bluuebunny/crossref_metadata_2025 huggingface dataset:
Variational Formulation and Numerical Implementation of Diffusion in Hydrogels at Finite Strains
Authors: Nateghi Aref , Mauthe Steffen , Miehe Christian
Published: October 2015

Hydrogels are polymeric materials with a cross‐linked network which can absorb water. Due to their bio‐compatibility, hydrogels have many applications in biology and medicine. Recently modeling the mechanical behavior of hydrogels has attracted a great deal of attention among researchers, see e.g., [1] and [2]. Following our previous works [3], [4] and [5] we now present a variational framework for swelling phenomenon in hydrogels. The variational formulation of the problem can be done using a saddle‐point principle or a minimization principle. Saddle‐point principle has to fulfill the Ladyzhenskaya‐Babuška‐Brezzi (LBB) condition in order to lead to a stable finite element scheme. The key aspect of our proposed minimization principle is its advantage with regard to an unconstrained fem implementation. In this work we aim to compare the numerical performance of these two variational formulations for swelling of hydrogels. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling of the Crosstalk Phenomenon by Bilateral Coupling of the Non‐Stationary Maxwell Equations and the Circuit Equations
Authors: Niroomand Rad Helia , Steinbrecher Andreas
Published: October 2015

In this paper, we introduce a general modeling approach for the crosstalk phenomenon within electro‐magnetic systems. We model the phenomenon by bilateral coupling of two sets of differential equations, namely non‐stationary Maxwell equations and circuit equations. Considering these two sets of equations as input‐output systems, the bilateral coupling approach connects the output of one system to the input of the other system and conversely, via coupling and re‐coupling relations. The coupling of these two sets leads to a set of partial differential‐algebraic equations modeling the crosstalk phenomenon. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Velocity Vector Field Optimization in Bioventing
Authors: Notarnicola Filippo
Published: October 2015

Bioventing is a technology used to remove some kinds of pollutants from the subsoil and it is based on the capability of some bacteria species to biodegrade contaminants. The biochemical reaction requires, among other things, oxygen and, therefore, oxygen is inflated into the subsoil by wells. The mathematical model describes the movement of the different fluids which are present in the subsoil – air, water, pollutants, oxygen and so on – and the bacteria population dynamics. The presence of source reactive terms in the continuity equations allows the contaminant biodegradation to be described.

The design of a subsoil decontamination intervention concerns bioavailability problems and, in particular, the oxygen concentration. Therefore, in order to enhance the biodegradation phenomenon, the optimization of the subsoil oxygen velocity field in the polluted area is required, by an appropriate choice of the well positions and of the well air inflating rates. In mathematical terms, the goal is to obtain the decontamination of the subsoil with an optimal value of an objective function by acting on some control variables which, in this case, are the well positions and the inflating rates. In this paper several kind of objective function are proposed. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Static condensation within the context of multifield elastoplasticity
Authors: Schröder Bettina , Kuhl Detlef
Published: October 2015

In the present paper a multifield approach towards ideal elastoplasticity is presented and its numerical implementation is touched. Furthermore, the strategy of static condensation is applied to this ansatz. With the help of an axisymmetric model problem its realization is demonstrated and compared to the pure multifield approach. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling of thermo‐electro‐mechanical coupling effects in ionic electroactive polymers within the Theory of Porous Media
Authors: Serdas Serdar , Bluhm Joachim , Schröder Jörg
Published: October 2015

In this contribution, a multiphase model will be presented in order to simulate ionic electroactive polymers (EAPs). The considered material model is developed within the framework of the Theory of Porous Media (TPM) which consists a thermo‐electro‐mechanical coupling. For the description of the model, a thermodynamically consistent formulation in consideration of the electrostatic forces and the fluid pressure will be derived. The presented model includes a charged polymer (solid) saturated by an electrolyte solvent (fluid). A boundary value problem (plate with a hole) is given. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Isogeometric analysis of surface elasticity: a comparison with isoparametric FEM
Authors: Stein Peter , Xu Bai‐Xiang
Published: October 2015

We report here on the isogeometric treatment of surface‐elastic effects and compare the results obtained from Finite Element simulations and Isogeometric Analysis. As expected, the latter delivers smoother solutions than a standard finite element approach. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Validation with Numerical Simulations of a Simplified Model of a Hybrid Rocket Motor
Authors: Frunzulica Florin , Stoia‐Djeska Marius , Mingireanu Florin
Published: October 2015

The hybrid propulsion offers some remarkable advantages like high safety and high specific impulse and thus it is considered a promising technology for the next generation launchers and space systems. The purpose of this work is to validate through numerical simulations a design tool for hybrid rocket motors (HRM). (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Critical velocities for flow induced vibrations of a U‐shaped belt
Authors: Strecha Johannes , Steinrück Herbert
Published: October 2015

Two excitation mechanisms for flow induced vibrations of a U‐shaped belt are described. Firstly, the belt can be excited by vortices forming in the cavity of the U. This mechanism is relevant at low reduced (dimensionless) flow velocities. Secondly, an excitation through the so called motion induced vortices can occur at larger reduced velocities. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The electrocaloric effect in ferroelectrics: nonlinear modeling and simulation
Authors: Wingen Marius , Ricoeur Andreas
Published: October 2015

In this paper, the theoretical background of a physically based constitutive model is presented. In addition to the nonlinear ferroelectric behavior, the model considers the nonlinear coupling of thermal and electromechanical fields. Results are presented in terms of a simple analytical solution for a single domain configuration. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Thermo‐mechanical computation of inelastic pavement structures under rolling tire loads
Authors: Wollny Ines , Hartung Felix , Kaliske Michael
Published: October 2015

A realistic and numerically efficient computation of the tire‐pavement interaction is essential for the investigation of the structural behavior of pavements under rolling tire load as base of the development of more durable pavement structures. The paper presents a thermo‐mechanical coupled simulation model based on an Arbitrary Lagrangian Eulerian (ALE) formulation that considers the inelastic and temperature dependent material properties of asphalt. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Phase field simulation of the intercalation‐induced stresses in the hyperelastic solids via isogeometric analysis
Authors: Zhao Ying , Stein Peter , Xu Bai‐Xiang
Published: October 2015

In this work the Cahn‐Hilliard‐type diffusion in a hyperelastic solid will be studied and simulated using isogeometric analysis. The Cahn‐Hilliard model is employed to account for the phase segregation phenomenon, in which a fourth‐order partial differential operator exists. In order to deal with this high‐order operator, isogeometric analysis is applied. Finally, simulation results of a disc is given. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Grain‐scale‐based simulation of granular material
Authors: Bidier Sami , Ehlers Wolfgang
Published: October 2015

In recent years, new developments in experimental mechanics, e. g., particle‐tracking methods using X‐ray micro‐tomography, have provided a new insight into the material behaviour of granular media. The possibility to capture the individual grain displacement and rotation of all particles within a sample provides a new fundament for a reliable numerical simulation of granulates. This is, in particular, the case for deformation localisation in shear zones as they are observed in bi‐ and triaxial compression tests, where the exact thickness of the localised zone as well as the amount of accompanying grain displacements and rotations are measurable in a precise and direct way. In this context, the Discrete‐Element (DE) Method has become a promising and frequently used modelling technique for granular materials. In contrast to macroscopically based continuum‐mechanical approaches, the DE approach treats each particle as a rigid and uncrushably body and is, therefore, defined on a microscopic level of description. This consequently allows a direct comparison with experimental data from grain‐scale tracking methods. In the present contribution, the DE method is applied in order to solve problems of localisation in granular media. Therefore, constitutive inter‐particle contact laws are formulated for forces and torques which are transferred between interacting particles. With a given solution of initial‐boundary‐value problems on the microscale, a computational homogenisation procedure leads to macroscopic quantities purely stemming from microscopic information. Herein, a particle‐centre‐based volume averaging technique leads to macroscopic quantities which correspond to quantities known from micropolar continuum theories. The contribution presents a framework for the homogenisation in all time steps in a fully 3‐dimensional context and discusses the activation of micropolar effects in the localised zone. Furthermore, the admissible size of the chosen Representative Elementary Volume (REV) is addressed. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A coupled two‐scale shell model for comb‐like sandwich structures
Authors: Heller Dominik , Gruttmann Friedrich
Published: October 2015

In this work a coupled two‐scale sandwich shell model is proposed, where 4‐node quadrilaterals are employed both on the global and the local scale. The coupled global‐local boundary value problem is derived by means of a variational formulation and ensuing linearization. A numerical simulation is carried out for linear elastic and elasto‐plastic material behavior with small strains.

The resulting coupled nonlinear boundary value problem is solved simultaneously in a Newton iteration with incremental load steps. Various types of sandwich models are investigated in the form of uni‐ and bidirectionally stiffened structures. For the unidirectionally stiffened beam, an analytical reference solution is present by means of classical beam theory. In addition, the numerical results of all coupled calculations are compared to full scale shell models, showing very good agreement while significantly reducing the size of occurring system matrices. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Experimental investigation and approximation of the temperature‐dependent stiffness of short‐fiber reinforced polymers
Authors: Kehrer L. , Müller V. , Brylka B. , Böhlke T.
Published: October 2015

In order to predict the effective material properties of a short‐fiber reinforced polymer (SFRP), homogenization of elastic properties with the self‐consistent (SC) scheme and the interaction direct derivative (IDD) method is performed by means of µCT data describing the microstructure of the composite material. Using dynamic mechanical analysis (DMA), the material properties of both, polypropylene and fiber reinforced polypropylene are investigated by tensile tests under thermal load. The measured storage modulus of the matrix material is used as input parameter for the homogenization scheme. The effective properties of SFRP are compared to experimental results from DMA. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Multi‐scale modeling of beam‐like structures: A new boundary condition concept for the RVE
Authors: Klarmann Simon , Gruttmann Friedrich
Published: October 2015

In this work a coupled two‐scale beam model using Timoshenko beam elements [1] with finite displacements on the macro scale and fully non‐linear 3D brick elements on the micro scale is proposed. The calculation is carried out with the so‐called FE2 concept. To achieve the coupling between the beam and the brick elements, the algorithm from [2] is adapted.

Within the degenerated concept of the Timoshenko beam, the introduction of a pure shear deformation leads to significant problems concerning the equilibrium condition on the micro scale. Applying this deformation mode on the RVE with periodic boundary conditions results in a rigid body rotation. Using linear displacement boundary conditions instead, the wrapping deformation is suppressed on the boundary, leading to a length dependency in the torsional deformation mode. In addition, the shear forces introduce a bending moment, which depends on the length of the RVE and adds spurious normal stresses and a length dependency of the shear stiffness.

To overcome these problems, periodic boundary conditions are applied and the displacement assumptions are modified such that the shear deformation is achieved with force pairs on both ends of the RVE. The resulting model leads to length independent results in tension, bending and torsion and a domain which is able to produce a pure shear stress state. Consequently, only this domain of the model should be homogenized which can be accomplished by modifying the variations in the algorithm [2]. The concept is validated by simple linear and non‐linear test problems. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Materials design of elastic properties of multiphase polycrystalline composites using model functions
Authors: Lobos Mauricio , Yuzbasioglu Tunc , Böhlke Thomas
Published: October 2015

For a chosen combination of materials for a multiphase polycrystalline composite, a crystallite orientation distribution function for each phase is formulated as a superposition of analytic central model von Mises‐Fisher functions. The chosen central model functions allow the analytic integration of orientation averages of arbitrarily anisotropic fourth‐order tensors. Based on this result, the first‐order bounds of Voigt and Reuss and the geometric average of the stiffness can be expressed explicitly in closed forms for arbitrarily anisotropic polycrystalline materials and number of phases depending on the volume fractions and the influence of the crystallographic texture of each constituent. These expressions can then be used for the materials design aiming the determination of volume fractions and orientation distribution of selected materials for prescribed effective properties. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Study on statistically similar RVEs for real microstructures based on different statistical descriptors
Authors: Scheunemann Lisa , Balzani Daniel , Brands Dominik , Schröder Jörg
Published: October 2015

A method for constructing statistically similar representative volume elements (SSRVEs) for a real dual‐phase (DP) steel microstructure is presented in this contribution. The advantageous material properties of such kind of steels originate from the interaction of the microstructure constituents of the material on the microscale. In order to capture these effects directly in the material modeling, the FE2 method is a suitable tool, where an RVE representing the microstructure of a material is used in the microscopic boundary value problem, which is solved at each Gauss‐point of the macroscopic boundary value problem. However, RVEs based on real microstructures typically implicate high computational expenses due to the complexity of the underlying microstructure and its discretization. SSRVEs, which have a lower complexity than conventional RVEs but are still able to represent the material, can be used instead. Here, different statistical measures for the construction of SSRVEs and their comparison are the main focus. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Polynomial shape functions on the logarithmic space: the LogFE method
Authors: Schröppel Christian , Wackerfuß Jens
Published: October 2015

We extend the Logarithmic finite element method, a novel finite element approach for solving boundary‐value problems proposed in [1], to a complete set of degrees of freedom, i.e. translational and rotational degrees of freedom in three dimensions. In contrast to the standard Ritz‐Galerkin formulation, the shape functions are given on the logarithmic space of the deformation function. Unlike existing formulations based on Lie groups, they may include polynomial functions of arbitrary degree. The method focuses on reducing the low‐frequency components in the error, while minimizing spurious high‐frequency deformations, a characteristic that is particularly advantageous in the context of a multigrid algorithm, in which the method may be used to construct an approximation for the coarse grid. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Cascade Continuum Micromechanics Model for the Effective Diffusivity of Porous Materials: Exponential Hierarchy across Cascade Levels
Authors: Timothy Jithender J. , Meschke Günther
Published: October 2015

The effective molecular diffusivity of porous materials such as cementitious, geological or synthetic materials is strongly affected by the complexity of the pore‐space which may span across multiple scales from the nanometer to the sub‐millimeter range. Recently, a semi‐analytical Cascade Continuum Micromechanics (CCM) Model [1,2] was proposed, which allows to compute estimates of the effective diffusivity given the porosity ϕ, the intrinsic diffusivity of molecules in the pore‐fluid D and a complexity parameter n. In contrast to existing micromechanics models, the CCM model is able to predict a physically consistent percolation threshold. In this paper, the classical CCM model is generalized so as to characterize a pore‐volume distribution and its influence on the effective diffusivity at a particular cascade level. The generalized CCM model shows an exponential pore‐volume distribution across cascade levels that is implicitly included in the classical CCM model. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Axisymmetric flow over a backward‐facing step in an annular pipe
Authors: Beladi Behnaz , Kuhlmann Hendrik C.
Published: October 2015

The incompressible flow of a Newtonian fluid over a backward‐facing step is investigated numerically. The geometry is an annular pipe in which the radius of the inner cylinder decreases suddenly. Keeping the radial expansion ratio fixed axisymmetric flows are computed for outlet radius ratios from 0.1 to 1 (ratio of the inner to the outer outlet radius). The Reynolds number at which the flow separates from the outer cylinder decreases as the outlet radius ratio decreases for constant inlet geometry. The growth with Reynolds number of the recirculation zone on the inner outlet cylinder just behind the step is strongly reduced when the recirculation zone on the outer cylinder is established. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Extreme event detection in near‐wall turbulence using reflection‐encoded readout of micropillar arrays
Authors: Hegner F. , Mikulich V. , Axtmann B. , Rist U. , Brücker Ch.
Published: October 2015

A method is presented which uses the intensity‐based encoding of deflection of micropillars to detect criticical events in near‐wall turbulence. The pillars are tailored to respond only to the streamwise or the spanwise component of the wall‐shear stress with larger deflection. Light reflected from the side‐walls of these structures is used to dected certain events in the flow that run along the wall. Examples are given for defined disturbances in a planar Couette flow. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Receptivity and non‐uniqueness of turbulent boundary layer flows
Authors: Scheichl Bernhard
Published: October 2015

The classical theory of firmly attached time‐mean turbulent boundary layers, exhibiting fully developed broadband turbulence, in the limit of large Reynolds numbers, Re, is extended in two ways, where the focus lies on their stability and receptivity. At first, the description of non‐unique equilibrium flows having a so‐called moderately large velocity deficit is generalised as weak spanwise variations and unsteadiness is taken into account. Here the time period of filtering the flow tends to infinity such that conventional Reynolds averaging is obtained as Re → ∞. Secondly, the method of matched asymptotic expansions is supplemented with a suitable multiple‐scales approach so as to capture the global effect of pronounced surface waviness on the time‐mean velocity profile of the boundary layer in a self‐consistent manner in terms of a memory decaying exponentially from the surface. Remarkably, the results of the asymptotic analysis are qualitatively independent of any turbulence closure. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
High‐Reynolds‐number effects on turbulent scalings in compressible channel flow
Authors: Modesti Davide , Bernardini Matteo , Pirozzoli Sergio
Published: October 2015

The effect of the Reynolds number in a supersonic isothermal channel flow is studied using a direct numerical simulation (DNS). The bulk Mach number based on the wall temperature is 1.5, and the bulk Reynolds number is increased up to Reτ ≈︁ 1000. The use of van Driest velocity transformation in the presence of heated walls has been questioned due to the poor accuracy at low Reynolds number. For this reason alternative transformations of the velocity profile and turbulence statistics have been proposed, as, for instance, semi‐local scalings. We show that the van Driest transformation recovers its accuracy as the Reynolds number is increased. The Reynolds stresses collapse on the incompressible ones, when properly scaled with density, and very good agreement with the incompressible stresses is found in the outer layer. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Asymptotic solutions of an extended Korteweg–de Vries equation describing solitary waves with weak or strong downstream decay in turbulent open‐channel flow
Authors: Müllner Markus , Schneider Wilhelm
Published: October 2015

Solitary waves in turbulent open‐channel flow over a strip of enlarged bottom roughness are considered. Slightly supercritical, fully developed flow far upstream and downstream is assumed. An analysis by Schneider [1] yielded an extended Korteweg–de Vries equation that is solved in the present paper by matched asymptotic expansions up to second order. Solutions for the surface elevation and the location of the wave crest are given. It is shown that a minimum enlargement of the bottom roughness is required for the stationary wave to exist. The surface elevation exhibits either a weak downstream decay, i.e. a shallow ‘tail’, or, if the enlargement of the bottom roughness equals an eigenvalue, the strong decay of the classical soliton solution. Numerical results available for the latter case [2] are in very good agreement with the present analytical solution. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Coarse‐Grid‐CFD for the Thermal Hydraulic Investigation of Rod‐Bundles
Authors: Viellieber Mathias , Class Andreas
Published: October 2015

A nuclear reactor core, that is a few meters in height and diameter is composed of hundreds of fuel assemblies which are again composed of tenth of fuel rods with a diameter of about 10 mm. The relevant length scales for a Computational Fluid Dynamics (CFD) simulations range from the sub millimetre range, relevant for the sub channels up to several meters. Describing such a multi‐scale situation with CFD is extremely challenging and the traditional approach is to use integral methods. These are sub channel and sub assembly analyses codes requiring closure by empirical and experimental correlations. A CFD simulation of a complete nuclear reactor set up resolving all relevant scales requires exceedingly large computational resources. However, in many cases there exists repetitive geometrical assemblies and flow patterns. Based on this observation the general approach of creating a parametrized model for a single segment and composing many of these reduced models to obtain the entire reactor simulation becomes feasible. With the Coarse‐Grid‐CFD (CGCFD) ( [1], [2]), we propose to replace the experimental or empirical input with proper CFD data. Application of the methodology starts with a detailed, well‐resolved, and verified CFD simulation of a single representative segment. From this simulation we extract in tabular form so‐called volumetric forces which upon parametrization is assigned to all coarse cells. Repeating the fine simulation for multiple flow conditions parametrized data can be obtained or interpolated for all occurring conditions to the desired degree of accuracy. Note, that parametrized data is used to close an otherwise strongly under‐resolved, coarsely meshed model of a complete reactor set up. Implementation of volumetric forces are the method of choice to account for effects as long as dominant transport is still distinguishable on the coarse mesh. In cases where smaller scale effects become relevant the Anisotrop Porosity Formulation (APF) allows capturing transport phenomena occurring on the same or slightly smaller scale compared to the coarse mesh resolution. Within this work we present results of several fuel assemblies, that were investigated with our methodology. In particular, we show Coarse‐Grid‐CFD simulations including a 127 pin LBE cooled wire wrapped fuel assembly. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modelling and simulation of mobile jet agitator for a biogas plant
Authors: Alimi Aria , Wünsch Olaf
Published: October 2015

This work deals with the modeling and simulation of mixture process in a biogas plant. This mixing process involves a closed pumping procedure, which pumps the constituents of the biogas plant using jet agitators inside the tank. For this purpose, an experimental model has been designed and built in reduced scale to study the mixture process. Furthermore, this process has been simulated numerically. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Simulation of mass transfer at free liquid/liquid interfaces
Authors: Heckmann Christian , Lakshmanan Peter , Ehrhard Peter
Published: October 2015

A numerical scheme for the simulation of mass transfer processes at free liquid/liquid interfaces using the interface tracking method is presented. Due to comparable diffusion coefficients in liquid/liquid systems, the mass transfer resistance in both phases is relevant for the entire transient mass transfer process. Exemplary, the extraction process from a free rising spherical droplet of constant shape is used. The presented approach can be used in general for any multiphase steady‐state mass transfer system. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Polymer Devolatilization in a Rotating Apparatus
Authors: Hirschfeld Stefan , Hermann Lutz , Wünsch Olaf
Published: October 2015

Devolatilization is an important unit operation in polymer processing, that is often performed in rotating devices. This work is concerned with the experimental study of film degassing in a simple rotating apparatus with a blade agitator. The experimental setup and procedure are presented. The results are evaluated with the surface renewal theory which is also known as penetration theory. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Gas bubbles in micro capillaries – hydrodynamics and mass transfer
Authors: Lakshmanan Peter , Ehrhard Peter
Published: October 2015

Process design of multi‐phase unit operations on the micro‐scale relies on the detailed knowledge of the hydrodynamics and mass transfer behavior of discrete disperse fluid particles. The present work examines the hydrodynamics and mass transfer of gas bubbles in vertical capillaries. The hydrodynamic behavior of a single bubble in a capillary including is examined numerically using a modified level‐set method [1]. Additionally, the influence of surface‐active contaminations (‘surfactants’) and the resulting Marangoni effects are taken into account [2]. This enables the differentiation between bubbles with a mobile, i.e. clean, interface and those with a immobile, i.e. contaminated, interface. Based on the hydrodynamics, the mass transfer is examined. In the present work, mass transfer is from the bubble into the bulk fluid. By using a very high mesh resolution, the local concentration field in and around the gas bubble can be resolved, which gives access to the local mass transfer. Results are in good agreement available correlations from literature. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical Modeling of Laser‐Induced Cavitation Bubbles with a Finite Volume Method
Authors: Lechner Christiane , Koch Max , Reuter Fabian , Köhler Karsten , Mettin Robert , Lauterborn Werner
Published: October 2015

We report on the numerical modeling of laser‐induced cavitation bubbles with the finite volume method using the open source software package OpenFOAM. The numerical model is validated by comparison to experimental data for the two cases of a bubble collapsing under normal ambient conditions in an unbounded liquid as well as close to a solid wall. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A circulating gravity wave in a cylindrical tank
Authors: Steinrück Herbert , Gusner Lorenz
Published: October 2015

A circular cylindrical vertical tank is partially filled with a liquid (Water) and a gas (air) above it. The top lid of the container rotates around the cylinder axis and induces a flow in the gas and the liquid. Above a critical rotational speed a large amplitude circulating gravity wave forms. The two phase flow problem will be reduced to a free surface single phase flow problem and the critical parameters, when the axis‐symmetric flow becomes unstable with respect to the circulating gravity wave will be determined. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Non‐destructive testing of porous media by means of sound wave analysis
Authors: Albers Bettina
Published: October 2015

The theoretical investigation of sound waves in porous materials is motivated by the possible construction of non‐destructive testing methods. Here, geotechnical applications are of interest where low frequencies from zero to 100 Hz occur but also systems with higher frequency ranges may be tested non‐invasively. Examples are concrete and other construction materials, road surfaces and pavements (some MHz), biological materials like bones and soft tissues, e.g. the surface of the heart (up to 3 MHz) right up to surface coatings by nanomaterials (approximately 100 MHz). (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A novel approach to mode‐tracing in SBFEM‐simulations: Higher‐order Taylor‐ and Padé approximation
Authors: Krome Fabian , Gravenkamp Hauke
Published: October 2015

This contribution presents the study of strange phenomena in wave mode representations of waveguides. For this study the waveguides are computed by means of the Scaled Boundary Finite Element Method (SBFEM). Different approaches of mode tracing are used to identify the characteristics of the resulting wave modes. Higher order differentials of the underlying eigenvalue problem are the basis for these approaches.

The main idea behind this mode tracing approach is to reduce the cubic computation time to solve the eigenvalue problem for each frequency of interest. This study identifies potentially critical frequency regions and attempts to formulate a solution process. The fascinating effects at critical frequencies are displayed and a suggestion for a stabilization for the solution process is made. This study bases its conclusion on a numerical viewpoint. Main aspects in this study include high order differentials of the eigenvalue problem and the corresponding Taylor and Padé approximations for the eigenvalue problem as a whole. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Forward and Inverse Viscoacoustic Modelling in a Tunnel Environment
Authors: Musayev Khayal , Hackl Klaus , Baitsch Matthias
Published: October 2015

In this work, the goal is to model forward acoustic waves in a tunnel environment with attenuation and to do full waveform inversion. In reality, there is no material without attenuation. Some materials, such as rocks, have so low attenuation that, in a small domain, the waves are almost not damped at all. At the same time, there are materials with high attenuation. In an environment with such materials, the attenuation has to be taken into account in order to model the waves properly. In this study, attenuation effect is integrated into acoustic equation by using Kolsky‐Futterman model ( [1], [2]) which only replaces velocity field with a complex‐valued field in frequency domain. Apart from attenuation, another objective is to consider an inhomogeneous density field. Mainly, acoustic equation with a constant density field is referred to in many studies. In many cases, it may suffice to model waves appropriately. However, in reality, the density field of ground can be highly inhomogeneous. The objective is to investigate the effect of the inhomogeneity in waves, and to search for density field ρ and attenuation parameter Q as well as pressure wave velocity c using full waveform inversion. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical Calculation of Acoustic Sources for the Landing Gear of Aeroplane during Take‐off and Landing
Authors: Rašuo Boško , Jazarević Vladimir
Published: October 2015

In this paper we present Orthogonal Sub‐grid scale stabilized method with static subscales applied on turbulent flow around landing gear of aircraft during take‐off and landing. Numerical results of proposed method are compared with famous LES Smagorinsky method for turbulent flow and it is shown how obtained results affect allocation of acoustic sources and then propagation of acoustic waves in computational domain. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Calculation of the effective speed of sound in corrugated pipes by multiple scales
Authors: Russo Serena , Fabre David , Giannetti Flavio , Luchini Paolo
Published: October 2015

The flow through corrugated pipes is known to lead to strong whistling tones which may be harmful in many industrial appliances. The mechanism is known to originate from a coupling between vortex shedding at the edges of the cavities forming the wall of the tube and the acoustical modes of the pipe. The latter depend upon the effective velocity of sound ceff within the corrugated pipe. The purpose of this paper is to compute accurately this effective velocity of sound through an asymptotic calculation valid in the long‐wave limit. Results are given for a number of geometries used in previous works, and compared with a simple model in which the effective speed of sound is function of the geometry of the pipe. The latter is found to work best for short cavities but significant disagreement is found for longer cavities. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On numerical simulation of tsunami run‐up
Authors: Shokina Nina
Published: October 2015

The improved adaptive grid method is presented for the numerical modelling of propagation of long surface waves in large water areas and their interaction with coasts. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical modeling of a sub‐sonic moving load front along a rod's skin
Authors: Weber Wolfgang E. , Balzani Daniel , Fangye Yannick F. , Zastrau Bernd W.
Published: October 2015

In this contribution the dynamical behaviour of a semi‐infinite rod subjected to a longitudinal load moving along the rod's skin is investigated both analytically and numerically. By means of the analytical results the numerical model is validated and thus can be used for more advanced studies e. g. concerning dynamic fibre pull‐out phenomena. These forthcoming studies involve spatially moving boundary conditions which are also modeled within the present model in a first step. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Potential flow simulations of Peregrine‐type deep water surface gravity wave packets
Authors: Wenzel Arne , Bünte Dennis , Hoffmann Norbert P.
Published: October 2015

Applying a higher order spectral method for potential flow we numerically determine the time evolution of non‐linear deep water wave packets originating from initial conditions derived from the Peregrine breather solution of the non‐linear Schrödinger equation (NLS). The spatio‐temporal evolution of the wave packets qualitatively agrees well with what would be expected from lowest order weakly nonlinear estimates (NLS). Some quantitative discrepancies do, however, exist: The maximum wave envelope amplification appears retarded with respect to the NLS predictions. The amplification factor slightly exceeds the factor known from the NLS solution. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Laminate structures in plastic composite materials with rigid layers
Authors: Christowiak Fabian , Kreisbeck Carolin
Published: October 2015

A variational model for composite materials with rigid horizontal layers is introduced within the framework of geometrically nonlinear single‐slip plasticity. Considering the orientation of the slip system, we discuss the effective material response in the case of vanishing layer thickness and give explicit examples of possible macroscopic deformations which are realized by simple laminate constructions. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A low volume‐fraction limit for martensic microstructures in shape‐memory alloys
Authors: Diermeier Johannes
Published: October 2015

We consider a variational model for the energy of deformations of shape‐memory materials. We restrict ourselves to a scalar‐valued, two dimensional simplification with two variants of martensite in which one of the variants has a much smaller volume fraction than the other one.

We study the transition between a single phase and fine microstructures and compute the Γ‐limit for one volume fraction tending to zero. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the use of potential fields in fluid mechanics
Authors: Marner Florian , Scholle Markus
Published: October 2015

In classical fluid mechanics, potential fields have been employed to enable the integration of the equations of motion. As is well known, Bernoulli's equation is obtained as a first integral of Euler's equations in the absence of vorticity and viscosity if the velocity vector is perceived as the gradient of a scalar potential. The so‐called Clebsch transformation [1] involving three scalar potentials allows for a further extension to flows with non‐vanishing vorticity; the resulting equations turn out to be self‐adjoint, allowing for a variational formulation. All attempts in classic literature, however, are restricted to inviscid flows and the finding of a potential representation enabling the integration of the Navier‐Stokes equations remains desirable.

Progress on this topic was reported by [3, 4] who constructed a first integral of the two‐dimensional incompressible Navier‐Stokes equations by making use of an auxiliary potential field and a representation of the fields in terms of complex coordinates. The new formulation proved to be useful in numerical applications and moreover, replacing the scalar potential by a tensor potential, the theory can be successfully generalised to encompass three‐dimensional Navier‐Stokes flow.

Related to the first integral a finite element method was presented in [2] based on a formulation involving the velocities and the first order derivatives of the introduced potential. This way the dynamic boundary condition could be incorporated elegantly and the system of equations fitted into the first order system least‐squares methodology. However, a promising alternative approach results if one considers the streamfunction and a slightly modified potential field as independent variables. This new approach involves Laplacian operators rather than mixed derivatives and allows for a convenient embodiment of the Neumann conditions on the streamfunction that is in contrast to the original stream function / potential formulation [4]. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Asymptotic sampling – a tool for efficient reliability computation in high dimensions
Authors: Bucher Christian
Published: October 2015

Monte Carlo methods are most versatile regarding applications to the reliability analysis of high‐dimensional nonlinear structural systems. In addition to its versatility, the computational efficacy of Monte Carlo method is not adversely affected by the dimensionality of the problem. Crude Monte Carlo techniques, however, are very inefficient for extremely small failure probabilities such as typically required for sensitive structural systems. Therefore methods to increase the efficacy for small failure probability while keeping the adverse influence of dimensionality small are desirable.

On such method is the asymptotic sampling method. Within the framework of this method, well‐known asymptotic properties of the reliability index regarding the scaling of the basic variables are exploited to construct a regression model which allows to determine the reliability index for extremely small failure probabilities with high precision using a moderate number of Monte Carlo samples. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Uncertainty quantification for linear elastic bodies with two fluctuating input parameters
Authors: Dridger Alex , Caylak Ismail , Mahnken Rolf
Published: October 2015

In this work, we present a numerical method for solving partial differential equations (PDEs) with stochastic coefficients for a linear elastic body. To this end, a stochastic finite element method is applied. We distinguish two different cases for an isotropic material with two fluctuating input parameters in order to analyse the optimal choice of input parameters. Using the GALERKIN projection, the final stochastic equation system is reduced to a system of deterministic PDEs. Subsequently, the solution is determined iteratively. Finally, a numerical example for a plate with a ring hole is presented. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On Gaussian approximation of the strength of Daniels' bundle with brittle Weibull fibers
Authors: Sadílek Václav , Vořechovský Miroslav
Published: October 2015

The paper deals with the classical fiber bundle model with brittle Weibull fibers and equal load sharing. This model is significant for the strength of fibrous materials and composites, and the generally random strength of quasi‐brittle structures. The model is also relevant for the analysis of the reliability of various parallel systems (computer components, infrastructure etc.). An improved closed‐form Gaussian approximation of the standard deviation of bundle strength is presented and compared with accurate solution calculated by recursive formula proposed by Daniels. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Jump Phenomena and Bifurcations in Stochastic Vehicle‐Road Dynamics
Authors: Wedig Walter V.
Published: October 2015

When vehicles ride on uneven roads, they are excited to vertical random vibrations whose stationary rms‐values (root‐mean‐square) strongly depend on the velocity of the vehicle. To investigate this vibration behavior, it is appropriate to introduce road models in way domain which are based on the theory of stochastic differential equations and transformed from way to time by means of velocity‐dependent way and noise increments.

The random base excitations by roads are applied to nonlinear quarter car models. They lead to stationary rms‐values of the vertical vehicle vibrations which become resonant for critical velocities and show jump phenomena similar to those of the Duffing oscillator under harmonic excitations. In the stochastic case, jump phenomena are only observable for narrow‐banded road excitations. They vanish for increasing car damping and excitation bandwidth.

For efficient simulations of the road‐vehicle model, the n state equations are utilized to derive n(n + 1)/2 stochastic covariance equations. For small step sizes, their numerical mean square solutions coincide with the nonlinear results of fix‐point iterations obtained when the noise terms of the covariance equations are omitted. It can easily be shown, that this deterministic approach leads to the correct stationary covariances in the linear case. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
About the design of morphing airfoils under uncertainties
Authors: Fusi Francesca , Quaranta Giuseppe , Guardone Alberto , Congedo Pietro Marco
Published: October 2015

The paper presents an optimization framework for dealing with morphing airfoils for helicopter rotor blades. With regard to the morphing strategy, a conformable camber line is considered to deal with variable flow conditions encountered in forward flight with the objective of increasing the aerodynamic performance on the advancing and retreating sides of the rotor. Another peculiarity of the method is that the optimal shape is sought to be minimally sensitive to uncertainty in the operating conditions. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Optimization of the double sided spiral groove thrust bearing: A comparison to approximate analytical solutions
Authors: Lehn Andreas , Schweizer Bernhard
Published: October 2015

Reliable high performance bearings are essential in rotordynamics. As speeds and loads are continuously increased the demands on bearing technology grow simultaneously. Optimization of bearing characteristics becomes more important under these circumstances. For hydrodynamic thrust bearings, recently a special design has been presented, which is supposed to enhance the load carrying capacity by 60% compared to the best known thrust bearing type. The bearing consists of two spiral grooved surfaces and is therefore called a double sided spiral groove bearing. Early calculations of the bearing performance base on approximate analytical methods.

In order to verify those results, a detailed numerical model of the bearing is presented by the authors. With the help of a particle swarm optimization method, optimal bearing parameters are determined and a comparison is drawn to other thrust bearing designs. It is shown that previously published results overestimate the performance of the double sided spiral groove bearing severly. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)