Documents published in Scipedia

• Simulation of phase transformations in polycrystalline shape memory alloys using fast Fourier transforms

  J. Waimann, C. Gierden, S. Reese

  eccomas2022.

  
  

  Abstract

  The properties of shape memory alloys (SMA) are mainly influenced by phase transformations between austenite and martensite. The complex material behavior is described by a variational method which describes the evolution of the phase fractions. We combined the method with a microstructural analysis based on fast Fourier transformations. Such a highly resolved microstructural analysis comes along with a high computational effort.To reduce the later one, we propose a model order reduction technique that uses just a reduced set of Fourier modes, which is adapted to the underlying microstructure. The presentation of the theoretical background as well as of the implemented algorithm is followed by numerical results that underline the performance of our method.

  Abstract
  The properties of shape memory alloys (SMA) are mainly influenced by phase transformations between austenite and martensite. The complex material behavior is described by [...]

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• Using a reduced set of Fourier modes in terms of a FFT-based microstructure simulation

  C. Gierden, J. Waimann, B. Svendsen, S. Reese

  eccomas2022.

  
  

  Abstract

  Given a heterogeneous material, the mechanical behavior of its microstructure can be investigated by an algorithm that uses the Fourier representation of the Lippmann-Schwinger equation. Incorporating a model order reduction technique based on calculations with a reduced set of Fourier modes, the computational cost of this algorithm can be decreased. It was shown that the accuracy of this model order reduction technique strongly depends on the choice of Fourier modes by considering a geometrically adapted rather than a fixed sampling pattern to define the reduced set of Fourier modes. Since it is difficult to define a geometrically adapted sampling pattern for complex microstructures, additionally a strain-based sampling pattern was introduced. The accuracy and adaptability of this strain-based reduced set of Fourier modes is shown by incorporating a polycrystalline microstructure.

  Abstract
  Given a heterogeneous material, the mechanical behavior of its microstructure can be investigated by an algorithm that uses the Fourier representation of the Lippmann-Schwinger [...]

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• Fast and simple creation of powder beds for selective laser melting

  L. Luberto, K. de Payrebrune

  eccomas2022.

  
  

  Abstract

  In selective laser melting, components are produced by layer-by-layer melting of a powder bed. To investigate the interaction between the powder bed and the laser energy in the process, it is necessary to generate different powder bed configurations with a defined particle size distribution. For this purpose, based on different particle contact approaches, a simple algorithm for planar particle bed configurations was developed in the Julia programming language. Based on the so called 0and 1-particle-contact approaches, a monodisperse sphere packing with a filling ratio of up to 64%, and with a normally distributed particle size with a filling ratio of up to 67% were generated. With the 0-particle-contact approach, the individual powder beds could be generated more quickly, but showed an insufficient degree of filling. In contrast, the 1-particle-contact approach can produce powder beds realistically. An extension for spatial problems, as well as variations in the contact approaches, is given by the simple algorithm design and shall be implemented and further investigated in simulations of selective laser melting.

  Abstract
  In selective laser melting, components are produced by layer-by-layer melting of a powder bed. To investigate the interaction between the powder bed and the laser energy in [...]

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• Efficient assessment of noise transmission through highly flexible slender structures

  F. Schneider-Jung, L. Burger, J. Linn

  eccomas2022.

  
  

  Abstract

  In this work, we propose an efficient methodology for the assessment of noise transmission through cables and hoses. An interactive simulation with a geometrically exact Cosserat rod enables simple and fast modelling of various configurations. Subsequently, we linearise the equations of motion at the static equilibrium for given boundary conditions and, using the resulting system matrices, compute the mechanical impedance matrix. The computation result, i.e. the impedance matrix, is available within seconds. The impedance matrix either can be used to compute reaction forces for given excitation or, if the excitation is unknown, allows to analyse the transmission of noise by looking at single matrix elements. The latter is especially useful in early, purely virtual development phases.

  Abstract
  In this work, we propose an efficient methodology for the assessment of noise transmission through cables and hoses. An interactive simulation with a geometrically exact Cosserat [...]

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• Homogenization of the constitutive properties of composite beam cross-sections

  M. Stavole, R. Sato, M. Lohk, S. Leyendecker

  eccomas2022.

  
  

  Abstract

  When modelling slender bodies made of composite materials as beams, homogenized stiffness coefficients must be obtained. In [2, 3], analytic expressions for these are obtained by comparing the solutions of some Saint-Venant extension, bending and torsion 3D linear elasticity problems with their corresponding beam theory counterparts. In [2], the authors provide general expressions for the determination of these coefficients for multilayered beams. The present work consists in the study of a homogenization procedure of the stiffness coefficients for circular cross-sections with two layers. This will help in the study of the constitutive behavior of unloaded shafts of endoscopes since their cross-section could be studied as a simplified model of a three-layers hollow circular cross-section. In preparation of this geometry, results of an experimental campaign carried out at KARL STORZ GmbH & Co. KG (Tallinn, Estonia) are presented in a second part of this paper. The purpose of the testing was the experimental characterization of the torsional stiffness of such devices.

  Abstract
  When modelling slender bodies made of composite materials as beams, homogenized stiffness coefficients must be obtained. In [2, 3], analytic expressions for these are obtained [...]

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• Modeling the Effective Inelastic Behavior of Multi-Wire Cables Under Mechanical Load Using Finite Elements

  M. Hawwash, V. Dörlich, J. Linn, R. Keller, R. Müller

  eccomas2022.

  
  

  Abstract

  In the development and manufacturing process of modern cars, cables and hoses are important system components. In automotive industry, virtual assembly planning and digital validation of system layouts require a fast and physically correct simulation of the mechanical behavior of cables and hoses. The mechanical response of cable systems and hoses under load is typically non-linear and inelastic due to their multi-component structure. However, those effects can hardly be observed and investigated separately in experiments. Thus, the authors recently presented simplified cable models using the commercial finite element tool ANSYS which take wire interactions into account. As cables in automotive applications are often subject to large deformations, finite beam elements with quadratic shape functions were used to discretize the single helix wires. The comparison of simulation results obtained for helix wire strands under bending with analytical results based on wire rope theory showed good agreement for the case of frictionless interactions. Furthermore, the modeling approach serves as a versatile toolbox for the investigation of material and structural inelastic effects which commonly occur when cables are deformed. A significant influence of structural parameters, such as the helix angle of the wires or the choice of friction model parameters, on the mechanical response could be found. In this work, this modeling approach is applied to the simulation of multi-wire strands consisting of parallel elastic wires under bending and torsion. The results of these mesoscopic simulations will be compared to experimental results.

  Abstract
  In the development and manufacturing process of modern cars, cables and hoses are important system components. In automotive industry, virtual assembly planning and digital [...]

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• Estimating stress fluctuations in polycrystals with an improved maximum entropy method

  M. Krause, T. Böhlke

  eccomas2022.

  
  

  Abstract

  The prediction of local field statistics from effective properties is an open problem in the field of micromechanics. Partial information on the local field statistics is accessible from homogenization assumptions. In particular, exact phase-wise second moments of stresses can be calculated analytically from the effective strain energy density. In recent years, full-field calculations have become efficient enough to sample large ensembles of microstructures in the plastic regime (e.g. Gehrig et. al [4]). In the present work, the maximum entropy method known from statistical thermodynamics is used to estimate first and second moments of local stresses from known eigenstrain distributions. The simple and refined formulations of the maximum entropy method proposed by Kreher and Pompe [9] are considered. While the simple method yields satisfactory results for a large amount of material classes (cf. Krause and Böhlke [7]), we prove that it does not respect the linearity of the eigenstrain problem. We further show that neither method corresponds to the exact second moments of stresses known from the effective strain energy density. By incorporating additional information, we find an improved maximum entropy method. As an example, we analyze stress fluctuations in polycristalline titanium.For the exact analytical solution and the maximum entropy methods, we use the singular approximation and the Hashin-Shtrikman bounds. For comparison, we numerically approximate full-field statistics using an FFT approach. In all methods, the stress fluctuations caused by the anisotropy of the single crystal strongly influence the elastic-plastic transition.

  Abstract
  The prediction of local field statistics from effective properties is an open problem in the field of micromechanics. Partial information on the local field statistics is [...]

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• Quantifying errors due to the Hertzian contact model in multi-sphere Discrete Element Modelling simulations

  S. Constandinou, J. Blackford, K. Hanley

  eccomas2022.

  
  

  Abstract

  In Discrete Element Modelling (DEM), non-spherical particles are often emulated using clusters of rigidly connected spheres that can be either overlapping or not. Within this multi-spherical approach, two sources of error directly affecting the normal contact forces present can be identified. One is due to the difference between the true particle shape and the multispherical approximation; the other arises from the contact model used in the DEM simulations. The potential for inaccuracy in multi-sphere DEM simulations is well known. However, for a DEM simulator it remains unclear what error might be expected when multi-sphere particles are adopted. This contribution focuses on the role of the contact model as a source of error for the special case of two-sphere particles. Considering a single multi-spherical rod consisting of two identical spheres and quasi-statically compressing it until a total of 5% strain has been applied, the force response obtained through Finite Element Analysis (FEA) was compared against the Hertzian contact model. The process was repeated for spheres with varying degrees of overlap, ranging from 0 to 100%, and the relative errors of the FEA models against the Hertzian contact model were calculated. Up to a 60% sphere overlap, Hertz underpredicts the normal contact forces beyond 0.5% strain, where the disparity between the FEA model and Hertz forces is increasing monotonically with strain. However, beyond an overlap of 70%, Hertz overpredicts the normal contact forces with the sphere overlap being the main driver of this deviation. Future research will involve comparing these errors with the `shape' source of error by compressing perfect spherocylinders, considering rods composed of more spheres, and investigating how the error is affected by the relative orientation of two contacting particles.

  Abstract
  In Discrete Element Modelling (DEM), non-spherical particles are often emulated using clusters of rigidly connected spheres that can be either overlapping or not. Within this [...]

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• Simulating Nonlinear Elastic Behaviour of Cables Using an Iterative Method

  T. Zhao, F. Schneider-Jung, J. Linn, R. Müller

  eccomas2022.

  
  

  Abstract

  This contribution introduces a novel approach to simulate the nonlinear elastic bending behaviour of cables. Bending tests on real cables with complex structures clearly show the existence of nonlinear constitutive bending behaviour. In our current framework, only constant effective stiffness parameters are used. In order to enable nonlinear bending behaviour within the current framework, we propose an iterative method where, at each step, constant stiffness parameters are used and are updated according to the current cable state. The presented method is demonstrated by means of numerical experiments. Moreover, the inverse problem, i.e. the determination of state-dependent bending stiffness characteristic, is considered.

  Abstract
  This contribution introduces a novel approach to simulate the nonlinear elastic bending behaviour of cables. Bending tests on real cables with complex structures clearly show [...]

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• Director-based IGA beam elements for sliding contact problems

  P. Wasmer, P. Betsch

  eccomas2022.

  
  

  Abstract

  The geometrically exact beam theory is one of the most prominent non-linear beam models. It can be used to simulate aerial runways or pantograph-catenaries, where a sliding contact condition between two or more beams is used. A smooth discretization of at least C1continuity is needed to not introduce any unphysical kinks. This can be achieved using the isogeometric analysis, which we apply to a director-based formulation of the geometrically exact beam. For a stable time integration scheme we use an energy-momentum conserving scheme. Using the notion of the discrete gradient, an energy-momentum conserving algorithm is constructed, including the case of sliding contact between beams.

  Abstract
  The geometrically exact beam theory is one of the most prominent non-linear beam models. It can be used to simulate aerial runways or pantograph-catenaries, where a sliding [...]

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