Transfer Lattice Boltzmann Simulations (RT‐LBM)
Authors: McHardy Christopher , Becker Deborah , Rauh Cornelia
Published: December 2018

The lattice Boltzmann framework provides a powerful tool to solve radiation transfer problems in participating media. Thereby, tuning of the collision rate to the numerical time step is necessary to ensure accurate solutions. One way of doing this is to scale the radiation characteristics of the medium by means of similarity relations. In the present contribution radiation characteristics of participating media are scaled to the numerical grid by means of the similarity relations to tune the accuracy of a recently proposed RT‐LBM. A free parameter was introduced and its effect on the solution is investigated. Also, the similarity of higher order angular moments is studied. The results show that conservation of the transport mean free path ensures the similarity of solutions.
Modeling and Simulation of Solid‐State Lasers: From Mathematics to Industrial Application
Authors: Pflaum Christoph
Published: December 2018

Solid‐state lasers are widely used for different industrial applications ranging from material processing to medical applications. For designing and optimization of a solid‐state laser an accurate simulation tool is need. Such a simulation tool has to be able to simulate different kind of physical effects like thermal effects, depolarization caused by stress inside a laser crystal, non‐linear gain, and mode competition. In order to calculate output power and beam quality, we apply an extension of the dynamic mode analysis concept (DMA) (see [1]). This model is based on a 3‐dimensional discretization of population inversion and a system of complex rate equations. The resulting mathematical equation system is a large system of ODE's, which has to be solved by a suitable method including time step control. The difficulty in such a simulation is the extreme change of parameters. As a consequence the output signal might be a pulsed signal with high output power of pulse width 1 ns and time period 1 ms. In order to solve such a system of ordinary differential equations accurately, we present a suitable numerical method. Simulation results with industrial applications are presented.
Sensitivity of a partially learned model‐based reconstruction algorithm
Authors: Boink Yoeri E. , van Gils Stephan A. , Manohar Srirang , Brune Christoph
Published: December 2018

We replace part of a model‐based iterative algorithm with a convolutional neural network in order to improve the quality of tomography reconstructions. We analyse its robustness against uncertainties in the image and uncertainties in system settings. Results are presented for the application of photoacoustic tomography in a limited angle setup.
Multiscale modelling of alkali transport and ASR in concrete structures
Authors: Iskhakov Tagir , Timothy Jithender J. , Meschke Günther
Published: December 2018

ASR is a microscopic process in concrete characterized by the formation of a hydrophilic alkali‐silica gel due to the reaction of the alkali in the pore‐fluid with silica in the aggregates. In the presence of moisture, the gel swells and induces an internal pressure that leads to microcracking, expansion and overall deterioration of the material. When subject to external alkali supply, the material is susceptible to higher levels of degradation. Transport of alkali ions at the structural scale in partially saturated concrete is modelled by coupling the diffusion equation with the Richards equation for moisture transport. The overall deterioration of concrete pavements due to ASR can be modelled by a synthesis of two sub‐models: 1) the alkali concentration is coupled to a meso‐scale reaction model describing the formation and evolution of the alkali‐silica gel; 2) the gel induced microcracking in the material is estimated using a semi‐analytical multiscale micromechanics model [1]. The model capabilities are evaluated using selected numerical examples and comparisons with experimental observations.
Efficient Computation of Reachable Sets for Critical Space Mission Phases
Authors: Chan Kai Wah , Seelbinder David , Theil Stephan , Knauer Matthias , Büskens Christof
Published: December 2018

To achieve true autonomy during critical mission phases in deep space, it is imperative to know which states are attainable from a given starting point using only admissible control inputs. These attainable states form the reachable set. If the latter is computed in real time, this can provide a system for Guidance, Navigation and Control on‐board of an autonomous spacecraft with knowledge of all the feasible and infeasible options in order to choose the correct course of action. Though several means exist to compute reachable sets, the most promising ones are based on optimization techniques. We currently explore an approach, in which we approximate a reachable set with an altering polytope. The center of a selected facet of the polytope is the starting point from which a new feasible vertex is placed in normal direction with the largest possible step size. This approximates the set boundary successively. Simultaneously, the underlying equations of motion must be satisfied. We formulate these tasks as an optimal control problem.
Overview of Craig‐Bampton Substructuring Approaches for Model Order Reduction of Nonclassically Damped Systems
Authors: Gruber Fabian M. , Rixen Daniel J.
Published: December 2018

The classical Craig‐Bampton method (1968) does not take any damping effects into account for the model order reduction of damped systems. One procedure to handle nonclassically damped systems is to transform the second‐order differential equations into state‐space representation. Solving the corresponding eigenvalue problem allows the damped equations to be decoupled, but complex eigenmodes and eigenvalues occur. A comparison between different formulations for nonclassically damped systems is given and demonstrated by an example.
A time‐space FCT‐FE formulation for 1D time dependent advection‐diffusion equation
Authors: Feng Dianlei , Neuweiler Insa , Nackenhorst Udo
Published: December 2018

We present a time‐space flux‐corrected transport (FCT) finite element formulation for solving the linear time‐dependent advection dominated advection‐diffusion equation. Solving advection dominated transport equations with conventional finite element (FE) methods suffers from drawbacks of excessive numerical dispersion which results in non‐physical, non‐monotonic solutions. The FCT algorithm is an effective method which suppresses the non‐monotonic behavior of the solution by applying a limited anti‐diffusion operator to a first order scheme. Applying the FCT algorithm to time‐space FE formulation, such as the time‐discontinuous Galerkin (TDG) method, benefits from the advantages of both the TDG scheme and the FCT algorithm. In another word, the time‐space FCT‐FE formulation achieves arbitrary odd order accuracy in time at the discontinuous time nodes. Large time steps can be applied and the scheme ensures monotonic solution when linear interpolation is used for spatial discretization.
Tikhonov regularization for ill‐posed backward nonlinear Maxwell's equations
Authors: Chen De‐Han , Yousept Irwin
Published: December 2018

Tikhonov regularization for ill‐posed backward nonlinear Maxwell's equations is considered. We present a convergence result with rate for the Tikhonov regularization under piecewise Hs‐type Sobolev regularity assumption on the exact initial data.
Numerical approaches for the simulation of a real multiphase flow in a fermentation tank
Authors: Klembt Daniel , Meironke Heiko
Published: December 2018

In the context of investigations of multiphase flows, the beer production is currently being investigated, especially fermentation, maturation and storage in cooperation with the local brewery. The university has its own 350 litre fermentation tank with comprehensive acoustic flow and temperature measurement technology for the systematical investigation of the influence of the fermentation activity, distribution of yeast and occurring convection phenomena. This paper deals with the numerical simulation of the fermentation tank and the combination of a numerical approach and an experimental investigation with the two Fluid Eulerian‐Eulerian time‐averaged model [3]. The Eulerian‐Eulerian model allows two sets of governing equations, continuity and momentum equations to be solved for either phase and their interactions are modelled using interface transfer terms for interfacial heat, mass and momentum exchanges. As a result, the numerical solution of a natural convection flow which is superimposed by rising gas bubbles will be presented.
Numerical investigations of polymer‐based fibre‐reinforced structures with fluidically actuated Compressible Constrained Layer Damping
Authors: Holeczek Klaudiusz , Koschichow Roman , Schlieter Tomasz , Ehrig Tom , Kostka Pawel
Published: December 2018

Lightweight‐focused design often leads to a problematic vibration susceptibility of designed components. To reduce potential environmental and health risks, excessive vibrations have to be mitigated preferably through lightweight‐compatible solutions. The presented studies aim at the establishment of almost weight‐neutral solutions for adaptive tuning of the dynamic behaviour of lightweight components. The proposed unique actuating principle is based on structural cavities generating evanescent deformations when supplied with fluidic medium. These cavities encapsulate compressible, viscoelastic elements which are combined with the surrounding layers and operate according to an extended principle of Constrained Layer Damping. The evanescent morphing is used to deliberately alter the geometrical and material properties of the viscoelastic elements through their compression in order to achieve a damping and stiffness capacity adaptation. The analysed Compressible Constrained Layer Damping (CCLD) object is configured as a three layered beam consisting of the load‐bearing structure as well as constraining layer and compressible viscoelastic layer. The main studies were conducted using a developed finite‐element model. Herein, the geometrical, material and load property range has been parametrised so that generalised conclusions about the CCLD dynamic behaviour could be drawn. The deformation kinematics of the CCLD under combined loads resulting from static tension and flexural vibrations has been analysed. Furthermore, the assessment of the dynamic behaviour adaptation potential for different compressible viscoelastic materials was carried out. The goal of this study was on the one hand to determine a feasible initial configuration of the CCLD for its successful application and on the other hand the assessment of its damping efficiency.
Simulation of thermoforming processes with directed air‐flow
Authors: Wagner Simon , Kayatz Fabian , Münsch Manuel , Majschak Jens‐Peter , Delgado Antonio
Published: December 2018

Thermoforming is a manufacturing process suitable for mass‐production of simply shaped plastic products. One of the main limitations of the common process is the resulting inhomogeneous wall thickness distribution. The authors show experimentally that it is possible to positively influence the wall thickness distribution by using directed air‐flow. In order to numerically reproduce the process, a simulation model is set up. The simulation results clearly show how the temperature distribution during deformation can be influenced.
Decoupling Structural Acoustic Systems: Investigation of Radiation Damping Mechanisms
Authors: Baydoun Suhaib Koji , Marburg Steffen
Published: December 2018

In the framework of the present project within the DFG priority program 1897 “Calm, Smooth and Smart,” dissipation of kinetic energy of vibrating structures into the acoustic far field is studied. It can be understood as radiation damping and is particularly relevant for weakly damped lightweight structures, music instruments and underwater applications. In this paper, the coupled equations of time‐harmonic elastodynamics and acoustics are addressed respectively by means of finite and boundary element methods and solved monolithically. The loss factor, which quantifies the extent of radiation damping, is determined subsequent to a harmonic analysis by relating radiated sound power to structure‐inherent power. First steps towards more efficient numerical formulations, which enable the consideration of radiation damping in structural simulations, are outlined. They comprise forming the Schur complement and a polynomial approximation of the resulting acoustic impedance matrices.
A direct method for dissipative dynamical systems by using the symplectic Brezis‐Ekeland‐Nayroles principle
Authors: Nguyen An Danh , Markert Bernd
Published: December 2018

We study a direct method for inelastic structures by using the symplectic Brezis‐Ekeland‐Nayroles variational principle, which provides a minimum regulation for whole trajectories. The null minimisation problem of the power balance is established and discretised by the use of the orthogonal collocation method. The proposed approach is illustrated with an example of a thick tube subjected to internal loadings. Numerical results are presented and compared with the analytical solutions.
A Multi‐fidelity Approach Using Physical and Mathematical Surrogates for Crash Optimization
Authors: Komeilizadeh Koushyar , Hefele Rafael , Duddeck Fabian
Published: December 2018

In the context of crash optimization, numerical simulations can be very time consuming, therefore efficient optimization algorithms are indispensable. If the original crash model is considered as the high‐fidelity (most accurate) one, low‐fidelity models trade accuracy for efficiency. A proper combination of high‐ and low‐fidelity models can lead to a more efficient optimization algorithm in total. We developed a new multi‐fidelity, or multi‐model optimization algorithm that is based on nonlinear crash simulations while being accelerated by gradients of the (initial) linear system used as low‐fidelity model.
Fast time‐explicit micro‐heterogeneous wave propagation
Authors: Maier Roland , Peterseim Daniel
Published: December 2018

Using explicit time stepping schemes in the context of wave propagation is very popular due to simplicity and fast computations. However, stability can only be guaranteed if a so‐called CFL condition holds that bounds the time step size with respect to the spatial mesh size. This is a severe restriction in case of micro‐heterogeneous media where spatial finescale features need to be resolved. We show how numerical homogenization in space both reduces the number of degrees of freedom in space and weakens the time step restriction.
A strong discontinuity approach to crystal plasticity theory
Authors: Fohrmeister Volker , Díaz Guillermo , Mosler Jörn
Published: December 2018

In this work, a novel, displacement‐driven approach to crystal plasticity based on embedded strong discontinuities (ESDA) is presented, cf. [1, 2]. In contrast to the classical strain‐driven approach, which connects the Schmid stress to the slip strain at a certain slip system, the novel approach applies a traction‐separation law to connect the Schmid stresses to the slip displacements. Surprisingly, both models show similar mathematical structures, which allows to develop a unifying algorithmic formulation. The elaborated algorithmic formulation is fully implicit and the inequalities characterizing rate‐independent crystal plasticity theory are solved efficiently by means of so‐called Fischer‐Burmeister NCP functions, cf. [3]. The resulting solution scheme is extremely robust – even for an arbitrary number of simultaneously active slip systems.
A CFD‐DEM approach to model the orientation and distribution of non‐spherical fibers in fresh concrete
Authors: Gerland Florian , Schomberg Thomas , Wünsch Olaf
Published: December 2018

Modern high performance concretes are reinforced by fibers to cast complex parts without reinforcing bars. The orientation and distribution of fibers influence the properties of the final solid and the flow properties of fresh concrete. Therefore it is important to predict the casting process adequately. A promising method for this is CFD‐DEM. The suspending phase is described as a continuum and can be solved using suitable methods such as Finite Volume Method (FVM). The suspended particles are modeled as rigid bodies and simulated using the Discrete Element Method (DEM).

This work is based on the CFDEM® engine which uses OpenFOAM® for the suspending phase and LIGGGHTS® for the particles. The modeling of fluid‐particle interaction forces and the momentum coupling between the phases is of outstanding relevance for the applicability of this method. Therefore the influence of particle to mesh size ratio on the accuracy of the coupling as well as the mapping of particle quantities to Eulerian fields is investigated.
Computational homogenization of nematic liquid crystal elastomers based on Landau‐de‐Gennes theory
Authors: Nadgir Omkar , Rambausek Matthias , Keip Marc‐André
Published: December 2018

Nematic liquid crystal elastomers represent a group of materials, which combine elastic properties of rubber with orientational properties of liquid crystals. The present contribution proposes a variational homogenization principle for nematic liquid crystal elastomers. A symmetric and traceless tensorial quantity represents the nematic order parameter, which is used as a phase field. The model is implemented in a finite element framework and the validation is done with two as well as three dimensional nemato‐mechanical boundary value problems.
Investigations on different Fischer‐Burmeister functions applied to the modelling of ferroelectrics
Authors: Schulte Robin , Bartel Thorsten , Menzel Andreas , Kiefer Björn , Svendsen Bob
Published: December 2018

Different selected approaches of Fischer‐Burmeister (FB) nonlinear complementarity problem (NCP) functions are investigated towards the local convergence properties and the possible parameter influences. The Fischer‐Burmeister functions are applied to a micromechanically motivated material model for ferroelectric materials. The particular model employed is a laminate‐based modelling approach to simulate the single‐ and polycrystalline tetragonal ferroelectric material behaviour. In this model, the occurring variant fractions are characterised via laminate fractions with additional inequality constraints. To solve the complementarity conditions of these internal variables, the FB approach provides a very efficient scheme compared to common solution schemes as, e.g. active‐set strategies.
Identification of Parameters on an Interpolated Function with Measurement Errors
Authors: Nostitz Niklas , Hendrik Kröger Nils , Ihlemann Jörn
Published: December 2018

While the identification of material parameters via FEM is an important basis for efficient simulations, the identification itself leads to new problems. In general, each optimization step and error function evaluation is gained with high computational effort. To speed up the identification, an alternative interpolation algorithm is introduced with a gradient free optimization. The combination of this algorithm with a Levenberg‐Marquardt algorithm improves the results with uncertain data.
Constrained Topology Optimization of Dynamic Mechanical Systems
Authors: Held Alexander , Kohlsche Thomas
Published: December 2018

We present a topology optimization procedure for flexible multibody systems, which is subjected to time‐ and space‐dependent constraints. The flexible bodies are parameterized using the solid isotropic material with penalization approach. For the efficient solution of the optimization problem, the pointwise time‐dependent constraints are discretized and aggregated into a single constraint using the Kreisselmeier‐Steinhauser function. The procedure is tested by optimizing the mass of a flexible piston rod, while the deformation within the design domain is constrained.
Thermomechanical mortar contact problems with hierarchical refined NURBS for adhesion and anisotropic friction
Authors: Krüger Melanie , Schulte Jonathan , Dittmann Maik , Hesch Christian
Published: December 2018

In this contribution, we present a novel thermodynamically consistent contact formulation [1]. The thermomechanical framework is written in terms of the first and second law of thermodynamics, providing suitable restrictions on the constitutive law. The contact formulation involves mechanical and thermal contributions across the interface. For the mechanical contribution we apply different contact reactions in normal and tangential direction and decompose the Piola‐traction vector t on the interface. The modeling of contact pressure and adhesion leads to an exponential constitutive model in terms of the normal gap function. Furthermore, the tangential traction is additively decomposed into isotropic and anisotropic parts. For the spatial discretization we employ hierarchical refined NURBS (B‐Splines) and apply a variationally consistent mortar method for the thermomechanical contact interface, see e.g. [2]. In particular, linear Lagrangian shape functions are used for the discrete traction field. The capabilities of this framework are shown within a representative example.
Parameter Identification for Micro Underwater Vehicles
Authors: Duecker Daniel Andre , Kreuzer Edwin , Maerker Gunnar , Solowjow Eugen
Published: December 2018

Detailed knowledge of model parameters is key for accurate forward simulations and control design. Identifying these parameters is especially challenging for underwater vehicles as they are subject to hydrodynamics effects which cannot be neglected in the equation of motion. In this work we present a method for hydrodynamic parameter identification of micro underwater vehicles which allow full‐size experiments due to their small size. The low‐cost experimental setup consists mainly on a free fall mass and an angular encoder. In an experimental series the hydrodynamic parameters of the micro underwater vehicle HippoCampus [1] are identified and compared with the analytically derived parameter set.
Time Optimal Path Tracking for Industrial Robots with Low Cost Computational Unit using Model Predictive Control
Authors: Jörgl Matthias , Gattringer Hubert , Müller Andreas
Published: December 2018

This paper deals with time optimal path tracking along prescribed geometric paths for robotic systems, like computerized numerical control (CNC) machines. These machines are typically controlled by a low cost microcontroller computational unit (MCU). Such MCUs are commonly used in industrial applications but are limited in view of computational performance. In many cases, these robotic systems have not only a MCU on which e.g. a motion controller is implemented, but also an associated desktop computer that serves as input device and transmits raw data to the MCU. Therefore, the calculation of the time‐optimal path following can be divided into two steps, where the paths are in our case defined as B‐Splines. On the desktop computer, an approximation of the solution is recursively calculated using a log‐barrier method, which solves a convex reformulated path tracking problem with velocity and torque constraints. This log‐barrier solution serves then as a reference generator for a model predictive controller (MPC), which is implemented as a trajectory tracking controller on the MCU. Due to the special formulation of the MPC, the continuity of the solution can be chosen arbitrarily. Thus the method is suitable for control of elastic systems, where C4 continuity is required to avoid vibrations. Assuming that the MPC works well as tracking controller, it is possible to consider only input constraints for the MPC and thus to minimize the computational effort. At last, a validation by means of simulation results is shown, in which the ACADO Toolkit is used for the MPC implementation.
Simulation‐based investigation of the influence of the micro‐structure and disorder on damage evolution in concrete
Authors: Gudžulić Vladislav , Khisamitov Ildar , Timothy Jithender J. , Meschke Günther
Published: December 2018

Concrete is a material with a random disordered microstructure across multiple scales. The effective macroscopic material behavior of concrete is strongly dependent on the material properties and the interactions of the individual constituents at the micro‐scale. Failure of concrete as a quasi‐brittle material is generally characterized by fracture processes occurring within the fracture process zone (FPZ) that governs strain softening behavior, followed by localization of damage eventually leading to structural failure. The aim of this study is to investigate the influence of micro‐structure and initial disorder on damage evolution in a strongly heterogeneous material such as concrete. The principal mechanism of failure is assumed to be governed by a cascade of localized micro‐cracking and re‐distribution of stresses [1]. This mechanism is modeled within the scope of this work using a voxel‐sized finite element approximation of the disordered micro‐structure with a non‐uniform distribution of strengths for each material phase. Further, the behavior of the crack and the fracture process zone is linked to a simple stochastic model for analyzing disorder ‐ the fiber bundle model.
Numerical analysis of thin‐walled structures based on the scaled boundary finite element method
Authors: Wallner Milan , Birk Carolin , Gravenkamp Hauke
Published: December 2018

The efficient load‐carrying behaviour of thin‐walled shells is one of the reasons for the continuing popularity of these structural elements across several fields of engineering. Locking effects limit the applicability of traditional finite element analysis (FEA) and require significant user experience in this context. Thus, shell formulations that do not show the emergence of locking effects are still a research subject. Since modelling of plates using the scaled boundary finite element method (SBFEM) showed no occurrence of locking effects the SBFEM seems to be a promising technique to avoid locking when modelling shell structures. This contribution presents the numerical analysis of thin‐walled shells using the SBFEM. Several benchmark problems for shell elements have been investigated and the results for the Scordelis‐Lo roof are presented in detail.
Structural optimisation on multiple scales based on numerical homogenisation techniques
Authors: Kijanski Wojciech , Barthold Franz‐Joseph
Published: December 2018

Structural analysis procedures and predictions of the physical behavior of complex structures with heterogeneous materials are usually based on the well‐known and established numerical homogenisation techniques with effective stress and material parameters, i.e. FE2 methods with effective

and

. The general goal is to enhance these methods with elements from variational sensitivity analysis and to formulate optimisation problems with objective functions, constraints and design parameters on multiple scales. The focus of this contribution is the sensitivity analysis of effective stresses or the corresponding Langrange multiplier 𝛌 respectively, which is incorporated in solution strategies based on the Lagrange formalism, as presented in [3] or [4]. The obtained sensitivity information can be used to setup optimisation problems for individual microscale representations and to control effective parameters within the overall optimisation procedure on single scales.
Single crystal plasticity – A mesoscale based approach for modeling the mechanics of additively manufactured Inconel 718
Authors: Kergaßner Andreas , Mergheim Julia , Steinmann Paul
Published: December 2018

In this contribution the mesoscopic material behavior of columnar grained Inconel 718 is modeled with a gradient enhanced crystal plasticity formulation and simulated by means of Finite Elements. A Voronoi tessellation based method is used to model the grain structure. On the mesoscale, the thermo‐mechanical behavior is modeled using a thermal gradient‐crystal‐plasticity model, allowing for relative misorientations on the grain boundaries. Computational homogenization and macroscopic experimental data are used to inversely identify elastic and plastic mesoscopic mechanical parameters. With the homogenized RVE at hand the parameters of a general anisotropic yield criterion for the macro scale are identified.
Internal Thickness Extrapolation
Authors: Töller Felix , Löhnert Stefan , Wriggers Peter
Published: December 2018

Modeling of thin joining zones is one application of Cohesive Zone Elements (CZE). Traction Separation Laws (TSLs) used as constitutive models in most CZEs that can be found in literature cannot fully capture all damage causing deformation modes induced by forming of hybrid components. An approach to overcome this deficiency by using bulk material models within a Cohesive Zone Element is presented.
An Anisotropic Phase‐Field Approach to Fracture in Coupled Electro‐Mechanics
Authors: Sridhar Ashish , Keip Marc‐André
Published: December 2018

Structural reliability analysis of piezoelectric ceramics needs the modeling of failure under coupled electro‐mechanical actions. Based on experimental results available in the literature, we suggest a non‐associative dissipative framework where the fracture phase field is driven by the mechanical part of the coupled electro‐mechanical driving force. Proposed degradation functions account for different electrical crack boundary conditions. The modeling capability of the framework is demonstrated by means of representative numerical examples.
A Method to Quantify Material Parameter Uncertainties Resulting from Microstructure Variation based on Artificial Microstructures
Authors: Miska Niklas , Balzani Daniel
Published: December 2018

The macroscopic behavior of many materials is dependent from their microstructure morphology. As the morphology is often random, the macroscopic response of the material is uncertain. In this paper we propose a method to capture the statistics of the variability of the morphology of the real material, transfer this variability to artificial microstructures and perform virtual tests to quantify the uncertainty of the resulting macroscopic response.
Intrinsically locking‐free formulations for isogeometric beam, plate and shell analysis
Authors: Oesterle Bastian , Bieber Simon , Sachse Renate , Ramm Ekkehard , Bischoff Manfred
Published: December 2018

In this contribution a class of formulations for beams, plates and shells is presented, which intrinsically avoids locking, independent of the utilized discretization scheme. The key idea is the reparametrization of the kinematic equations to avoid locking on theory level – prior to discretization. Thus, the resulting formulations are locking‐free for any equal‐order interpolation. As demonstrator, we present both mixed and primal concepts for Timoshenko beams in both weak and strong form, as well as their theoretical relationships. Besides a weak form Galerkin‐type solution using B‐Splines, we show the generality of the presented concepts by employing isogeometric collocation based on the corresponding Euler‐Lagrange equations of the boundary value problem. The quality of both stress resultants and displacements is investigated. Although the underlying concept addresses beams, plates and shells, the present contribution illustrates the methodology for the Timoshenko beam.
Limitation of an adjustable two degree‐of‐freedom damper system for directional damping
Authors: Tan Aditya Suryadi , Dahlmann Martin , Sattel Thomas
Published: December 2018

For a better and more flexible damping, a smart damper is required. Such damper should be able to adjust the damping magnitude and damping direction independently. In this work, two degree‐of‐freedom (DOF) damping with two fixed orthogonal damping directions is investigated. The damping magnitude can be adjusted independently for each damping direction. This kind of adjustment can be realized through the implementation of field responsive fluid, such as electro‐ or magnetorheological fluid. In order to describe the behavior of the damping system, investigations were conducted for several combinations of damping magnitude and velocity directions. It is shown that fully independent damping adjustment is only possible to be realized along the fixed orthogonal damping directions. Therefore, it is not possible to control the direction of the damping independently with only two damping elements. It can be concluded, that the possibility to influence the damping direction is found to be still challenging.
Dynamical Modeling and LQR Control of a Gyroscopically Stabilized Bicycle
Authors: Gattringer Hubert , Reiter Alexander , Müller Andreas , Wagner Daniel , Mauernböck Tobias
Published: December 2018

This contribution focuses on the dynamical modeling and control of a self‐balancing bicycle. The bicycle is equipped with two flywheels rotating at constant speed mounted via a hinge that is actuated by an additional motor and allows for rotation about the vertical axis. Due to the balance of angular momentum, a torque is generated around the axis perpendicular to the hinge and spinning axis, i.e. an axis along the forward motion direction. This gyroscopic effect is exploited for the stabilization of the bicycle. Two cases are distinguished: 1) For the stabilization of the non‐moving bicycle an LQ–controller based on a linear model is used. 2) For the moving bicycle, a non‐linear dynamic model in terms of non‐holonomic velocities is derived and based on the linearized model at constant driving speeds the stability of the bicycle is analyzed. The model reveals the self‐stabilization behavior of a bicycle without flywheels. At a speed of about 17km/h, the linearized model has only eigenvalues with negative real parts and is hence stable. Experimental as well as simulation results are presented.
Anisotropic wave dispersion and band‐gaps in mechanical metamaterials via the relaxed micromorphic model
Authors: d'Agostino Marco V. , Madeo Angela , Barbagallo Gabriele , Ghiba I. Dumitrel , Eidel Bernhard , Neff Patrizio
Published: December 2018

We propose a continuum model (the relaxed micromorphic model) to describe band‐gap phenomena in metamaterials.
Modelling and experimental testing of expanded granules as crash‐absorber for double hull ships
Authors: Woitzik Christian , Chaudry Mohsin Ali , Wriggers Peter , Düster Alexander
Published: December 2018

In this contribution, expanded glass granules are investigated, which will be used to increase the crashworthiness in ship construction. Therefore, an experimental setup is presented. This setup represents a simplified side hull structure of a double hull ship. The empty space between the double hull structure can be filled with the granular material which acts as crash absorber.

The described experiment will be used to validate the finite element simulation of the penetration of the double hull with the bulbous bow. To model the granules the Mohr‐Coulomb material model is taken advantage of. Based on the experimental data the suitability of the Mohr‐Coulomb model will be discussed.
The research of viscoelastic mechanical behaviour of human periodontal ligament based on stress‐relaxation tests
Authors: Wu Bin , Ma Songyun , Yan Bin , Heider Yousef , Markert Bernd
Published: December 2018

In this paper a dynamic thermomechanical analyzer was used to perform stress‐relaxation tests on human periodontal ligament samples and a viscoelastic model is employed to correlate the test data. The results show that the stress‐strain curves of the three samples can be predicted by the used constitutive model, which uses five parameters. The correction coefficients are larger than 0.99 for all tests, indicating that the five‐parameter viscoelastic model is suitable for describing the viscoelastic behaviour of human periodontal ligament.
Chondrocyte migration in an acellular tissue‐engineered cartilage substitute
Authors: Nachtsheim Julia , Dursun Gözde , Markert Bernd , Stoffel Marcus
Published: December 2018

Acellular tissue‐engineered cartilage substitutes are promising replacement materials to mend small focal defects. The underlying therapeutic idea is to initially stabilise the defect zone and in a long‐term manner allowing for remodelling processes towards a hyaline cartilage tissue. Crucial for remodelling processes inside the implant, is the cell migration from the adjacent tissue, which will be assessed in this study.
Wetting phenomena with ALE interface tracking
Authors: Gründing Dirk , Bothe Dieter , Marschall Holger
Published: December 2018

An arbitrary Lagrangian Eulerian (ALE) interface tracking method is applied to multiphase flows involving wetting phenomena. The method is implemented in OpenFOAM and validated for the static shape of a drop deformed by gravity influence. Results for a constant contact angle model are compared to approximate analytic solutions for the limiting cases of vanishing or infinite Eötvös numbers. Results between the two limiting cases are compared to numerical results from literature.
A hybrid stochastic domain decomposition method for partial differential equations with localised possibly rough random data
Authors: Gruhlke Robert , Eigel Martin , Hömberg Dietmar , Drieschner Martin , Petryna Yuri
Published: December 2018

The presence of air voids in adhesive bonds, possible introduced in a manufacturing process, is regarded as one main reason for failure of rotor blades. Building up a model for material with random inclusion, we numerically solve for it with the help of domain decomposition techniques. This introduces a hybrid method which combines advantages of sampling and stochastic Galerkin strategies based on generalized multi‐element polynomial chaos expansion (gHPCE).
From Experiment to Material Parameter Identification
Authors: Hartmann Stefan , Gilbert Rose Rogin
Published: December 2018

Constitutive modeling requires the calibration of the constitutive model to experimental data. This calibration is called material parameter identification. Simple experiments lead to specified deformation and stress states, which is not guaranteed in all situation. Thus, finite elements must be drawn on to calculate the deformation state solving the entire boundary‐value problem. There are several basic questions, which must be addressed apart from experiments doable for the material under consideration: first, what optimization technique is suitable? Second, are the material parameters identifiable by the given experiments, and what is the quality of the result? Third, there have been open questions of the connection between engineering and mathematical literature showing that in Engineering Science the procedures have already been developed in Numerical Mathematics. These question will be discussed in this overview.
Optimization Approaches for Durable Reinforced Concrete Structures considering Interval and Stochastic Parameter Uncertainty
Authors: Freitag Steffen , Edler Philipp , Kremer Katharina , Hofmann Michael , Meschke Günther
Published: December 2018

The durability of reinforced concrete structures is dominated by steel reinforcement corrosion and uncertain service loads, which have to be considered in the lifetime oriented structural design. The transport of corrosive substances into the structure is considerably influenced by load induced cracking. The crack width therefore is a major controlling factor for the lifetime of reinforced concrete structures. To improve the design for durability, finite element models in combination with optimization approaches for polymorphic uncertain data are presented. Here, the crack width at the reinforcement layer is used as the optimization objective to be minimized. The structural reliability is treated as a constraint of the optimization task in terms of the accepted failure probability. The concrete covers of the reinforcement layers are chosen as interval design parameters, with midpoints to be optimized and a given radius to take construction imprecision into account. The structural loading, the Young's modulus of concrete and the corresponding tensile strength are considered as stochastic a priori parameters within the optimization, which is solved by a particle swarm optimization approach in combination with an artificial neural network surrogate model. The polymorphic uncertain structural response is computed by a combination of Monte Carlo simulations and optimization‐based interval analysis to consider the stochastic and interval parameters within the optimization task, respectively. An application example demonstrates the performance of the proposed approach.
Stress‐based Finite Element Methods for Sea Ice Dynamics
Authors: Bertrand Fleurianne
Published: December 2018

A first‐order system least squares formulation for the sea‐ice dynamics is presented. In addition to the displacement field, the stress tensor is used as a variable. As finite element spaces, standard conforming piecewise polynomials for the displacement approximation are combined with Raviart‐Thomas elements for the rows in the stress tensor. Computational results for a test problem illustrate the least‐squares approach.
Adaptive trust‐region POD for optimal control of the Cahn‐Hilliard equation
Authors: Alff Jan Oke , Gräßle Carmen , Hinze Michael
Published: December 2018

We consider the optimal control problem of a phase field system with distributed control. A reduction of the computational complexity is achieved by a POD‐Galerkin approach where the expensive high‐fidelity PDE systems are replaced by low‐dimensional approximations. The POD basis functions are computed from snapshots which are space‐adapted finite element solutions of the governing equations. Within the trust‐region framework, the accuracy of the surrogate models is controlled in the course of the optimization. In the numerical example we compare the use of a relaxed double‐obstacle free energy with a smooth free energy concerning the influence on the accuracy of the solution and the optimization performance.
Characterization and propagation of uncertainties associated with limited data using a hierarchical parametric probability box
Authors: Hoang Truong‐Vinh , Rosić Bojana , Matthies Hermann G.
Published: December 2018

Uncertainty of random variables is commonly characterized from measurement data. In practice, data might be insufficient in order to obtain an accurate probability model. In this work, we assume that the type of distribution of the considered random variable is known a priori, and use a hierarchical parametric probability box (p‐box) – which is a set of distributions whose parameters are uncertain – to account for the limited data. Using Bayes' rule, knowledge about the variability of these parameters is updated. Propagation of these uncertainties through a computational model usually suffers from computational burden. A surrogate model approximating the computational model is constructed to reduce computational cost.
Crystallization and flame‐retardant properties of polylactic acid composites with polyhedral octaphenyl silsesquioxane
Authors: Jia Lin , Tong Bin , Li Dinghua , Zhang Wenchao , Yang Rongjie
Published: December 2018

To develop environmental‐friendly and flame‐retarded polymer composites, bio‐based polylactic acid (PLA) was loaded with thermally stable polyhedral octaphenyl silsesquioxane (OPS). Pure PLA and PLA/OPS composites with the OPS of 1, 3, 5, and 10 wt% were prepared by extrusion and injection molding, respectively. The scanning electron microscopy (SEM), polarized optical microscope (POM), differential scanning calorimetry (DSC), X‐ray diffraction (XRD), and thermal gravimetric analysis (TGA) were used to analyze the dispersion of the OPS in the PLA matrix and the effects of OPS on the crystallization and thermal stability properties of PLA/OPS composites, respectively. Limited oxygen index (LOI) and cone calorimeter (CONE) measurements were used to study flame retardancy of PLA and PLA/OPS composites. In order to study the flame‐retardant mechanism, the char residues were investigated by SEM, Fourier transform infrared spectra (FTIR), and X‐ray photoelectron spectroscopy (XPS). TGA‐FTIR was used to analyze the gaseous products of their thermal decomposition. The results show that the OPS particles were submicron in the PLA and could increase the crystallization rate of PLA and form small‐sized secondary α‐form crystalline compared with the pure PLA spherulite. The PLA and OPS decomposed individually in the PLA/OPS composites by TGA. According to the LOI tests, the PLA with the OPS loading exhibited very small reduction of LOI. However, the CONE tests indicated that the OPS could improve the flame retardancy of the PLA by means of low peak heat release rate and average heat release rate. It was obtained that the degree and type of the PLA crystalline for the pure PLA and PLA/OPS affect their flame retardancy. In the max thermal decomposition stage of PLA and PLA/OPS, their gaseous products were similar; at high temperatures, the PLA/OPS produced simple and clear gaseous products of PLA with solid SiO2 in the gas phase.