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Kurt Magnus (1912–2003) is one of the personalities who shaped research and teaching in applied mechanics during the 20th century. Through his work with his doctoral supervisor Max Schuler at the University of Göttingen, gyrodynamics became his most important field of work, which also led to his research in oscillations, multi‐body systems, and mechatronics. Magnus made significant contributions in all these fields. He was regarded as a gifted lecturer, and the close connection between scientific research and practical application was important to him. Life and scientific work of Kurt Magnus were, however, also characterized by his 7‐year deportation to the USSR in 1946. Despite this fate, he was able to continue his research under certain restrictions during this time. After returning to Germany, he became Professor of Mechanics at the University of Stuttgart in 1958. His appointment coincided with the gradual resumption of industrial activities in Germany in the field of gyro technology—activities that had come to a standstill at the end of World War II. In the years that followed, Magnus' institute became the scientific center for gyrodynamics in Germany. The activities of that time are reflected in a preserved collection of gyro instruments for research and teaching as well as in the co‐founding of an annual international conference on inertial technology, which continues to this day. Magnus' subsequent move to the Technical University of Munich in 1966 did nothing to change this. At that time, he was regarded as a doyen of gyro technology. After a short biography of Kurt Magnus, the paper addresses the recent revision and digitization of the gyro instrument collection and presents an outline of the history of the conference series providing details on how gyro technology has developed since his work in Stuttgart. [ABSTRACT FROM AUTHOR]

The lever law of Archimedes is widely known since classical antiquity. It is used in many practical applications. Ample experience confirms its validity. Therefore, the lever law sometimes appears obvious or trivial. Its manifestation in the literature of physics ranges from common ignorance through rare marked appreciation to erroneous application of its mathematical content. Since medieval times, the groundbreaking findings of Galilei and Newton concerning the motion of bodies have shaped mechanics as an important branch of physics. On the contrary, it appears that the statics of antiquity with its essential element, the lever law, has gained less popularity despite its importance. In the following, this is demonstrated in terms of citations. For engineering mechanics, this implies to base the fundamental assumptions on the ideas of Archimedes and Newton as consistently as possible. [ABSTRACT FROM AUTHOR]

The effect of vibration on the condition of sensitive works of art continues to be of great importance to museums. Vibrations contribute to irreversible changes in the complex materiality of art and cultural heritage. In cooperation with the Klassik Stiftung Weimar, the Institute of Engineering and Computational Mechanics at the University of Stuttgart accompanied an exhibition setup. The museum and partners designed free‐standing columns in the exhibition hall to support valuable works of art. Due to their original design, these are susceptible to vibrations. Thus, the question arises as to what extent these columns should be modified in order to reduce these vibrations. In this study, measurements were taken on the floor and on the columns using a variety of measuring techniques. It was investigated which excitations from the environment propagate to the artwork. It was confirmed that vibrations from the environment, such as road traffic and museum visitors in the exhibition room, are sources of excitation. Experimental modal analysis was used to identify the characteristic vibration behaviour of these columns. By using finite element methods, a simulation model was set up allowing to investigate modifications to the columns in order to predict the change in vibration behaviour. Based on the simulation modifications, structural changes were made to the system through stiffening of individual components and redistribution of masses. [ABSTRACT FROM AUTHOR]

In this paper by Kikis et al. [[1]], on page 6, the research funding organization was not included.The correct acknowledgement should be:ACKNOWLEDGMENTThis research was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)–SFB/TRR 280. Projekt‐ID: 417002380. Open access funding enabled and organized by Projekt DEALWe apologize for this error. [Extracted from the article]

In the present study, thermally induced interlaminar crack initiation emanating from the free edge of a bi‐material junction is investigated by the example of a uniformly cooled epoxy‐glass bi‐material specimen taken from literature. For this purpose, the coupled stress and energy criterion within the framework of finite fracture mechanics is applied. Interlaminar stresses and energy dissipation due to crack onset are determined efficiently using the semi‐analytical scaled boundary finite element method (SBFEM). Moreover, the effect of the layer thicknesses on crack initiation is studied. For this purpose, dimensional analyses yield simple scaling laws for interlaminar stresses and energy dissipation with respect to the layer thickness such that only few model evaluations are required. The obtained results are compared to a finite element reference solution. For validation purposes, a cohesive zone model is applied additionally. Finally, the obtained predictions are compared to experimental findings from literature. [ABSTRACT FROM AUTHOR]

The article is an editorial from the journal PAMM, which served as the publishing platform for the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) held at Technische Universität Dresden. The conference has a long history, with the first meeting taking place in Dresden in 1925. The article highlights the strong connection between TU Dresden and GAMM, as well as the challenges faced in organizing larger meetings in recent years. The editorial expresses gratitude to the organizers and emphasizes the enthusiasm and spirit of the conference. [Extracted from the article]

Volume 21 (2021), Issue 1 of PAMM "Proceedings in Applied Mathematics and Mechanics" assembles the contributions to the 92nd Annual Meeting of the Gesellschaft für Angewandte Mathematik und Mechanik (GAMM), organized in 2021 by Universität Kassel, Germany, and held as a virtual conference. The contributions are grouped according to the minisymposia and sessions of the conference. Overview of the Sections GAMM related DFG Priority Programmes DFG‐PP 1886 Polymorphic Uncertainty Modelling for the Numerical Design of Structures DFG‐PP 1897 Calm, Smooth and Smart – Novel Approaches for Influencing Vibrations by Means of Deliberately Introduced Dissipation DFG‐PP 2020 Cyclic Deterioration of High‐Performance Concrete in an Experimental‐Virtual Lab DFG‐PP 2256 Variational Methods for Predicting Complex Phenomena in Engineering Structures and Materials Minisymposia MS 1 Computational Photonics MS 2 Symbolic computation methods for differential equations, dynamical systems, and control theory MS 4 Advanced experimental and computational techniques in polymer mechanics Sections 1–24 S1 Multi‐body dynamics S2 Biomechanics S3 Damage and fracture mechanics S4 Structural mechanics S5 Nonlinear oscillations S6 Material modelling in solid mechanics S7 Coupled problems S8 Multiscales and homogenization S9 Laminar flows and transition S10 Turbulence and reactive flows S11 Interfacial flows S12 Waves and acoustics S13 Flow control S14 Applied analysis S15 Uncertainty quantification S16 Optimization S17 Applied and numerical linear algebra S18 Numerical methods of differential equations S19 Optimization of differential equations S20 Dynamics and control S21 Mathematical signal and image processing S22 Scientific computing S24 History of mechanics Young Researchers' Minisymposia YRM1 Algorithms for coupled multi‐physics problems YRM3 Recent developments in isogeometric analysis for flow problemes YRM6 Novel discretization methods for phase‐field modeling in fracture mechanics [ABSTRACT FROM AUTHOR]

Shape optimization methods, as commonly applied in aerodynamic design applications, have recently been adapted for use in nuclear fusion divertor target design. The resulting algorithms are very efficient compared to the standard use of numerical edge plasma simulations as analysis tools only. In this paper, we highlight some numerical aspects of the underlying algorithm, focusing on a correct, nine-point discretization of the fluxes and the need for an adjoint pressure correction equation. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Data sets in high-dimensional spaces are often concentrated near low-dimensional sets. Geometric Multi-Resolution Analysis (Allard, Chen, Maggioni, 2012) was introduced as a method for approximating (in a robust, multiscale fashion) a low-dimensional set around which data may concentrated and also providing dictionary for sparse representation of the data. Moreover, the procedure is very computationally efficient. We introduce an estimator for low-dimensional sets supporting the data constructed from the GMRA approximations. We exhibit (near optimal) finite sample bounds on its performance, and demonstrate the robustness of this estimator with respect to noise and model error. In particular, our results imply that, if the data is supported on a low-dimensional manifold, the proposed sparse representations result in an error which depends only on the intrinsic dimension of the manifold. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

This contribution deals with the mathematical description and algorithmization of expert knowledge so that this expert knowledge can be used within automatic optimization procedures with a focus on the topology optimization of crashworthiness structures. Up to now, a purely mathematical topology optimization of crashworthiness structures is not possible. The reasons for that are the nonlinearities coming from the large displacements and rotations, contact phenomena and complex material behaviour (e.g. plasticity, failure and strain rate dependency). One approach to overcome these problems by using heuristics based on expert knowledge and an application example are shown in this contribution. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In the automotive industry, there is a growing demand for real-time simulation of dynamic physical models. This work investigates the capability of the parareal algorithm to meet these requirements for those physical models that are described by a system of ODEs. For this purpose, it is investigated in numerical simulations how different choices for some of the degrees of freedom arising in the implementation of parareal affect the accuracy and run time of the numerical integration in case of a benchmark task. Furthermore, the stability of the parareal scheme is investigated theoretically in case that the coarse stage uses a simplified model. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Volume 20 (2020), Issue 1 of PAMM "Proceedings in Applied Mathematics and Mechanics" assembles the contributions to the 91st Annual Meeting of the Gesellschaft für Angewandte Mathematik und Mechanik (GAMM), organized in 2020 by Universität Kassel, Germany, and held as a virtual conference. The contributions are grouped according to the minisymposia and sessions of the conference. Overview of the Sections GAMM related DFG Priority Programmes DFG‐PP 1748 Reliable Simulation Techniques in Solid Mechanics. Development of Non‐Standard Discretization Methods, Mechanical and Mathematical Analysis DFG‐PP 1881 Turbulent Superstructure DFG‐PP 1886 Polymorphic Uncertainty Modelling for the Numerical Design of Structures DFG‐PP 1897 Calm, Smooth and Smart – Novel Approaches for Influencing Vibrations by Means of Deliberately Introduced Dissipation DFG‐PP 2020 Cyclic Deterioration of High‐Performance Concrete in an Experimental‐Virtual Lab Minisymposia MS 1 Computational Photonics MS 3 Dissipativity, turnpikes and optimal control MS 4 Advanced experimental and computational techniques in polymer mechanics Sections 1–24 S1 Multi‐body dynamics S2 Biomechanics S3 Damage and fracture mechanics S4 Structural mechanics S5 Nonlinear oscillations S6 Material modelling in solid mechanics S7 Coupled problems S8 Multiscales and homogenization S9 Laminar flows and transition S10 Turbulence and reactive flows S11 Interfacial flows S12 Waves and acoustics S13 Flow control S14 Applied analysis S15 Uncertainty quantification S16 Optimization S17 Applied and numerical linear algebra S18 Numerical methods of differential equations S19 Optimization of differential equations S20 Dynamics and control S21 Mathematical signal and image processing S22 Scientific computing S24 History of mechanics Young Researchers' Minisymposia YRM1 Algorithms for coupled multi‐physics problems YRM2 Rank structured matrix and tensor techniques YRM6 Novel discretization methods for phase‐field modeling in fracture mechanics [ABSTRACT FROM AUTHOR]

Volume 21 (2021), Issue S1 of PAMM "Proceedings in Applied Mathematics and Mechanics" assembles the contributions to the 8th GAMM Juniors' Summer School (SAMM 2021) which took place from 26th to 30th July 2021 in Graz (Austria). The meeting took place in hybrid form as an in‐person meeting at Graz University of Technology and as a virtual event due to the restrictions caused by the COVID‐19 pandemic. The contributions are listed below. Shape and Topology Optimization Posters Théodore Cherrière, Luc Laurent, Sami Hlioui, François Louf, Hamid Ben Ahmed, and Mohamed GabsiMulti‐material topology optimization of a rotating electrical machine with a density‐based methoddoi:10.1002/pamm.202100259 Nico Goldammer and Kathrin WelkerOptimization on diffeological spacesdoi:10.1002/pamm.202100260 Philipp Hofer, Fabian Sturm, and Erich WehrleTopology Optimization of a Cableway Pylon with Assessment of Uncertain Loadingdoi:10.1002/pamm.202100263 Rozan Rosandi and Bernd SimeonA Hilbert space framework for sensitivity filtering and vertex morphingdoi:10.1002/pamm.202100258 Tim Suchan and Kathrin WelkerViscous energy dissipation reduction by optimization of multiple shapesdoi:10.1002/pamm.202100261 [ABSTRACT FROM AUTHOR]

Nowadays many shipyards have their own floating docks for both new buildings and repairs. In view of all the challenging projects these days, many yards have to produce designs which are close to or even beyond the structural limits of their docking facilities. This paper presents a first principle based method to calculate the key numeric values to extend the scope of application of floating docks and platforms. [ABSTRACT FROM AUTHOR]

Volume 19 (2019) of PAMM "Proceedings in Applied Mathematics and Mechanics" assembles the contributions to the 90th Annual Meeting of the Gesellschaft für Angewandte Mathematik und Mechanik (GAMM), organized on February 18–22, 2019 by Technische Universität Wien, Austria. The contributions are grouped according to the minisymposia and sessions of the conference. Overview of the Sections GAMM related DFG Priority Programmes DFG–PP 1748 Reliable Simulation Techniques in Solid Mechanics. Development of Non–Standard Discretization Methods, Mechanical and Mathematical Analysis DFG–PP 1886 Polymorphic Uncertainty Modelling for the Numerical Design of Structures DFG–PP 1897 Calm, Smooth and Smart – Novel Approaches for Influencing Vibrations by Means of Deliberately Introduced Dissipation DFG–PP 2020 Cyclic Deterioration of High–Performance Concrete in an Experimental–Virtual Lab Minisymposia MS 1 Mathematical modeling, analysis and simulation of drug distribution for efficient pharmacotherapy MS 2 Topology optimization of structures considering elaborate constraints and variables MS 3 Research software and –data: How to ensure replicability, reproducibility, and reusability MS 4 Coupled problems in rotating machinery Sections 1–24 S1 Multi‐body dynamics S2 Biomechanics S3 Damage and fracture mechanics S4 Structural mechanics S5 Nonlinear oscillations S6 Material modelling in solid mechanics S7 Coupled problems S8 Multiscales and homogenization S9 Laminar flows and transition S10 Turbulence and reactive flows S11 Interfacial flows S12 Waves and acoustics S13 Flow control S14 Applied analysis S15 Uncertainty quantification S16 Optimization S17 Applied and numerical linear algebra S18 Numerical methods of differential equations S19 Optimization of differential equations S20 Dynamics and control S21 Mathematical signal and image processing S22 Scientific computing S23 Applied operator theory S24 History of fluid mechanics and history, teaching and popularization of mathematics Young Researchers' Minisymposia YRM1 Modeling and control of Port–Hamiltonian systems YRM2 Recent advances in Galerkin methods based on polytopal meshes YRM3 Recent developments in damage mechanics YRM5 Multi–physics modeling of elastomers [ABSTRACT FROM AUTHOR]

Smart or functional materials are in focus in broad fields of recent research. In particular, electroactive polymers (EAPs) with their large actuator strains are used for innovative design in robotics. These materials become practical as soon as the material is robust, reliable and long lived. However, EAPs suffer from different types of instabilities, such as unstable thinning of actuators, local buckling induced by coexistent states and electrical breakdown. One distinguishes between structural instability, i.e. instabilities in the global structural response like buckling or wrinkling and local or material instability, e.g. the formation of microstructures and phase decompositions. These effects are well known and analyzed for purely mechanical phenomena, but not fully developed in the context of electro-mechanically coupled problems. To this end, we develop new variational-based stability criteria in finite electro-elastostatics, by postulating an electro-mechanical quasi-convexity condition for weakly convex energy and weakly convex-concave energy-enthalpy formulations. Starting from distinct variational principles, we develop criteria for local and global stability and construct stability checks, which accompany equilibrium paths for the detection of critical points in finite element models. Numerical examples validate the developed concepts for boundary value problems. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Common actuating principles e.g. solenoids or piezo-elements have mostly exploited their potential as electromechanical transducers. A new technology based on Dielectric Electro-active Polymers (DEAPs) enables major progress in efficiency and functionality for actuators. In order to use the advantages of this new technology in a feasible application, a silicone based DEAP diaphragm actuator was tested experimentally. Here, the mechanical properties of the fundamental parts of the DEAP diaphragm actuator, namely the stressstrain behaviour of an equibiaxially pre-stretched hyperelastic polymer and the mechanical response of a DEAP diaphragm actuator, were determined by appropriate test benches. The investigated DEAP diaphragm actuator consists of a dielectric, which corresponds to a thin elastic silicone film sandwiched between two compliant electrodes. Furthermore, DEAPs are pre-stretched, actually up to five times their in-plane dimensions, in order to improve their performance. In that context, the influence of the pre-stretched state on the actuator performance was investigated. In addition, a viscoelastic finite-element model of the electromechanical system has been developed and validated with the experimental results. The mechanical part of the DEAP diaphragm actuator was realized with an incompressible isotropic elastic model, whereas the electrical part was approximated with a circular parallel-plate capacitor. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The current work proposes a finite deformation strong discontinuity approach based modeling of failure in anisotropic materials with reorientation based micromechanical network model for the bulk response. These materials consist of randomly cross-linked one dimensional filaments at their microstructure which undergo non-affine deformation as well as reorientation upon loading before undergoing complete failure. The computationally efficient strong discontinuity approach allows to capture the failure kinematics by introducing a local problem where a strong discontinuity exists, thereby leading to an enhanced deformation gradient. A precise evaluation of the bulk response is done by homogenizing the physical microscopic response of constituent filaments where reorientation is introduced with an initial straightening effect of fiber undulations. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

We develop a new abstract strategy for proving ergodicity with explicit computable rate of convergence for diffusions associated with a degenerate Kolmogorov operator L. A crucial point is that the evolution operator L may have singular and nonsmooth coefficients. This allows the application of the method e.g. to the degenerate Nparticle Langevin dynamics. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Lightweight structures become more and more important and one great class within these structures are parts produced by injection moulding. To improve the mechanical properties of these parts short fibers are injected within the molten plastics. Now a way to describe these properties without knowing the fibre orientation exactly is needed. We show an intuitive way, how mechanical properties of short fibre reinforced composites for linear thermoelasticity can be described and show the relation to other approaches. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In order to simulate elastoplasticity within metal forming processes different approaches towards numerical implementation have been realized. Nevertheless, most of them or consider only the quasistatic case or use distinct time discretization schemes for the balance and the evolution equations. In the following, the effects of latter will be outlined on the basis of a numerical example exploiting a conventional ansatz towards finite elastoplasticity. This access should serve as a motivation for identifying why it is still important to investigate the implementation of elastoplastic phenomena beyond the well established methods. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Methane (CH4), which has a 25 times higher global warming potential than carbon dioxide (CO2), can be oxidated by methanotrophic bacteria into carbon dioxide and water. The biological oxidation of methane can be considered in the passive aftercare phase of landfills in order to reduce climate-damaging methane emissions. Methanotrophic bacteria are situated within the landfill cover layer and convert the harmful methane emissions arising from the degradation of organic waste to the less harmful carbon dioxide. Hence, the passive aftercare of landfills in terms of methane oxidation layers is an efficient method to reduce contributions to the greenhouse effect. To model the coupled processes during phase transition from methane to carbon dioxide, the well-known Theory of Porous Media (TPM) combined with the Mixture Theory has been used in order to develop a multi-component Finite Element calculation concept, see [1, 3]. The thermodynamic consistent model analyzes the relevant gas productions of methane, carbon dioxide and oxygen. The model also accounts for the driving phenomena of production, diffusion and advection. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In this work, a multiphase material model will be presented in order to simulate self-healing effects in a polymer. The material model is developed using the Theory of Porous Media (TPM). In order to describe the damage behavior of the polymer, the well known (1 − D)-approach is included, and for the description of the healing, a phase change between the liquid like healing agents and the solid healed material is considered. This phase change depends on the amount of catalysts inside the polymer matrix. The applicability of the developed model, in order to describe the time dependency of the healing mechanism, will be shown by a virtual experiment of a self-healing tapered double cantilever beam (TDCB). (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Surface interaction among non-overlapping bulk-fluid and porous-medium bodies occurs in different situations, e. g., the interaction of blood with a blood vessel wall, a body of water with an earth dam structure, or acoustic waves with acoustic panels used in soundproofing. These are multi-field phenomena, comprising various surface- and volume-coupling mechanisms that should be reflected in the corresponding mathematical models. These models, together with appropriate initial and boundary values, assemble a coupled problem, the solution of which reveals the behaviour of the system under external excitations. The solution is commonly done numerically, following a monolithic or a decoupled approach. Here, the focus is on the latter. To design an efficient decoupled scheme, different types of coupling within the problem are addressed. These are the volume coupling between the degrees of freedom (DOF) within each subdomain, and the surface coupling between the DOF on the common boundaries. In particular, the latter constrains the feasible space of the solution of the problem. In this regard, local Lagrange multipliers (LLM) are employed to reformulate the problem in an unconstrained form. Unlike other domain decomposition methods which are based on using global Lagrange multipliers, the LLM method yields a complete separation of the subdomains and, consequently, facilitates parallel solution of the sub-problems. Moreover, within the subdomains, the penalty method is used to decouple pressure from other DOF. This procedure, on the one hand, reduces the size of the problem that should be solved at the interface and, on the other hand, removes the burden of using mixed finite elements within the subsystems. In the next step, the stability behaviour of the resulting staggered approach is analysed, and the unconditional stability of the method is established. Finally, the method is employed to solve a benchmark example, and using the numerical results, the reliability of the outcomes of the stability analysis is investigated. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In this paper a damage model for ferroelectric materials is presented. It is implemented in terms of a user element in the commercial FEM-code Abaqus. The model is based on micromechanical considerations of domain switching and its interaction with microcrack growth and coalescence. Finite element analysis of a multilayer actuator is performed, showing principal stresses leading to crack initiation and damage of the actuator. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

A condensed model for ferroelectric solids with tetragonal unit cells is presented. The approach is microelectromechanically and physically motivated, considering discrete switching processes on the level of unit cells and quasi-continuous evolution of inelastic fields on the domain wall level. To calculate multiple grain interactions an interaction tensor is introduced. Hysteresis loops are simulated for pure electric and electromechanical loading, demonstrating e.g. the influence of a compressive preload on the poling process and interaction between statistically arranged crystallits. The residual stresses and the corresponding principle stresses are used to simulate fatigue damage in ferroelectric materials. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Dielectric elastomer actuators (DEA) are composed of a series of single cells, each one equipped with two conductive layers separated by insulating dielectric silicone. As with capacitors, when an external voltage is applied to the conductive layers, an electric field is established. Due to electrostrictive effects of the silicone, the formation of dipoles leads to a contraction of the DEA. These effects are described by the Maxwell equations, the balance of momentum and constitutive material laws. Based on a model for non-linear electroelasticity that covers the static case only, inertia terms are added in order to obtain a description of the deformation process depending on time. A potential energy function that is composed of Neo-Hooke material behaviour, electric field energy and coupling terms covers the strong formulation. Combined with the kinetic energy, a Lagrangian forms the basis in a variational setting of the model. By applying a discrete version of Hamilton's principle, a structure preserving integration scheme for DEAs is obtained. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

To model the contact behavior including dynamical effects, a two dimensional mechanical model of elastic rough contact is developed. This model can simulate the contact behaviour between two rough surfaces depending on normal pressure, sliding speed and roughness profiles. The contact between two rough surfaces is reduced to a rough rigid and a rough elastic layer. The elastic layer is modeled by point masses connected by spring-damper elements. The total system is described by coupled ODEs. The number of ODEs and thus the degree of freedom of the model depends on the varying contact conditions. The contact conditions are monitored during the simulation and the simulation interrupts, in case the contact conditions change. The equations of motion are then adapted with respect to the contact constraints. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Contact between arbitrary curved ropes and arbitrary curved rough orthotropic surfaces has been revised from the geometrical point of view. Variational equations for the equilibrium of ropes on orthotropic rough surfaces are derived, first, using the consistent variational inclusion of frictional contact constraints via Karush-Kuhn-Tucker conditions expressed in Darboux basis. Then, the systems of differential equations are derived for both statics and dynamics of ropes on a rough surface depending on the sticking-sliding condition for orthotropic Coulomb's friction. Three criteria are found to be fulfilled during the static equilibrium of a rope on a rough surface: 'no separation', condition for dragging coefficient of friction and inequality for tangential forces at the end of the rope. The limit tangential loads still preserve the famous 'Euler view' T= T0eω s for the curves and surfaces of constant curvature. It is shown that the curve of the maximum tension of a rough orthotropic surface is geodesic. Equations of motion are derived in the case if the sliding criteria is fulfilled and there is 'no separation'. Various cases possessing analytical solutions of the derived system, including Euler case and a spiral rope on a cylinder are shown as examples of application of the derived theory. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The behaviour of foams at rest, but particularly during fluid mechanical transport is not sufficiently investigated yet. The present article deals with protein foams as they have a great importance in food production. In the first part, the foaming process of a highly viscous liquid due to gaseous materials dispersed under pressure in the liquid and mass transport of volatile components dissolved in the liquid is considered. The aim is to calculate the foam volume and the concentration of the dissolved, volatile components as a function of the material and process parameters. In the second part, material equations for bubble suspensions with gas volume fractions φ ≤ 0.6 and small bubble deformations (i.e. NCa ≪ 1) are presented. The basics form two constitutive laws which are used for describing a steady shear flow. If the rates of work of the two models are compared, material equations for the shear viscosity and the normal stress differences can be derived. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

At the Helmholtz-Zentrum Dresden-Rossendorf an experimental plant is developed to investigate the formation of magnetic fields in flows of liquid metals. Because of the enormous hazard potential of the used liquid sodium it is essential to avoid any damages during operation and so a detailed analysis using the finite element method is necessary considering the various mechanical and thermal loads. Therefore several tens of thousands load cases have to be taken into account. Hence an algorithm is developed to identify the relevant stresses referring to FKM guideline which are used for the static and fatigue strength assessment. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The contact between tires and the rough road surface is characterized by large local deformations of the tread rubber at high frequency, which result from the penetration of the tread blocks by the highest asperities. These deformations have an influence on the overall performance of tires regarding rolling resistance, sustainability as well as noise radiation. As the mechanical behavior of rubber compounds is strongly rate dependent these deformations cause local energy dissipation. The induced temperature increase affects the mechanical properties of the rubber. A description of the interdependence of mechanical and thermal behavior requires the solution of a coupled problem. In this contribution the tread rubber compound is modeled with an incompressible, thermo-visco-elastic constitutive law in the regime of finite deformations taking into account internal friction and the Gough-Joule effect. The thermomechanical coupling is treated with the isothermal operator split scheme. Here, the mechanical subproblem is solved in a first phase at a constant temperature. Within this phase, the rough surface contact problem of the tread block with the road is treated. The road surface is a representation of a measured real road texture, which has been obtained by applying the fast Fourier transform. In the subsequent thermal phase the heat conduction problem is solved. Here, the mechanical dissipation within the bulk material acts as a heat source. The developed algorithm is applied for a detailed study on the thermomechanical effects occurring in the tire-road contact interface. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

A mathematical two-phase model is used to numerically investigate physical and rheological effects on small, individual bubbles in high-viscosity liquids under pressure impact. It is found out that bubbles remain stable over time at high viscosity and surface tension. The steady case is considered and connected to the stability behavior of the bubble. An upper bound for the bubble radius is derived and the new equilibrium state of the bubble can be predicted by means of stability theorems of differential equations. Finally, the interaction of a limited number of well separated bubbles in an Hele-Shaw flow is mathematically analyzed to visualize and physically interpret their trajectories. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

This contribution deals with the modelling and simulation of curing phenomena in adhesively bonded piezo metal composites which consists of a piezoelectric module enclosed by an adhesive layer which in turn is surrounded by two metal sheets. A short survey on the neccessary experimental investigations to characterise the adhesive's material behaviour is given and important aspects on the corresponding phenomenological modelling approach are presented. Both steps take into account the curing reaction, changes of volume, like chemical shrinkage, and inelastic mechanical behaviour which is temperature and curing dependent. Finally, the simulation strategy for the modelling within a finite element environment is depicted. By this, residual stresses, secondary deformations and loads on the piezo modules can be predicted, which is exemplified by a comparative study verifying a novel manufacturing strategy. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Elastic stress state of a thick-walled cylindrical panel, which is subjected to a positive temperature gradient in the radial direction, is investigated under generalized plane strain conditions. In particular, the stress distributions in the panel at the elastic limit according to von Mises' yield criterion are studied. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Linear time-periodic systems arise whenever a nonlinear system is linearized about a periodic trajectory. Stability of the solution may be proven by rigorous bounds on the solution. The key idea of this paper is to derive Chebyshev projection bounds on the original system by solving an approximated system. Depending on the smoothness of the original function, we formulate two upper bounds. The theoretical results are illustrated and compared to trigonometric spline bounds by means of two examples which include an anisotropic rotor-bearing system. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In the present work, we discuss the benefits, limitations and restrictions for the high order phase fitted variational integrators, derived specifically for the numerical integration of systems with oscillatory solutions. To do that, we study linear stability properties of these methods using the eigenvalues of the amplification matrix. The obtained stability region verifies their good behavior, when used for the numerical solution of highly oscillatory problems. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In order to carry out a preliminary axial fan design, established assumptions are made onto the flow structure within the fan at the design point. As an example the very common hypothesis of radial equilibrium, states that the radial velocity component downstream the fan is zero, and that the flow in this area is axisymmetric. With the help of this hypothesis, the flow is idealized in order to draw quantitative conclusions. The present communication aims at extending these assumptions on the whole flow regime in order to help fan designers to reduce the try-and-error cycle number. An analytical formulation for axial fan velocity distributions at design and off design conditions is proposed for an arbitrary work distribution. It is shown that the total pressure characteristics can be described by means of hyperbola and straight line. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

During chip formation in turning processes, mechanical work is dissipated into thermal energy by plastic deformations and frictional processes. In case of dry cutting, the generated heat is in part removed with the chips while the rest flows into the tool and the workpiece. Within the latter, the temperature increases due to this heat flow, which in turn causes thermal expansions that increase the cutting depth and thus induce deviations from the nominal workpiece geometry. These effects are treated separately by a local model for the chip formation and a global model for the whole workpiece in order to determine the temperature distribution inside the workpiece and the dependent thermal expansion. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The detection of singular points of DAEs is a challenging task, which has not been sufficiently considered so far. Combining automatic differentiation (AD) with the projector based analysis of DAEs, it becomes possible to monitor singularities while integrating the DAE. In this brief outline we restrict our considerations to linear DAEs. The corresponding treatment of nonlinear DAEs is based on linearization and can be found in the cited literature. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Modelling physical systems with fast moving components leads to PDEs with highly oscillatory sources. Often, the time scale of the oscillation is much below the scale of the interesting variables. Time integrators must follow the scale of the fast motion, leading to long simulation times. For mechanical systems, methods like heterogeneous multiscaling and stroboscopic averaging are quite satisfactory. In case of semidiscretized PDEs, their advantage is limited. Here, we derive a smooth source term which generates a solution that coincides with the solution of the oscillatory system in stroboscopic points. The derivation involves the solution of a linear system with the solution operator of the PDE being the linear operator. Several preconditioners are developed and compared for those systems. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Sheet and bulk metal forming are widely used manufacturing methods. The interaction between worktool and workpiece in such a process causes friction which has a remarkable impact on the expended energy of the process. Therefore the influence of friction is important. Friction can be split into shearing and ploughing [1]. Ploughing is the plastic deformation of a soft surface by a hard contact partner. Shear forces are only transferred in the real contact area where material contact occurs. The investigation of the contribution of both ploughing and shearing to the total friction resistance is done with the use of an elasto-plastic halfspace model. The multiscale character of surfaces demands a fine discretization, which results in numerical effort. While a finite element method takes into account both surface and bulk of the contact partners, the halfspace model only regards the contact surfaces and thereby consumes less computing capacity. In order to identify the friction resistance, two rough surfaces get into contact. After full application of the normal load, the surfaces are moved relatively to each other. New asperities of the contact surfaces get into contact and are plastically deformed. These deformations are used to estimate the ploughing effect in dependency on the relative displacement. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The aim of this paper is to present the available modeling strategy available for description of the packaging behavior, which often takes place in the foams. The packaging process is modeled by means of approaches, which are used in the phase transformation theory. The constitutive model is based on the double-well elastic potential, which is defined for small strains. Two principal approaches are used for the research: discrete method based on the Voronoi tessellation and phase-field method. Discrete modeling approach is required for the estimations of the critical stresses in foams, which leads to the initiation of the packaging process. The phase-field approach is the continual approach, which is required for description of the packaging propagation in the foam. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Split-explicit Runge-Kutta methods provide an efficient integration procedure for hyperbolic systems with coupled slow and fast wave phenomena. They are generalized to multirate infinitesimal step methods (MIS) in order to develop an order to provide order conditions and to establish stability properties. The construction of MIS methods is based on an underlying Runge-Kutta method. This method is choosen to be total variation diminishing (TVD) to improve the stability properties of the method. Here, the maximum Courant number is improved by a factor of 4. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The present work deals with the solution of geometrically nonlinear elastic problems solved by the least-squares finite element method (LSFEM). The main goal is to obtain an improved performance and an accurate approximation in particular for lower-order elements. Basis for the mixed element is a first-order stress-displacement formulation resulting from a classical least-squares method. Similar to the ideas in SCHWARZ ET AL. [1] a modified weak form is derived by the introduction of an additional term controlling the stress symmetry condition. The approximation of the unknowns follows the same procedures as for a conventional least-squares method, see e.g. CAI & STARKE [2]. The proposed modified formulation is compared to recently developed classical LSFEMs, in order to show the improvement of performance and accuracy. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

The present work investigates a reliable method of integrating the evolution equations of constitutive models for amorphous thermoplastics that typically utilize a power-law or exponential-type flow rule. When it comes to sudden changes in the external stress (e.g. element deletion technique in explicit finite element analysis) these functional dependencies need a special treatment to assure a numerically stable integration of the evolution equations. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Important industrial rubber components like tyres, driving belts and air springs are usually reinforced by twisted polymer cords. A cord itself is a twisted structure of several multifilament yarns. Each yarn is a twisted strand consisting of a large number of polymer filaments. In this work, an anisotropic large strain plasticity model is presented which captures the yarn's filament structure and frictional behaviour. The material model is implemented in Abaqus adopting its user subroutine UMAT and validated by a simulation of a cord's twisting process and the comparison with microscope images. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

We prove, that a Hamiltonian with infinitely many δ-point interactions in the plane can be approximated in the norm resolvent sense by a family of Schrödinger operators with regular, local scaled short-range potentials. Similar well known results from the 1D and the 3D case are complemented thereby. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]