bluuebunny/crossref_metadata_2025_split huggingface dataset:
Generative adversarial networks for three‐dimensional microstructure generation
Authors: Henkes Alexander , Wessels Henning 
Published: March 2023

AbstractMultiscale simulations are demanding in terms of computational resources. In the context of continuum micromechanics, the multiscale problem arises from the need of inferring macroscopic material parameters from the microscale. If the underlying microstructure is explicitly given by means of µCT‐scans, convolutional neural networks can be used to learn the microstructure‐property mapping, which is usually obtained from computational homogenization. The convolutional neural network (CNN) approach provides a significant speedup, especially in the context of heterogeneous or functionally graded materials. Another application is uncertainty quantification, where many expensive evaluations are required. However, one bottleneck of this approach is the large number of training microstructures needed.This work closes this gap by proposing a generative adversarial network tailored towards three‐dimensional microstructure generation. The lightweight algorithm is able to learn the underlying properties of the material from a single µCT‐scan without the need of explicit descriptors. During prediction time, the network can produce unique three‐dimensional microstructures with the same properties of the original data in a fraction of seconds and at consistently high quality.
A first analysis of possible elementary causes of self‐excited vibrations in roller coaster rides
Authors: Zamora Agustí Marc Guillem , Kecskeméthy Andrés 
Published: March 2023

AbstractThe emergence of vibrations during a roller coaster ride is a recurring phenomenon that can deteriorate the overall experience and accelerate material fatigue. Nevertheless, the causes of such vibrations are still not completely understood and are consequently not fully predictable during the design process. One possible source lies on the irregularities of the rails, acting as a forced external excitation. However, a spectral analysis shows deviations with respect to real measurements [1], as the frequencies are not synchronous with the car velocity divided by the spatial irregularity period. Therefore, there is an indication that the vibrations may be due to self‐excitation and/or that the developed models should consider other phenomena not yet contemplated. This investigation analyses –for the first time to the knowledge of the authors– the plausibility of various causes of self‐excited vibrations during a roller coaster car motion. Given the complex structure of a real roller coaster train and the intricate geometry of the track, the study considers as a first step minimal dynamical models running along a straight track. The cause analyzed in this paper is the contribution of the transversal friction force component that develops in the wheel‐rail contact interface to the destabilization of the longitudinal motion, as well as the effect of the various geometrical and inertial parameters. In this first analysis, no external excitation is considered. For a range of parameters, the minimal system presents a Hopf bifurcation. The results are plausible from the general behavior and thus this cause may be retained as a candidate for the real vibrations occurring in roller coasters. However, the applicability of these preliminary results to general roller coaster motions is not yet confirmed, but a superposition with other causalities may render effective. In further investigations, a complete train motion on curved tracks and external perturbations will be studied to determine the share of the different causes.
A finite strain gradient theory for viscoplasticity by means of micromorphic regularization
Authors: Hamdoun Ayoub , Mahnken Rolf 
Published: March 2023

AbstractStretching of polycarbonate films leads to the formation of shear bands in the necking zone [1]. Standard viscoplastic material models render mesh size dependent results, which requires a mathematical regularization. To this end, we present a finite strain gradient theory for a viscoplastic, isotropic material model where we extend the model presented in [2] to a micromorphic model by introducing a new micromorphic variable as an additional degree of freedom with its first gradient [3, 4]. The variable here has the meaning of a micro plastic strain, and is coupled with the macro plastic by a micro penalty term, forcing the macro‐plastic strain to be close to the micro‐plastic strain for the targeted shear band regularization effect. We have implemented the model equations as a three dimensional initial boundary value problem in an in house FE‐tool, to simulate different geometries with different thickness and to compare it the experimental tests. The analysis is performed for a uniaxial tensile geometry as well as for a biaxial tensile geometry. The numerical examples show the ability of the model to regularize the shear bands and solve the problem of localization.
Modelling and simulation of time‐dependent damage and failure within silicone‐based, polymeric adhesives
Authors: Lamm Lukas , Pfeifer Jan Mirco , Holthusen Hagen , Brepols Tim , Reese Stefanie 
Published: March 2023

AbstractHyperelastic adhesive joints are used successfully in many areas of industry. Besides all their inherent advantages, materials used for the construction of such bonds show a vast variety of non‐linear effects in their response to mechanical loading, which poses a challenge in modelling and predicting their material response. Recent experiments have shown a strong temporal response when it comes to damage and failure within these materials. This contribution aims to propose a simple but yet flexible formulation to predict time‐dependent damage effects within polymeric adhesives. Besides the main aspects of the thermodynamically consistent development, we also show numerical examples to demonstrate the capabilities of the model.
A Stability Analysis of Modified Patankar–Runge–Kutta methods for a nonlinear Production–Destruction System
Authors: Izgin Thomas , Kopecz Stefan , Meister Andreas 
Published: March 2023

AbstractModified Patankar–Runge–Kutta (MPRK) methods preserve the positivity as well as conservativity of a production–destruction system (PDS) of ordinary differential equations for all time step sizes. As a result, higher order MPRK schemes do not belong to the class of general linear methods, i. e. the iterates are generated by a nonlinear map g even when the PDS is linear. Moreover, due to the conservativity of the method, the map g possesses non‐hyperbolic fixed points.Recently, a new theorem for the investigation of stability properties of non‐hyperbolic fixed points of a nonlinear iteration map was developed. We apply this theorem to understand the stability properties of a family of second order MPRK methods when applied to a nonlinear PDS of ordinary differential equations. It is shown that the fixed points are stable for all time step sizes and members of the MPRK family. Finally, experiments are presented to numerically support the theoretical claims.
Computing tensor operator exponentials within low‐rank tensor formats with application to the parameter‐dependent multigrid method
Authors: Grasedyck Lars , Werthmann Tim A. 
Published: March 2023

AbstractUncertainties in physical models can lead to parameter‐dependent linear systems. The representation and solution of these systems are an important task in numerical mathematics. We summarize our previous results on how to represent these systems using low‐rank tensor methods and how to solve these systems using the parameter‐dependent multigrid method. We propose a new approach to compute the tensor operator exponential, by which we mean the matrix exponential applied to a tensor operator, directly within low‐rank tensor formats. This approach is based on classical matrix methods combined with low‐rank arithmetic. The tensor operator exponential within a low‐rank tensor format is used to approximate the inverse diagonal of a low‐rank operator. This approximation is then used as Jacobi smoother for the parameter‐dependent multigrid method. Using this we observe in numerical experiments a grid size independent convergence rate of the multigrid method. Instead of inverting only diagonals of tensor operators, our approach also allows for the inversion of all symmetric positive definite tensor operators.
Topology optimisation of lattice structures to increase damping
Authors: Daniel Christian , Woschke Elmar 
Published: March 2023

AbstractLattice structures are lattice‐like assemblies that are inspired by organic systems. The structure inside is made up of cells whose edges form rod‐shaped elements. The size of the cells and the dimensions of the rods can influence the mechanical properties of the entire structure. For the use of lattice structures within engineering applications, stiffness and damping are important parameters. In monolithic designs, the outer contour or the material itself must be modified to change the stiffness and damping. In the case of a lattice structure, moreover, the structure of the inner cells can be adapted, resulting in greater flexibility [1]. Numerical simulations of the structural dynamic behavior will be used to optimize the damping, while heuristic methods are applied to account for the large parameter space. To adjust the simulation model, the damping is measured frequency‐dependent on a real structure which is subsequently used for model adjustment.
Cohesive failure modeling based on the phase‐field approach
Authors: Yin Bo , Zhao Dong , Kaliske Michael 
Published: March 2023

AbstractRegarding resolving the crack‐induced strong discontinuity problems, e.g., crack faces separating, contact and friction, the recent established approach based on the Representative Crack Element (RCE) framework is developed to describe a robust crack kinematics or crack deformation. The work at hand presents cohesive fracture by elaborating phase‐field modeling within the RCE approach. It constitutes a classical traction‐separation exhibition at the crack faces of the RCE. As such, a phenomenological cohesive adhesion in the RCE can be modeled. In the sequel, the overall material status is interpolated by an intact material state (continuous description) and a fully broken state (RCE description) using the phase‐field degradation function. This allows not only to model a cohesive debonding failure for tensile and shearing deformation, but also to yield an expected contact algorithm when the crack is closing. Furthermore, the unknown crack deformations are solved according to virtual power principle, which provides a consistent framework for the comprehensive constitutive laws of this model.
A path‐independent domain integral to characterize fatigue crack propagation by cyclic material forces
Authors: Khodor Jad , Kaliske Michael 
Published: March 2023

AbstractA lot of structures undergoing cyclic loading fail at load values smaller than their ultimate design loads. In the framework of fracture mechanics, the crack propagation process can be separated into three different stages. In the first stage, micro‐cracks propagate and form together a macro‐crack. The macro‐crack propagates stably in the second stage, which is also known as the PARIS' regime. In the third stage, the crack propagates unstably leading to the failure of the structure. The pioneering law characterizing the stable crack growth is PARIS' law. The aforementioned law correlates the crack growth rate to the cyclic stress intensity factor. Unfortunately, the cyclic stress intensity factor is limited to cases where the theory of linear elastic fracture mechanics is applicable. To overcome the limitations of the cyclic stress intensity factor, domain‐integrals evaluated by configurational forces or material forces are used as a fatigue crack growth criterion. However, the aforementioned domain‐integrals are path‐dependent. The aim of the study at hand is to derive a path‐independent domain integral to characterize fatigue crack propagation in elastic‐plastic and linear viscoelastic solids at small strains. First of all, the cyclic material forces are derived using the cyclic free energy. Furthermore, the path‐independence of the cyclic material forces approach is illustrated by numerical examples. Finally, the cyclic material force approach is validated by comparing it to experimental results.
Strategies for Finding Training Snapshots for the Hyperreduction Method ECSW in Magnetodynamic Systems
Authors: Maierhofer Johannes , Rixen Daniel J. 
Published: March 2023

AbstractModel order reduction for nonlinear magnetodynamic systems can be approached, using hyperreduction methods such as DEIM and ECSW. Typical for this methods is the data‐driven approach. Therefore, the full order model has to be solved several times to generate a sufficient data basis to extract all the necessary information for the reduced order model.Hyperreduction is a two step process. First, a new (much smaller) solution space needs to be found where the model is projected into without significant loss of information. Second, a subset of elements has to be chosen and weighted such that the hyperreduced model preserves the result in an appropriate manner.This contribution focuses on the Energy Conserving Sampling and Weighting (ECSW) method and shows different heuristic strategies to find appropriate training snapshots.
Application of the Coupled Eulerian Lagrangian method to the prediction of single‐grain cutting forces in grinding
Authors: Furlan Tim , Tsagkir Dereli Tountzer , Schmidt Nils , Biermann Dirk , Menzel Andreas 
Published: March 2023

AbstractContinuous technological advancements in the field of grinding technology and improved grinding tools have contributed to the development of high performance grinding processes. One example of such a process is internal traverse grinding (ITG) with electroplated cBN grinding wheels, where the tool consists of a conical roughing zone and a cylindrical finishing zone. Since the tool is fed in axial direction into a revolving workpiece, spindle deflections induced by varying process forces can lead to contour errors along the bore. Numerical simulations are a valuable tool to overcome the challenges associated with such high performance processes. Whenever spindle deflections need to be considered, accurate prediction of the process forces is paramount. Finite Element (FE) simulations have been widely used for the prediction of forces in cutting processes such as turning and milling, where only a small number of active cutting edges is considered, and where the geometry of these cutting edges is clearly defined. Grinding tools, on the other hand, contain a large number of grains with varying geometric characteristics. We recently proposed a multi‐scale simulation system for the simulation of ITG processes, where a geometric kinematic grinding simulation, based on a database of digitalised grains of a real grinding wheel, was used to determine the grain engagements [1]. The process forces were obtained from summation of the contributions of all active grains at any given time, based on a force model on the individual grain level. The force model takes the material removal rate and an approximation of the rake angle into account, and was calibrated via finite element simulations.In recent years, the Coupled Eulerian Lagrangian method (CEL), which is part of the commercial finite element software Abaqus, has been applied to simulate various cutting processes. No remeshing is necessary in this framework, and separation of chips from the workpiece can be modelled without element deletion. The application of CEL to the simulation of single grain cutting is therefore a promising approach to further improve the force model included in the process simulation of ITG. In this work, the kinematics of ITG are incorporated into a single grain cutting simulation, and the suitability of the CEL method for the problem is evaluated with a focus on the chip formation, separation and self‐contact between the chip and the workpiece.
Sparse super resolution and its trigonometric approximation in the p‐Wasserstein distance
Authors: Catala Paul , Hockmann Mathias , Kunis Stefan 
Published: March 2023

AbstractWe consider the approximation of measures by trigonometric polynomials with respect to the p‐Wasserstein distance for general p ≥ 1. While the best approximation error decreases inversely with the polynomial degree n for every p, convolution with the Fejér kernel achieves just a 𝒪(n−1/p) rate if p > 1. Near best are approximations by convolution of the measure with higher powers of the Fejer kernel or the de la Vallée‐Poussin kernel. Finally, we consider the pointwise approximation of trigonometric polynomials interpolating the value one at the support of atomic measures.
On the dynamic simulation of viscoelastic structures with random material properties using time‐separated stochastic mechanics
Authors: Geisler Hendrik , Nagel Jan , Junker Philipp 
Published: March 2023

AbstractSimulating stochastic structures with inelastic material behavior is often done with Monte Carlo simulations. The method is robust but needs a huge computational effort. We propose a new approach for the dynamic simulation of viscoelastic stochastic structures with a computational effort in the magnitude of one deterministic simulation. It is based on a separation of the viscous evolution equation in time‐dependent but deterministic and stochastic but time‐independent terms. We present the calculation of the effective quantities as stresses and reaction forces with the time‐separated stochastic mechanics. Numerical experiments showcase the high approximation quality compared to reference Monte Carlo simulations.
Mechanical modeling of the maturation process for textile reinforced tissue‐engineered heart valves
Authors: Sesa Mahmoud , Holthusen Hagen , Lamm Lukas , Böhm Christian , Jockenhövel Stefan , Reese Stefanie 
Published: March 2023

AbstractBiohybrid tissue‐engineered implants offer promising possibilities to treat cardiovascular diseases. The ability of tissue‐engineered implants to grow and remodel can be utilized to produce implants that can adapt to changes in the physiological conditions within the patient body. To improve the mechanical properties of the implant, a fibre‐reinforced textile scaffold is used. The embedment of a load‐oriented textile scaffold in the implant acts as biomimetic reinforcement and guides the direction of the extracellular matrix (ECM) growth. Our main objective is to design biohybrid heart valves that can withstand tough physiological loading conditions for decades. That makes it necessary to develop accurate and efficient models to support the design process.In this paper, the focus is on the macro‐mechanical modeling of the maturation process for textile reinforced heart valves. A biohybrid heart valve is modeled as a composite structure. The constitutive model is constructed by defining the total Helmholtz free energy as the sum of energies of the valve constituents. The two main constituents are (i) the extracellular matrix (ECM) and (ii) the fiber‐reinforced textile scaffold. The density of protein fibers such as collagen and elastin fibers are treated as internal variables. We introduce a new approach for modeling the densification of protein fibers during the cultivation process which is capable of considering both static and dynamic cultivation processes. The model considers the density change caused by the immunological response as well as the density change due to mechanical stimulation. The textile scaffold anisotropic behavior is introduced using structural tensors. The constitutive models are then embedded into a special finite element technology with reduced integration that enables efficient computations. The finite element simulation results are then validated using the experimental data provided by BioTex (Institute of Applied Medical Engineering, RWTH Aachen University, Germany). In the end, a finite element simulation for an exemplary valve is presented.
First steps towards modeling the interaction of cardiovascular agents and smooth muscle activation in arterial walls
Authors: Nurani Ramesh S. , Uhlmann K. , Saßmannshausen L. , Rheinbach O. , Klawonn A. , Heinlein A. , Balzani D. 
Published: March 2023

AbstractNumerical simulation of the response of healthy and pathological arteries to cardiovascular agents can provide valuable information to the physician in the treatment of diseases such as hypertension, atherosclerosis, and the Marfan syndrome. Here, we provide a first step towards a computational framework to model the effects of antihypertensive agents on the mechanical response of arterial walls. A material model is developed by extending an existing formulation for wall tissue to incorporate the effects of calcium‐ion channel blockers. The resulting coupled deformation‐diffusion problem is then solved using the finite element method. Simulation results with drug activity show that, indeed, an increased lumen diameter due to reduced contraction is obtained. Additionally, a decrease in the rate of arterial contraction is observed, which is also consistent with expected behavior. Finally, we compare results for an implicit or explicit treatment of the the deformation‐diffusion coupling, and we observe that both coupling schemes yield comparable results for a wide range of time step sizes.
Total Variation‐Based Reconstruction and Phase Retrieval for Diffraction Tomography with an Arbitrarily Moving Object
Authors: Beinert Robert , Quellmalz Michael 
Published: March 2023

AbstractWe consider the imaging problem of the reconstruction of a three‐dimensional object via optical diffraction tomography under the assumptions of the Born approximation. Our focus lies in the situation that a rigid object performs an irregular, time‐dependent rotation under acoustical or optical forces. In this study, we compare reconstruction algorithm in case i) that two‐dimensional images of the complex‐valued wave are known, or ii) that only the intensity (absolute value) of these images can be measured, which is the case in many practical setups. The latter phase‐retrieval problem can be solved by an all‐at‐once approach based utilizing a hybrid input‐output scheme with TV regularization.
Modeling the DC and AC electromechanically coupled effects in CNT‐based nanocomposite sensors
Authors: Xia Xiaodong , Hellebrand Sonja , Brands Dominik , Schröder Jörg 
Published: March 2023

AbstractThe direct current (DC) and alternative current (AC) electromechanically coupled phenomena have been reported in carbon nanotube (CNT)‐based nanocomposite sensors. In this contribution, a unified micromechanics‐based model is established for the DC and AC strain sensors. The electric damage and volume change of nanocomposite are considered to be responsible for the electromechanically coupled effects in CNT‐based nanocomposite sensors. The predicted DC resistance change ratio, AC dielectric loss change ratio and corresponding strain sensitivity factors of CNT‐based nanocomposite sensors are all consistent with the experimental results. High strain sensitivity is achieved for CNT‐based nanocomposite sensors with a low CNT‐content. This study confirms the advantage of adopting CNT‐based nanocomposite sensors via the dielectric loss over the electric resistance. The present electromechanically coupled homogenization theory can be utilized to rapidly determine the macroscopic DC and AC sensing performance by choosing a specific set of microstructural parameters, and further simplify the design process of CNT‐based nanocomposite sensors.