bluuebunny/crossref_metadata_2025 huggingface dataset:
Stress analysis of a circular hole in an orthotropic plate with finite width using complex potential method
Authors: Nguyen-Hoang Minh , Becker Wilfried
Published: December 2021

Open holes are essential design features in technical structures. However, stress concentrations arise and for a safe and lightweight optimal design, precise stress analysis means are crucial. Scope of this paper is the stress field determination of an open hole in an orthotropic rectangular plate of finite width using complex potential method. To derive results of high precision, the stress boundary conditions at the straight edges as well as along the hole boundary need to be fulfilled. In doing so, the stress field of the corresponding infinite‐dimensions problem is supplemented with auxiliary functions, which are based on a novel periodic arrangement technique and enable to take into account the stress‐free straight edges of the finite‐domain problem.
Parameter identification aspects of tribological systems containing hard particles
Authors: Bilz Raphael , Sridhar Praveen , de Payrebrune Kristin M.
Published: December 2021

Tribological systems are often characterized based on time‐averaged quantities such as wear rates, friction coefficients and material properties. It is well known that some tribological metrics show variations depending on the laboratory conducting the study and the reproduction method selected. Perhaps the key to overcome this problem is to avoid a strong compression of the information generated. In this context, the arising forces and the coefficient of friction in three‐body wear systems are investigated in more detail. The mean value of a time series of these physical quantities is only a single property and by no means an exhaustive description. A more detailed consideration of the variances could be a necessary condition to allow an appropriate comparison of tribological parameters and a correct interpretation of the properties of tribological systems. For this purpose, we examine two very simple tribological systems exemplarily and take a closer look at the properties of some characteristic process quantities.
A robust hybrid‐element family for strongly compressed hyperelastic materials
Authors: Schneider Patrick , Schönherr Josef Arthur , Mittelstedt Christian
Published: December 2021

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

In general, the numerical ill‐posedness of irreducible (purely displacement‐based) finite element formulations for quasi‐incompressible materials demands for a hybrid/mixed finite element implementation. State of the art hybrid/mixed‐elements still suffer from numerical stability issues that can be greatly amplified by the usage of nonlinear compression models.

In the talk, a robust hybrid‐element family is introduced that can readily be used in combination with any isotropic, invariant‐based hyperelastic material model. The mesh convergence behavior and the numerical stability of the new element family are assessed by benchmark testing and compared to classical Simo‐Taylor‐Pister (STP) elements as well as the hybrid‐element family (C3D8H, C3D20H, C3D10H) implemented in the commercial finite element code Abaqus Standard, Simulia (Dassault Systèmes). The presented finite element family is free of volumetric locking and more robust than STP or Abaqus hybrid‐elements, especially in combination with strongly nonlinear compression models.
Intermittent chaotic flows in the weakly magnetised spherical Couette system
Authors: Garcia Ferran , Seilmayer Martin , Giesecke André , Stefani Frank
Published: December 2021

Experiments on the magnetised spherical Couette system are presently being carried out at Helmholtz‐Zentrum Dresden‐Rossendorf (HZDR). A liquid metal (GaInSn) is confined within two differentially rotating spheres and exposed to a magnetic field parallel to the axis of rotation. Intermittent chaotic flows, corresponding to the radial jet instability, are described. The relation of these chaotic flows with unstable regular (periodic and quasiperiodic) solutions obtained at the same range of parameters is investigated.
An embedded domain method for non‐linear structural membranes
Authors: Fries Thomas-Peter , Schöllhammer Daniel
Published: December 2021

An embedded domain method for structural membranes in large displacement theory is outlined. The membrane is immersed in a three‐dimensional background mesh with level‐set data at the nodes. The mechanical model for the implicitly defined membrane is formulated using the Tangential Differential Calculus (TDC). The embedded domain method has to properly consider the numerical integration and boundary conditions within the background elements cut by the membrane. Furthermore, stabilization is required to address linear dependencies and conditioning issues.
Structural design of additively manufactured porous Zr‐based bulk metallic glass
Authors: Shi Jianye , Ma Songyun , Markert Bernd
Published: December 2021

Recently, designing light‐weight BMGs with high‐strength has attracted much attention. Additive manufacturing (3D‐printing) using selective laser melting (SLM) enables the production of porous bulk metallic glasses (BMGs), which is difficult to achieve by applying traditional manufacturing techniques. In this study, different porous structural prototypes of 3D‐printed Zr‐based BMGs are comparatively studied. Main focus is put on the strength optimization by varying pore arrangement and pore morphology. A constitutive model based on Mohr‐Coulomb theory with multi‐slips system is applied to describe the shear banding behaviors of 3D‐printed amorphous BMGs.
Constitutive modeling of viscoplasticity including phase transformations for graded thermo‐mechanical processing
Authors: Westermann Hendrik , Reitz Alexander , Mahnken Rolf , Grydin Olexandr , Schaper Mirko
Published: December 2021

Tailored materials are of particular interest in modern engineering applications due to their potentially high strength and residual ductility. During hot forming processes, such as press hardening, microstructure transformations in low carbon steels are considered to achieve the production of tailored components. The relevant microstructure mechanisms during thermo‐mechanical processing are visco‐plastic deformation and phase transformations. Thus, we present an extension to an existing thermodynamically consistent continuum mechanical model. The evolution of phase transformations under inhomogeneous temperature loading in a homogeneous tensile specimen are illustrated.
Back Calculation of Internal Forces of Concrete Skyscrapers by means of In Situ Monitoring
Authors: Müllner Herbert W. , Wallisch Wolfgang , Kremnitzer Peter
Published: December 2021

The static design of skyscrapers is mostly based on Finite Element calculations of the supporting structure whereas 3d calculations are required to consider the influence of horizontal forces such as wind loads and earthquake, respectively. In addition 2d calculations are performed to determine unfavorable internal force variables of carrying elements such as columns and walls, respectively. Nevertheless the comparison of these calculations of the same building shows differences up to 100 percent depending on the height of the building. To minimize these differences a research project in cooperation with Vienna University of Technology has started.
A remeshing approach for the finite cell method applied to problems with large deformations
Authors: Garhuom Wadhah , Hubrich Simeon , Radtke Lars , Düster Alexander
Published: December 2021

The finite cell method (FCM) is based on an immersed boundary concept with high‐order finite elements. When solving nonlinear problems using the FCM, it is often difficult to reach to the desired load step because of the large distortion of the mesh, particularly when badly broken cells are existing in the mesh. To overcome this problem, a global remeshing strategy is proposed to allow the nonlinear computation to proceed even for very large deformations where the distortion of the cells becomes significant. The core concept is to perform a computation up to a specific deformation state where the distortion of the cells becomes significant. Then, to continue the analysis, a new mesh is introduced. The performance of the proposed method is illustrated using two numerical examples of hyperelasticity.
Influence of passive mechanical properties in healthy and infarcted rat myocardium on the cardiac cycle
Authors: Martonová Denisa , Alkassar Muhannad , Seufert Julia , Holz David , Tuan Duong Minh , Reischl Barbara , Friedrich Oliver , Leyendecker Sigrid
Published: December 2021

Passive mechanics plays an important role during the electromechanically coupled cardiac cycle and its behaviour strongly changes after myocardial infarction. In the present work, the cardiac tissue is modelled as a mixture of an active orthotropic intact myocardium and a passive transversely isotropic fibrotic scar structure. We apply the constitutive model on the fully electromechanically coupled simulation of a cardiac cycle using a generic geometry of a rat left ventricle. Finally, the ejection fractions for various parameter sets based on the fitting to experimental data in different animal species as well as for a varying amount of fibrosis are compared. We show that both, the choice of species‐specific passive material parameters and the amount of fibrosis, have a significant influence on the cardiac performance measured by the ejection fraction of the left ventricle.
Design improvement by a simulative investigation of the locomotion of a snake‐like soft robot
Authors: Lamping Frederik , de Payrebrune Kristin M.
Published: December 2021

This work aims to improve the design of a snake‐like soft robot in terms of its velocity of locomotion by a geometric model. Therefore, we determine the locomotion of the snake‐like soft robot as the result of a given excitation curvature and a given friction anisotropy between the robot and the ground.

Varying the design parameters of the robot in the model allows to identify important parameters to increase the velocity of locomotion of the snake‐like soft robot. Whereas its body design is sufficient, the transverse friction of its artificial skin is the main parameter to be improved. The transverse friction can be adjusted by turning the scales of the artificial skin. The velocity of locomotion of the robot increases significantly by this simple trick.
Experimental Approach on Lamb Wave Dispersion Diagrams Using 2D Fourier Transformation and Laser Vibrometry
Authors: Barth Tilmann , Lammering Rolf
Published: December 2021

Lamb wave based Structural Health Monitoring (SHM) is a well‐known approach in today's mechanical engineering [1, 2]. One possible approach to determine the behavior of Lamb waves experimentally lies in the use of a frequency‐based approach using a 2d Fourier transform (2d‐FT) [3–5]. A closer look at this approach reveals that it has been used to represent dispersion relationships in large frequency ranges, but its potential for high accuracy has not been fully exploited. In this work a measurement and evaluation system for the experimental determination of dispersion diagrams is developed. It is able to cover large frequency ranges and it additionally shows a high degree of automation and accuracy. This allows a broadband examination of influences, which have only a small effect on the wave propagation. To verify the accuracy of the developed measurement and data evaluation method, experimental results of an aluminum specimen are compared with those from analytical solutions. A good agreement is achieved.
Reduced Flow Model for Plastics Melt Inside an Extrusion Die
Authors: Key Fabian , Ballarin Francesco , Eusterholz Sebastian , Elgeti Stefanie , Rozza Gianluigi
Published: December 2021

In this work, we study the application of Model Order Reduction (MOR) to the flow of plastics melt in an extrusion die. The process is described with a non‐linear model consisting of the Stokes equations in combination with a shear‐thinning material model. The reduction is performed through a Proper Orthogonal Decomposition (POD) approach with subsequent projection. We perform an a‐posteriori error analysis for a quantity of interest, based on the full‐ and reduced‐order solutions. Finally, we explore the computational speedup to prove the aptitude of the reduced model in the context of many‐query scenarios.
Integral‐type non‐local damage simulation of composites using mean‐field homogenization methods
Authors: Lenz Peter , Mahnken Rolf
Published: December 2021

This paper deals with non‐local damage behaviour of composites subjected to eigenstrains. Examples for eigenstrains are thermal, chemical or plastic strains and any combination. Modern materials are often decomposed into several distinct materials, e.g. some reinforcements and a matrix material. A manufacturing process for these modern materials often induces eigenstrains, reversible and non reversible. The induced eigenstrains could lead to an initial damage. It is known that damage leads to mesh dependent simulation results. Therefore, non‐local integral‐type damage for multiphase composites subjected to eigenstrains is considered.
Asymptotically Justified Boundary Conditions for a Viscoelastic Two‐Phase Fiber Model
Authors: Ettmüller Manuel , Arne Walter , Marheineke Nicole , Wegener Raimund
Published: December 2021

In this work we present asymptotically justified boundary/interface conditions for a viscoelastic two‐phase fiber model with flow‐enhanced crystallization. While the model equations are well‐established in the literature, the choice of boundary conditions is still under discussion as they might cause artificial layering at the crystallization onset. We show that our conditions avoid such layering, yielding a regularly perturbed boundary value problem with either continuous or discontiunous interface.
A semi‐analytical approach for the efficient predicition of thermally induced interface crack initiation at bi‐material free edges
Authors: Dölling Sebastian , Bremm Sophia , Kohlstetter Alexander , Felger Julian , Becker Wilfried
Published: December 2021

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.
An extended version of the Intermediate Axis Theorem for a freely rotating rigid body
Authors: Leine Remco , Capobianco Giuseppe
Published: December 2021

Current numerical schemes for 3D rockfall simulation are not able to correctly represent the stability properties of a freely rotating body. Here, we give a proof using Lyapunov functions of an extended intermediate axis theorem, which not only involves the angular momentum equations but also the orientation of the body. Inspired by the stability proof, we present a novel scheme which respects the stability properties of a freely rotating body and which can be incorporated in numerical schemes for the simulation of rigid bodies with frictional unilateral constraints.
Reanalysis of structures with varying cross‐sectional values based on influence functions
Authors: Carl Oliver , Hartmann Friedel , Zhang Chuanzeng
Published: December 2021

Digital building data models are increasingly employed in the design and construction planning of buildings, so that almost the entire planning process is covered with three‐dimensional (3D) models. Starting with available detailed CAD data it is easy to generate 3D models for the design analysis. However, this comes with a price since the complexity of the 3D models requires a high computational effort. Considering the fact that the structural engineer often must investigate numerous design variants and system modifications during the planning stage to reach an optimal solution it makes sense to facilitate the multitude of these recalculations by an easy‐to‐use reanalysis technique.

The approximation method we use for reanalysis is referred to as the Sensitivity Analysis with Green's functions (SAGF). The basic principles of the SAGF method can be found in [2,3]. It can be used very advantageously for reanalysis purposes, especially in the presence of complex computational models, and allows for a quick comparison of different design variants. In this paper, the method is used to determine how the system responses (internal forces, displacements) are affected by local changes in the stiffness of frame elements as they are typical for modifications of cross‐sectional values in steel structures such as when haunches are added at nodes.

In [1] Abdank already presented an approach to determine the changes in structural response of beams from the subsequent consideration of haunches without performing a complete recalculation. In comparison to this, the presented SAGF method is applied very beneficially in connection with 3D models.

Furthermore a 2D implementation of the presented reanalysis technique can be found in the program BE‐FRAMES [4]. It allows for a fast and simple “one‐click”‐reanalysis of various design variants since the designer can traverse the different designs forward and backwards – in a blink of an eye, with simple mouse clicks. An additional benefit is that the program can display influence functions for any displacement and force component so that with this graphical tool the engineer can predict the effects of design changes quite easily.
Learning Mechanical Systems by Hamiltonian Neural Networks
Authors: Dierkes Eva , Flaßkamp Kathrin
Published: December 2021

The great success of machine learning in image processing and related fields also motivated its application to dynamical system identification. In particular, neural networks are trained to learn equations of motion and thus provide an alternative to first‐principle modeling. While these black‐box algorithms are quite flexible regarding the system structure, they often have difficulties in learning basic physics laws which are intrinsic system properties. Recently, Hamiltonian neural networks (HNN) were introduced to explicitly learn the total energy of a system in order to overcome the lack of physical rules. However, Hamiltonian systems often also contain other structures such as symmetries in terms of further invariances. In this contribution, we extend HNN such they respect system invariances in addition to the Hamiltonian. The proposed extension leads to a trade off between energy conservation and conservation of invariance properties, which we investigate exemplarily.
Development of Fibrous SF/PCL Tympanic Membrane Scaffolds via Electrospinning: Modeling and Experimental Verification
Authors: Chen Zhaoyu , Benecke Lukas , Graetz Jonas , Hümbert Martina , Bornitz Matthias , Aibibu Dilbar , Cherif Chokri , Neudert Marcus
Published: December 2021

The ideal tympanic membrane (TM) replacement should meet the requirement of low resistance for dynamic pressures up to about 1 Pa but high resistance for large static pressures up to about 5 kPa. Although electrospun membranes have a great potential to be used as a TM replacement, it is necessary to adjust its microstructure in order to mimic the acousto‐mechanical properties of human TM. Hence, in this work, homogenization modeling and FEM simulation of the middle ear were used to combine the microstructure of electrospun membranes to its macroscale function as TM scaffolds. The simulation results were finally verified with experimental data.
Passage through resonance of two coupled exciters
Authors: Yüzbasioglu Tunc , Fidlin Alexander
Published: December 2021

A minimal model of two coupled exciters is considered to investigate passage through resonance of self‐synchronizing systems. An averaging method for partially strongly damped systems [1] is used for asymptotic analysis. Stationary solutions of the system is derived and compared with previous work [2]. The dependency of such solutions on damping and excitation power is shown.
Study on model reduction for position optimization of acoustic black holes
Authors: Meyer Christian H. , Lerch Christopher , Rothe Sebastian , Hoffmann Steffen , Langer Sabine C. , Lohmann Boris , Rixen Daniel J.
Published: December 2021

Noise radiation of plate structures is a common problem with the design of machines in mechanical engineering. Noise can be reduced by designing passive damping measures. One of these measures can be the application of an ‘acoustic black hole’ (ABH). It is a targeted adaptation of the thickness of plate‐like structures to direct the acoustically critical bending waves to a certain region – the ABH. There, an applied damping material can dissipate the vibration energy very efficiently. A major challenge in design of this measure is to find an optimal position of the ABH with respect to low vibrations. Optimization can be a tedious task, especially for complex industrial geometries where the dicretized equations of motion can have millions DoF.

This contribution shows on the example of a study on a rectangular plate how model reduction can help to reduce the computational costs for this position optimization. Three different reduction methods are shown: First, a condensation of internal state variables from the viscoelastic evolution equations via Schur complement. Second, modal truncation applied to the condensed equations from the first method and third, moment matching applied to the full order model. Computed mean squared‐admittance levels are compared to show the accuracy of the methods. Speed‐up and accuracy results show that Schur complement and moment matching are promising approaches while a naive modal truncation can lead to wrong results.
Unique identification of stiffness parameters for nonlinear, anisotropic textile fabrics based on full‐field measurements on a single experiment
Authors: Makhool Lubna , Balzani Daniel
Published: December 2021

This work discusses a hybrid experimental‐numerical framework by which the stiffness parameters for nonlinear anisotropic textile fabrics can be uniquely identified. In the experimental part, a non‐standard setup has been designed to activate the deformation modes in a free energy function describing the mechanical material behavior. As a result, one inhomogeneous deformation field is captured by means of measuring full‐field kinematics, which includes sufficient information regarding the nonlinear response for varying deformation modes and intensities. In the numerical part, the measured full‐field data are inserted into a suitable discretized model of the specimen. Reformulating the free energy function to be linear in material parameters is considered in order to enable the definition of a quadratic objective function in terms of differences of discrete internal and external forces and hence to assure the uniqueness of the parameter identification. Finally, the sensitivity of the method to noisy data is studied.
Influence of Residual Stresses and Fiber Orientation on Smooth Muscle Contraction in Arterial Walls
Authors: Uhlmann Klemens , Balzani Daniel
Published: December 2021

In this contribution, we present a combined material model which couples three aspects of the arterial wall: a smooth muscle model embracing a stretch‐dependent calcium function, residual stresses induced by growth, and fiber reorientation. The model enables the investigation of the respective influence of all three aspects on each other. For this purpose, simulation results of arterial rings under varying intravascular pressure are analyzed.
On the forward simulation and cost functions for the ultrasonic material characterization of polymers
Authors: Itner Dominik , Gravenkamp Hauke , Dreiling Dmitrij , Feldmann Nadine , Henning Bernd , Birk Carolin
Published: December 2021

In this contribution, we describe the identification of the elastic properties of polymers in use‐specific setups, in particular the high‐frequency behavior (compared to quasi‐static or low‐frequency behavior that is usually characterized). Such a parameter search can be expressed as an inverse problem by comparing experimental measurements with adequate simulated data. We employ an axisymmetric scaled boundary finite element formulation to model the propagation of ultrasonic guided waves through cylindrical polymeric samples as the so‐called forward model of an optimization procedure. The simulated dynamic response is compared to a reference signal, and gradient descent‐based optimization is used to find the best possible material parameter fit. We present a cost function based on the wavelet convolution that results in a locally convex cost surface well suited for gradient descent optimization.
Stochastic modeling of transient neutral and stably‐stratified Ekman boundary layers
Authors: Klein Marten , Maier Roland Erich , Schmidt Heiko
Published: December 2021

Neutral and stably‐stratified Ekman boundary layers (EBLs) are numerically investigated with a stochastic one‐dimensional turbulence (ODT) model. EBLs achieve the bulk‐surface coupling in Earth's atmosphere. They are numerically challenging due to transient and non‐universal turbulence properties even at small scales. ODT addresses this problem by distinguishing turbulent‐advective from molecular‐diffusive transport processes for a vertical column along which all relevant scales of the flow are resolved. We demonstrate the model's capabilities for economical, accurate, and stratification regime independent simulation of EBLs for the wind‐turning angle. ODT reproduces and extrapolates reference direct numerical simulation results consistent with observations. We conclude that ODT may be useful for modeling of atmospheric surface layers.
Nonlinear vibrations of rotating rings and shells under the usage of the finite element method
Authors: Schmidt Rico , Ams Alfons
Published: December 2021

Until now several studies of rotating structures like rings or shells have been done. To model such problems in a right way, geometrical nonlinearity has to be considered. Different methods can be used, to solve the corresponding eigenvalue problem. In this article the focus will be placed on the finite element method.

In contrast to flat elements curved ones can cause some numerical inconveniences. They include a tremendous loss of convergence on the one hand, on the other hand the appearance of zero energy modes. In addition, centrifugal and Coriolis effects have to be taken into account. For certain examples the results of different FE‐models are shown and compared with global approaches as well as measurement data.
Phase field modeling and simulation of the evolution of twelve crystallographic martensite variants in austenitic parent grains – three‐dimensional simulations
Authors: Graf Marius , Kuntz Matthias , Autenrieth Hermann , Diewald Felix , Müller Ralf
Published: December 2021

Due to its outstanding strength martensitic microstructures are of great importance in steels. Accordingly, this work deals with a simulation model capable of simulating the evolution of the martensitic microstructure. The focus is on the consideration of twelve crystallographic martensite variants corresponding to the Nishiyama‐Wassermann orientation relationship. For this, the phase field method, which regularizes sharp interfaces as smooth transition zone on basis of order parameters is used. The order parameters are used to interpolate between the initial parent phase austenite and the final product phase martensite. The evolution of a martensitic microstructure initiated by a supercooling under isothermal conditions is considered. In order to define the displacive characteristics of the martensite variants, the well‐known phenomenological theory of martensite crystallography is deployed. Three‐dimensional simulations using the finite element method in the small strain context show the applicability of the model to polycrystalline structures.
Variational Settings and Domain Decomposition Based Solution Schemes for a Coupled Deformation‐Diffusion Problem
Authors: Kiefer Björn , Prüger Stefan , Rheinbach Oliver , Röver Friederike , Roth Stephan
Published: December 2021

Our general goal is to study chemo‐mechanical problems at various length scales by means of a fully‐integrated approach in terms of a co‐design of variational formulations and tailored parallel solvers. Based on prior experience in electro‐magneto‐mechanics [1], we know that the advantages and disadvantages of different variational settings for such coupled problems is always multifaceted. Theoretical characteristics, physical interpretability and numerical aspects may even play competing roles in this regard. In this work, we particularly consider the swelling of hydrogels as a first model problem featuring finite deformation coupled to the diffusive solute transport. The 3D finite‐element simulation of a free‐swelling cube under solute flux control is studied as a representative numerical example. As a first step towards seamless integration, we discuss the implementation of the hyperelastic subproblem into the open source finite element library deal.II which directly interfaces with the Fast and Robust Overlapping Schwarz (FROSch) preconditioner. Using this environment, an additional numerical study is performed with respect to the scaling behavior of the finite deformation Neo‐Hookean model in parallel computations.
Differentially definable functions: a survey
Authors: Jiménez-Pastor Antonio , Pillwein Veronika
Published: December 2021

Most widely used special functions, such as orthogonal polynomials, Bessel functions, Airy functions, etc., are defined as solutions to differential equations with polynomial coefficients. This class of functions is referred to as D‐finite functions. There are many symbolic algorithms (and implementations thereof) to operate with these objects exactly. Recently, we have extended this notion to a more general class that also allows for good symbolic handling: differentially definable functions. In this paper, we give an overview on what is currently known about this new class.
On a tangential‐conforming finite element formulation for the relaxed micromorphic model in 2D
Authors: Sarhil Mohammad , Scheunemann Lisa , Neff Patrizio , Schröder Jörg
Published: December 2021

The relaxed micromorphic model is a generalized continuum model that reduces the complexity of the general micromorphic theory [1] and shows many advantages such as the bounded stiffness for small sizes [2–4]. It keeps the full kinematics of the micromorphic theory but employs the matrix Curl operator of a second‐order micro‐distortion field for the curvature measurement. The solution of the micro‐distortion exists in H(curl) while the displacement is still in H1. In this work, we introduce an H1 × H(curl) finite element formulation of the relaxed micromorphic model. The presented mixed formulation satisfies the tangential continuity of the micro‐distortion field on the element boundaries. We compare the convergence behavior of the mixed formulation with the classical H1 × H1 finite element formulation using numerical examples. Finally, we show the model's main characteristics and the scale‐dependency of the model's components where the relaxed micromorphic model gives the different Cauchy elastic limit cases with determined elasticity tensors.
Semi‐automated Data‐driven FE Mesh Generation and Inverse Parameter Identification for a Multiscale and Multiphase Model of Function‐Perfusion Processes in the Liver
Authors: Lambers Lena , Mielke André , Ricken Tim
Published: December 2021

Biomechanical modeling enables a better understanding and prediction of various processes in the human body. To make this simulation more patient‐specific, realistic geometries of liver lobules are included in an existing knowledge‐based model for the simulation of hepatic function‐perfusion processes in the human liver. This model allows the simulation of liver diseases such as the non‐alcoholic fatty liver disease (NAFLD) or tumor development. The basis of this calculation is a continuum‐biomechanical multiscale and multiphase model based on the Theory of Porous Media. To capture the function‐perfusion and growth processes in the liver, partial differential equations (PDEs) on the lobule scale are coupled to ordinary differential equations (ODEs) describing metabolic processes on the cellular scale. Additionally, we used manifold learning techniques on in silico data for the identification of inverted fat zonation during NAFLD.
A comparative study of FE‐schemes for micromagnetic simulations
Authors: Reichel Maximilian , Xu Bai-Xiang , Schröder Jörg
Published: December 2021

With ongoing development of new technological devices, the demand for efficient magnetic materials and composites has significantly increased. Micromagnetic simulations can predict the magnetization distribution on sub micrometer scales. Due to performance purposes these simulations are often run on finite differences schemes. In contrast to the finite differences method, finite element based micromagnetic simulations posses high flexibility with geometry. One key aspect is the accurate discretization of geometrical structures, representing a big advantage in the analysis of complex microstructures. To describe the evolution of the magnetization vector the Landau‐Lifshitz‐Gilbert (LLG) equation is applied. A central point of the latter equation is the preservation of the Euclidean norm on the magnetization vector through the simulation. In this contribution first results of comparisons of different micromagnetic simulations are presented.
Work‐conjugacy of stress and strain tensors and its role in 3D hyperelastic isotropic material formulation
Authors: Dutzler Andreas , Guggenberger Werner
Published: December 2021

In accordance with the framework of hyperelastic isotropic material description it appears possible to replace work‐conjugate stress and strain quantities by alternative pairs of work‐conjugate stress and strain quantities while other things left unaltered, i.e. based on a retained architecture of the strain energy density function. This replacement results in formally representing different kinds of material response behavior. This may be recognized from the various comparable forms of resulting uniaxial force versus axial stretch behavior in the representative 3D principal axes system. Clarifying and achieving comprehensive understanding of these observations is the main purpose of this paper.
Numerical investigation of the Poisson's ratio of an amorphous bilayer 2D network material
Authors: Stratmann Jan , Bamer Franz , Kataria Satender , Lemme Max Christian , Markert Bernd
Published: December 2021

This paper investigates the transverse contraction of amorphous bilayer 2D Silica with varying network heterogeneities under uniaxial tensile loading using athermal molecular simulations in LAMMPS. It turns out that the transverse contraction increases nonlinearly with the x‐strain while it decreases with increasing network heterogeneity. We show that it is possible to engineer the heterogeneity of amorphous network materials, making them potential candidates for nano‐electromechanical applications.
On the inverse Cauchy problem for linear ordinary differential equations
Authors: Chartouny Maya , Cluzeau Thomas , Quadrat Alban
Published: December 2021

The Cauchy problem characterizes the solutions of a linear ordinary differential equation that satisfies initial conditions. In this paper, we investigate the converse problem, namely, given a function that is known to satisfy a linear ordinary differential equation of a fixed order, determine the coefficients of the ordinary differential equation and the initial conditions. The techniques used to investigate the inverse Cauchy problem come from the algebraic estimation problem introduced by Fliess and Sira‐Ramírez. From the perfect observation of the solution, i.e., without external perturbation and noise corrupting it, the initial value problem can be explicitly reconstructed using only iterative indefinite integrals of the solution.
Darcy's law for evolving microstructure
Authors: Wiedemann David , Peter Malte A.
Published: December 2021

A Darcy law for evolving microstructure is derived by homogenisation of Stokes flow. We transform the Stokes equations from the locally evolving domain onto a periodic reference domain. There, we pass to the homogenisation limit by employing the method of two‐scale convergence. After transforming the limit back to its original two‐scale domain, we obtain a Darcy Law for evolving microstructure. This Darcy Law does not only capture the space‐ and time‐dependent permeability, but also includes how the change of the porosity induces pressure. In order to give uniform a priori estimates, we derive a Korn‐type inequality for this two‐scale transformation method as well as a family of ϵ‐scaled operators div−1ϵ.
Applicability of the lead field approach in virtual laboratory studies: comparison with full numerical simulations based on the bidomain model
Authors: Ogiermann Dennis , Perotti Luigi E. , Balzani Daniel
Published: December 2021

The lead field approach is likely the most widely adopted method to compute electrocardiograms (ECGs) from electrophysiology (EP) simulations. Since this approach introduces several simplifying assumptions, this raises the question of its applicability in laboratory scenarios. Laboratory experiments can be used to validate and calibrate EP models by utilizing, amongst other techniques, unipolar and/or bipolar pseudo‐ECG measurements, which therefore need to be computed accurately. In this work, we present a computational study within a previously proposed validation framework based on the Antzelevitch's laboratory model of transmural wedges. In order to investigate the applicability of the lead field approach in this scenario, the unipolar and bipolar measurements computed from bidomain simulations are compared with measurements obtained with the lead field approach. Our study suggests that unipolar measurements are not well captured by the lead field approach, while bipolar measurements obtained with the lead field approach exhibit reasonable qualitative agreement with measurements computed from full bidomain simulations.
Experiments, hyperelastic modeling and finite element simulation of 3D‐printed thermoplastic polyurethane
Authors: Landgraf Ralf , Oelsch Erik , Steiniger Vincent , Ihlemann Jörn
Published: December 2021

A combined experimental and numerical investigation on the mechanical behavior of 3D‐printed thermoplastic polyurethane is presented. In particular, the behavior under monotonic loading until rupture is considered. For this purpose, tensile test specimens are analyzed, which were produced by conventional injection molding and by an extrusion‐based additive manufacturing process. The additively manufactured test specimens have notched surfaces that influence the failure behavior due to stress and strain concentrations. For the numerical analysis, a finite element modeling approach is presented with which the experiments are simulated. It is shown that the tensile curves can be simulated using a hyperelastic material model and that first indicators can be found that enable a prediction of failure under monotonic tensile loading.
FFT‐based homogenization using a reduced set of frequencies and a clustered microstructure
Authors: Waimann Johanna , Gierden Christian , Schmidt Annika , Svendsen Bob , Reese Stefanie
Published: December 2021

To capture the material behavior of composite microstructures, Moulinec and Suquet [5] proposed a homogenization scheme making use of fast Fourier transforms (FFT) and fixed‐point iterations. To reduce the computational effort of this spectral method, Kochmann et al. [3] introduced a model order reduction technique, which is based on using a fixed reduced set of frequencies for the computations in Fourier space. Within the current work, we improved the accuracy of the approach by use of a geometrically adapted set of frequencies, see [1]. Since the constitutive relations are still evaluated in real space, the technique is most beneficial for a linear material behavior. Considering nonlinear material behavior, most of the computing time is related to solving the constitutive relations. Therefore, the total speed‐up is lower. To achieve a further reduction of the computational effort for a nonlinear material behavior, the earlier proposed model order reduction technique is coupled with a clustering analysis [4]. The whole microstructure is thus divided into clusters, which show a similar material behavior. Within these clusters, the micromechanical fields are assumed to be constant which leads to a significant reduction of computational costs compared to the highly resolved solution.
On computing reduced‐order bilinear models from time‐domain data
Authors: Gosea Ion Victor , Karachalios Dimitrios S. , Antoulas Athanasios C.
Published: December 2021

We propose a procedure for identification of reduced‐order bilinear models from time‐domain data, i.e., sampled values of the control input and of the observed output. To accomplish this, we require two sets of data corresponding to the response of the system to two differently‐scaled step functions, as control inputs. Then, the Markov parameters for two time‐varying linear models are extracted, and from this information, we are able to infer a reduced‐order bilinear model.
Selected historical aspects of wave phenomena in the context of dynamical systems, and applications in seamless learning
Authors: Gunesch Roland
Published: December 2021

This article gives an overview of a few selected historical examples of the mathematical investigation of wave phenomena, ranging from one of the earliest cases of the systematic study of periodic oscillations to modern mathematical methods and various applications. Hooke's analysis of the mass‐spring problem, population dynamics with periodic behavior, and chemical oscillations are discussed. Many examples of real‐world wave phenomena from everyday life are also mentioned.

I also explain a few aspects and ideas of the modern method of teaching the underlying science of wave dynamics to a general audience with the help of easily accessible computer‐based tools (an example of seamless learning).
Thin film nanocomposites from a novel poly(keto ether sulfone) to remove metal ions from wastewater
Authors: Mehdipour‐Ataei Shahram , Babanzadeh Samal , Khodami Samaneh
Published: December 2021

According to the clean water crisis, purification of water resources is so imperative. Reverse osmosis is the best method for the purification of wastewater. In this article, a new diol and resulting poly(keto ether sulfone) was synthesized and characterized successively. Innovative nanocomposites were prepared with the novel poly(keto ether sulfone) and various nanomaterials including clay, graphene oxide, multi‐walled carbon nanotube, and sepiolite. Polydopamine (PDA) was used to modify the hydrophilic nature of the nanoparticles surface. Thin‐film nanocomposites as reverse osmosis membranes were made by depositing of polyamide on the mentioned nanocomposites and investigated for removing metal ions like Cu (II), Co (II), Cr (II), Hg (II), Ni (II), Zn (II), and Pb (II) from water. The efficiency of membranes constructing from pristine poly(keto ether sulfone) and different nanocomposites as supporting layer of thin‐film nanocomposite were compared. The prepared membrane based on PDA‐modified MWCNT showed the best performance results including pure water flux of 215 L.m−2.h−1 and rejection of 98% for Cr (II).
Poly(ε‐caprolactone)/montmorillonite nanocomposites via Diels–Alder click reaction
Authors: Ozdogan Tasci Reyhan , Arslan Mehmet , Tasdelen Mehmet Atilla
Published: December 2021

Synthesis of nanocomposites by employing inorganic materials as nanofillers is one of the most effective ways to improve the mechanical and thermal properties of conventional polymers. To design and create new nanomaterials with unprecedented functional attributes, the fabrication techniques and chemistries employed often have utmost importance to attain a better structure–property relationship. In this respect, click chemistry‐based functional methodologies hold great promise in the fabrication of polymeric nanocomposites due to their excellent features. In this contribution, poly(ε‐caprolactone)/clay nanocomposites were prepared by Diels–Alder (DA) click reaction of maleimide end‐group containing poly(ε‐caprolactone) and furan functionalized montmorillonite (MMT). The methodology includes furan modification of MMT clay and ring‐opening polymerization of ε‐caprolactone that was initiated with a masked maleimide group containing alcohol and following retro DA reaction to obtain maleimide end group functional poly(ε‐caprolactone). Subsequently, polymer nanocomposites were efficiently fabricated via DA click reaction of functional poly(ε‐caprolactone) polymer and modified clay in thermal heating conditions at 80°C. The characterization of poly(ε‐caprolactone)/clay nanocomposites was carried out by thermogravimetric analysis, Fourier transform‐infrared spectroscopy, X‐ray diffraction spectroscopy, and transmission electron microscopy. Obtained results demonstrated that DA click reaction can be fruitfully employed in the fabrication of MMT‐based polymeric nanocomposites.
Screening for borderline personality pathology on college campuses
Authors: Cano Kiana , Sumlin Eric , Sharp Carla
Published: December 2021

Although borderline symptoms show a normative decline throughout adulthood, severe psychosocial impairment often remains. Identifying personality pathology in college‐age students may help prevent “adaptive failure” that can occur during the critical period of development from puberty through the late 20s and thus reduce impairment later in life. The aims of the current study were to estimate the prevalence of borderline personality disorder (BPD) in a diverse college sample, determine which symptoms confer the greatest relative risk of screening positive for BPD and examine the utility of the Personality Inventory for DSM‐5 brief form (PID‐5‐BF) in identifying BPD. Participants were 1456 undergraduate students, and 312 individuals (21.4% of the sample) screened positive for BPD. Chronic feelings of emptiness conferred the greatest relative risk of any symptom; students who endorsed this symptom were 15 times more likely to screen positive for BPD than those who did not. Scales and composite scores of the PID‐5‐BF demonstrated diagnostic accuracy ranging from sufficient to excellent. The current study contributes to literature concerning best practices in screening for personality pathology in young adults. Results suggest that chronic feelings of emptiness are significant for detecting at‐risk students and implications for the use of the PID‐5‐BF are discussed.