bluuebunny/crossref_metadata_2025 huggingface dataset:
Strategies for Finding Training Snapshots for the Hyperreduction Method ECSW in Magnetodynamic Systems
Authors: Maierhofer Johannes , Rixen Daniel J.
Published: March 2023

Model 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

Continuous 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

We 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

Simulating 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

Biohybrid 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

Numerical 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

We 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

The 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.
Mathematical Modeling of Coolant Flow in Discontinuous Drilling Processes with Temperature Coupling
Authors: Fast Michael , Mierka Otto , Turek Stefan , Wolf Tobias , Biermann Dirk
Published: March 2023

Nickel‐based alloys, like Inconel 718, are widely used in industrial applications due to their high‐temperature strength and high toughness. However, machining such alloys is a challenging task because of high thermal loads at the cutting edge and thus extensive tool wear is expected. Consequently, the development of new process strategies is needed. We will consider the discontinuous drilling process with coolant. The main idea is to interrupt the drilling process in order to let the coolant to flow around the cutting edge and to reduce thermal loads. Since measurements inside the borehole are (nearly) impossible, simulations are a key tool to analyze and understand the proposed process.

In this paper, a 3D fluid flow simulation model with Q2P1 Finite Elements in combination with the Fictitious Boundary Method is presented to simulate the coolant flow around the drill inside the borehole. The underlying equations are transformed into a rotational frame of reference overcoming the challenges of mesh design for high rotational domains inside the fluid domain. Special treatment of Coriolis forces is developed, that modifies the ‘Pressure Poisson’ Problem in the projection step improving the solver for high angular velocities. To further take high velocities into account, a two‐scale artificial diffusion technique is introduced to stabilize the simulation. Finally, Q1 Finite Elements are used to simulate the heating and cooling processes in both the tool and the coolant during the complete discontinuous drilling process. The simulation is split into a ‘contact’ and a ‘no contact’ phase and a coupling strategy between these phases is developed. FBM is utilized to switch between the two configurations, thus only one unified grid for both configurations is needed. The results are used to gain insight into the discontinuous drilling process and to optimize the process design.
Modeling the moving boundary value problem of electrochemical machining
Authors: van der Velden Tim , Ritzert Stephan , Reese Stefanie , Waimann Johanna
Published: March 2023

Two evolving surfaces define the moving boundary value problem in electrochemical machining. On the side of the work piece, the anodic dissolution yields the evolution of the machined surface. A novel approach for modeling the dissolution process of the anode has recently been proposed by [6], which is based on internal variables and effective material parameters that are inserted into the balance equation of electric charge. Thereby, the resulting distributions of the electric current densities ‐ the driving forces of the dissolution process ‐ are accurately captured without the necessity to adapt the finite element mesh in each time step. On the tool side, an efficient methodology to incorporate the movement of the cathode into the simulation without remeshing had been lacking so far. Thus, we proposed to extend the modeling approach of [6] to model the cathode also based on effective material parameters whilst using a constant finite element mesh (see [7]). The procedure allows for the consideration of arbitrarily complex geometries that additionally may possess differently oriented feed vectors. In this paper, a new anisotropic rule of mixture is put forward. The presented example is restricted to a stationary cathode, but focuses on a detailed investigation of the new methodology and a comparison with existing rules of mixture, which are a key component of the methodology and equivalently applicable to moving boundary value problems.
Fast formation and assembly for spline‐based 3D fictitious domain methods
Authors: Marussig Benjamin
Published: March 2023

Standard finite element methods employ an element‐wise assembly strategy. The element's contribution to the system matrix is formed by a loop over quadrature points. This concept is also used in fictitious domain methods, which perform simulations on a simple tensor‐product background mesh cut by a boundary representation that defines the domain of interest.

Considering such d‐dimensional background meshes based on splines of degree p with maximal smoothness, Cp−1, the cost of setting up the system matrix is 𝒪(p3d) per degree of freedom. Alternative assembly and formation techniques can significantly reduce this cost. In particular, the combination of (1) sum factorization, (2) weighted quadrature, and (3) row‐based assembly yields a cost of 𝒪(pd+1) for non‐cut background meshes. However, applying this fast approach to cut background meshes is an open challenge since they do not have a tensor‐product structure.

This work presents techniques that allow the treatment of cut background meshes and thus the application of fast formation and assembly to fictitious domain methods. First, a discontinuous version of weighted quadrature is presented, which introduces a discontinuity into a cut test function's support. The cut region can be treated separately from the non‐cut counterpart; the latter can be assembled by the fast concepts. A three‐dimensional example investigates the accuracy and efficiency of the proposed concept and demonstrates its speed‐up compared to conventional formation and assembly.
Experimental investigation of carbon long fiber reinforced polyamide 6 exposed to environmental conditions
Authors: Christ Nicolas , Montesano John , Hohe Jörg
Published: March 2023

To enhance the possibilities in lightweight constructions in terms of processability and recyclability, fiber reinforced thermoplastics are a promising class of materials. In this context, the fiber‐matrix interface has a major influence on the mechanical properties of the composite. With polyamide 6 (PA6) being a hygroscopic thermoplastic, the effects of elevated humidity and temperature on the mechanical behavior must be considered [1]. This study aims to characterize the micro‐mechanical material properties of carbon long fiber reinforced PA6 in quasi‐static tensile tests after exposure to elevated temperature and humidity levels. Therefore, the specimens are conditioned in different climates and tested afterwards. In order to determine the initiation and propagation of matrix cracks, interface failure, and fiber fracture, the experiments are conducted on a micro‐scale with an average cross‐section of 0.03 mm2. The damage patterns are captured using optical microscopy and SEM images. The effects of conditioning at various temperature and humidity levels are discussed. The main results are the qualitative description of the degradation of mechanical properties due to hydrothermal effects.
FFT‐based simulation of evolving microstructures utilizing an adapting reduced set of Fourier modes
Authors: Gierden Christian , Waimann Johanna , Svendsen Bob , Reese Stefanie
Published: March 2023

The mechanical behavior of a periodic heterogeneous microstructure may be predicted by using a fast Fourier transform (FFT) based simulation approach. To reduce the computational effort of this method, we introduced a model order reduction (MOR) technique utilizing a reduced set of Fourier modes for the computations in Fourier space. To increase the accuracy of this MOR technique we developed a geometrically adapted sampling pattern for choosing the considered Fourier modes based on the representation of phases within the microstructure. Since the phase distribution of, for example, martensite and austenite in a polycrystalline microstructure evolves with increasing mechanical or thermal loads, the set of considered Fourier modes should also evolve according to the underlying micromechanical fields. We present the accuracy and the adaptability of this adaptive reduced set of Fourier modes by investigating the micromechanical fields of a polycrystal considering such phase transformations.
Mechanical Characterisation of Cables in Different Loading Directions
Authors: Sharma Prateek , Hildebrandt André , Düster Alexander , Diebels Stefan
Published: March 2023

The mechanical characterisation of cables can help improving the production and lifetime of various products, for example a robotic arm. Cables however form a class of composite structures, that is highly anisotropic and dissipates energy due to the reorientation of its constituents which is superimposed by the dissipation due to the deformation of the polymer components. Cables also have a degree of randomness in their structure. Moreover, the stiffness in one loading direction is coupled to the stiffness in another loading direction.

In this work, experimental investigations on the mechanical properties of the cables are presented. An experimental setup has been constructed to test the cables in tensile, torsion and the bending directions individually as well as coupled to each other. Free bending tests were conducted where axial forces were compensated during the bending to dissociate the tensile and the bending properties of the cables. To apply larger tensile and torsional loads on cables a commercial testing device was also used. To characterise the influence of bending on torsion, free bending tests were conducted with a combination of torsional load. Thus, a complete mechanical characterisation of a cable is presented.
Remarks on rank‐one convexity and quasiconvexity for planar functions with an additive volumetric–isochoric split
Authors: Martin Robert J. , Voss Jendrik , Sander Oliver , Neff Patrizio
Published: March 2023

We study convexity properties of isotropic energy functions in planar nonlinear elasticity in the context of Morrey's conjecture, which states that rank‐one convexity does not imply quasiconvexity in the two‐dimensional case. Recently, it has been shown that for the special case of isochoric energy functions on GL+(2) = {F ∈ ℝ2×2 | det F > 0}, i.e. for any isotropic function W : GL+(2) → ℝ with W(aF) = W(F) for all a > 0, these two notions of generalized convexity are, in fact, equivalent. Here, we consider the more general case of functions on GL+(2) with an additive volumetric–isochoric split of the form

urn:x-wiley:16177061:media:PAMM202200185:pamm202200185-math-0001

with an isochoric function Wiso on GL+(2) and a function Wvol on (0, ∞). In particular, we investigate the importance of the function

urn:x-wiley:16177061:media:PAMM202200185:pamm202200185-math-0002

and its convexity properties; here, λmax ≥ λmin > 0 are the ordered singular values of the deformation gradient F ∈ GL+(2). This function arises naturally as an “extremal” case in the class of volumetric–isochorically split energies with respect to rank‐one convexity.
Closed‐loop adaptive model predictive control of a bluff body wake
Authors: Gaina Ghiroaga Calin , Morton Chris , Martinuzzi Robert
Published: March 2023

A machine learning methodology is outlined to achieve robust closed‐loop feedback control of a bluff body turbulent wake. A Long Short‐Term Memory (LSTM) Neural Network is implemented with Model Predictive Control (MPC) to achieve closed‐loop flow control. The LSTM model is trained using actuation and pressure sensor data to forecast future pressure states. The candidate system is a square cross‐sectional cylinder with two modulated moving surface actuators embedded in the windward face leading corners. The controller performance is tested experimentally for three objective functions: recovery of mean‐base pressure set‐point after perturbation; and minimization of drag or wake fluctuation intensity. An adaptive learning strategy is implemented to adjust the model to new Reynolds number (Re) conditions without user intervention, thereby extending the controller performance and achieving more robust control. The identified minimum drag and wake fluctuation cases are analysed using velocity field data measured with particle image velocimetry.
Reduced order modeling of modular parameter dependent structures based on proper orthogonal decomposition and mesh tying
Authors: Ritzert Stephan , Macek Domen , Simon Jaan-Willem , Reese Stefanie
Published: March 2023

A model order reduction technique in combination with mesh tying is used to efficiently simulate many different structures that are assembled from a set of substructures. The stiffness matrices of the substructures are computed separately and assembled into a global stiffness matrix with tied contact formulation. Reducing the degrees of freedom of each substructure with a projection‐based model order reduction technique further decreases the computational time. The mode matrices that project the system into the low‐dimensional subspace are computed for each module separately with proper orthogonal decomposition and the method of snapshots. For the development and optimization of new construction strategies for fiber‐reinforced concrete, many different combinations of the modules have to be tested. The mechanical behavior of these modules depends on a set of parameters. Here the parameters are the fiber directions for transversely isotropic material behavior and parameters that describe the shape of the module. The sensitivity of the model order reduction technique to parameter changes requires a mode adaption technique to obtain reasonable results. Mode matrices for any parameters are computed by interpolating in a tangent space to the Grassmann manifold.
Study on an hp‐Adaptive Finite Element Solver for a Chemo‐Mechanical Battery Particle Model
Authors: Castelli Giuseppe Fabian , Dörfler Willy
Published: March 2023

We consider a Cahn–Hilliard‐type phase‐field model for phase separation and large deformations in battery electrode particles. For the numerical solution we employ an hp‐adaptive finite element solution algorithm coupled to a variable‐step, variable‐order time stepping scheme. Numerical experiments show the adaptive meshing and distribution of the locally varying polynomial degrees of the finite element method. In particular, for a sufficient large range of polynomial degrees we achieve significant computational savings compared to an h‐adaptive algorithm.
Injection molding of semi‐crystalline polymers in a space‐time framework
Authors: Ferrer Fabón Blanca , Alms Jonathan , Behr Marek , Hopmann Christian
Published: March 2023

The challenges in the numerical simulation of the polymer injection molding process are manifold. Such simulation involves a two‐phase flow formulation and the physical modeling of complex material, i.e., molten polymer. This paper presents a complete macroscale simulation approach for the filling stage of injection molding with semi‐crystalline polymers, applied on polypropylene as example. Accurate and efficient results are obtained using a space‐time finite‐element discretization. Heading towards more efficient computations, we search for a reduction of the polymer's physical model, which includes variable viscosity, density, and several crystallization models. The final contribution of the present work is a model sensitivity analysis, which evaluates the relevance of each material model during the filling stage of injection molding.
Objectivity and accuracy enhancement within ANN‐based multiscale material modeling
Authors: Heider Yousef , Sun WaiChing
Published: March 2023

Nowadays, supervised machine learning (ML) via artificial neural network (ANN) is increasingly applied within multiscale material modeling and homogenization to generate data‐based, physics‐informed material models as an alternative to conventional material models. This application is associated with many benefits, such as increasing of computational efficiency and accuracy. However, the establishment of a reliable data‐based or ML‐based material model requires the availability of a proper and sufficiently large database from small‐scale simulations and appropriate processing of these data as part of the model building steps. In this connection, this contribution discusses the method to generate ML‐based material models, which strictly fulfill a number of restrictions, such as objectivity (or material frame‐indifference) and thermodynamic consistency (second‐law of thermodynamics) for an elasto‐plastic material response. While focusing in this contribution on anisotropic crystal plasticity, the two aforementioned restrictions can be fulfilled via the utilization of informed‐graph NN and the application of data representation in spectral form. The numerical results show that learning the ML model to explicitly predict the plastic strain as an intermediate step not only enhances the fulfillment of thermodynamic consistency but also improves the accuracy of the final prediction.
Aggregated type handling in CoDiPack
Authors: Sagebaum Max , Gauger Nicolas R.
Published: March 2023

The development of algorithmic differentiation (AD) tools focuses mostly on handling floating point types in the target language. Taping optimizations in these tools mostly focus on specific operations like matrix vector products. Aggregated types like std::complex are usually handled by specifying the AD type as a template argument. This approach provides exact results, but prevents the use of expression templates. If AD tools are extended and specialized such that aggregated types can be added to the expression framework, then this will result in reduced memory utilization and improve the timing for applications where aggregated types such as complex number or matrix vector operations are used. Such an integration requires a reformulation of the stored data per expression and a rework of the tape evaluation process. We will demonstrate the overheads on a synthetic benchmark and show the improvement when aggregated types are handled properly by the expression framework of the AD tool.
Modelling of time‐dependent fatigue crack growth of hydrogels
Authors: Liu Dongxu , Ma Songyun , Markert Bernd
Published: March 2023

The service life of hydrogel‐based devices is strongly influenced by the anti‐fatigue capability of hydrogels. While recent advancements in the synthesis of hydrogels have improved their fatigue resistance, the underlying mechanisms that dominate the time‐dependent fatigue crack growth of hydrogels are still poorly understood. In this study, a computational method is developed to predict the fatigue crack of hydrogels. A physics‐based poro‐visco‐hyperelastic model is developed within the framework of the Theory of Porous Media at finite strains to describe the mechanical behaviour of hydrogels. A Bell model‐based chain evolution law is adopted to describe the time‐dependent breaking/reforming kinetics of physical chains. An energy‐based fatigue crack growth model is proposed to predict the fatigue crack growth of hydrogels. The averaged elastic energy density surrounding the crack tip is calculated as the driving force of fatigue crack growth. The effects of viscoelasticity, physical chain kinetics and fluid transport on the fatigue crack growth are analysed. The results indicate that these time‐dependent mechanisms cannot be ignored in predicting the fatigue crack behaviour of hydrogels.
A partitioned computational framework for damage evolution in stress corrosion cracking utilizing phase‐field
Authors: Kandekar Chaitanya , Ravikumar Aravinth , Höche Daniel , Weber Wolfgang E.
Published: March 2023

Dissolution‐driven stress corrosion cracking is a complicated multi‐physics phenomenon consisting of coupling between mechanical stress and corrosion. In this coupled electro‐chemo‐mechanical problem, the combined effects of mechanical field, localised corrosion and the microstructure with the effects of grain boundaries are investigated. Therein, corrosion kinetics are accelerated by mechanical straining and also affected by the different material properties along the grain boundaries. A phase‐field modelling approach, a method for regularizing sharp interfaces with smooth gradients, is utilized to describe the metal‐electrolyte interface during localized metal dissolution. The current contribution presents a partitioned computational framework, as an extension of recently published works for solving pitting corrosion and stress corrosion cracking at the micro‐scale. In this extension, mechanically assisted corrosion is coupled bi‐directionally and solved on two software instances facilitating simulation at different time scales, using an open‐source coupling software. The performance of the proposed computational framework is demonstrated through various deterioration model system situations in 2D.
Influence of the correlation length on the probabilistic material modeling of short fiber‐reinforced composites on the component level
Authors: Widera Ilona M. , Klatt Eduard , Rauter Natalie
Published: March 2023

In this study, an approach to numerical modeling of short fiber‐reinforced composites is presented. Based on the multi‐scale approach, elastic material parameters are transferred from the mesoscale to the macroscale, while maintaining their stochastic properties. For this, a complete description of the stochastic properties, consisting of mean, standard deviation and correlation structure in the mesoscale is determined. This information provides a basis for the creation of second order Gaussian random fields, which are used for a FEM simulation. An analysis of the numerical simulation, including a comparison with experimental values, shows the influence of the correlation length on the global material behavior. What is more, it can be demonstrated that the standard deviation is a function of the correlation length, while the mean value remains independent of it.
Analysis of viscous incompressible flows of micropolar fluidswith thermal convection and mixed boundary conditions
Authors: Beneš Michal
Published: March 2023

The Navier‐Stokes equations do not take into account the microstructure of the fluid in the sense that they do not consider the angular momentum of small particles of the fluid due to their rotation. The model of micropolar fluid represents a generalization of the well‐established Navier‐Stokes equations, in such a way that it introduces a new kinematic vector field called microrotation (the angular velocity field of rotation of particles) and adds a new vectorial equation, expressing the conservation of the angular momentum. We will be concerned with the initial boundary value problem for the flow of micropolar heat conducting fluids in a two‐dimensional channel with mixed boundary conditions. The considered boundary conditions are of three types: the Dirichlet boundary conditions on the inflow, the Navier type conditions on solid surfaces and Neumann‐type boundary conditions on the outflow of the channel. The homogeneous Dirichlet boundary conditions on solid surfaces for the microrotation is commonly used in practice. However, imposing such condition is doubtful from the physical point of view. For that reason, more general boundary conditions for the microrotation were proposed throughout the engineering literature to take into account the rotation of the microelements on the solid boundary, linking the velocity and microrotation through the so‐called boundary viscosity. The well‐posedness of problems with different types of boundary conditions for microrotation are completely unexplored. The present contribution is devoted to the analysis of the existence and uniqueness of the solution.
Efficient simulation of waves in heterogeneous domains using the scaled boundary finite element method
Authors: Nattoji-Shara Sharath , Birk Carolin , Gravenkamp Hauke
Published: March 2023

Simulation of wave propagation phenomena is very challenging due to the restrictions placed on the spatial as well as on the temporal discretization. Image‐based domain discretization using hierarchical meshes (2D polygonal elements) in conjunction with the scaled boundary finite element method provides an efficient numerical simulation tool. In this setting, the computational effort is reduced as only a limited number of unique cell patterns are formed. This is beneficial while computing element matrices in the preprocessing stage. When solving the dynamic system, the advantages of similar elements can only be fully exploited for the explicit time‐stepping schemes in connection with mass lumping when the domain is discretized using low‐order elements (p ≤ 2). On the other hand, the time step size may be limited by the stability criterion. Moreover, high‐order elements require fewer degrees of freedom. Hence for a specific application, it is not straightforward to predict superiority of one time‐stepping scheme over the other. A comparative study of implicit and explicit time‐stepping schemes is presented using an artificial two‐material model.
The concept of unequally and nonlinearly weighted averaging operators as a fundamental homogenization framework in phase‐field modeling
Authors: von Oertzen Vincent , Kiefer Bjoern
Published: March 2023

In recent years, the phase‐field method has gained tremendous potential to serve as a continuum modeling approach of micro structural evolution mechanisms for multiple applications such as alloy solidification, phase transitions, and fracture. By replacing sharp interfaces between phases with a diffusive formulation, additional degrees of freedom, namely order parameters, enter the continuum model to locally describe the current phase composition at each material point. Single phase properties thus need to be interpolated carefully within diffuse interface regions by applying mixture rules subject to specific constraints in an underlying homogenization framework, c.f. [1,2]. However, there exists a variety of well established nonlinear interpolation schemes that can only partially, or not at all, comply with conventional homogenization approaches.

To this end, an extension towards unequally and nonlinearly weighted averaging operators is presented, in which conventional unweighted homogenization represents a special case. The embedding of nonlinearly interpolated Reuss‐Sachs, Taylor‐Voigt and rank‐one homogenization models within the given framework is demonstrated by means of energy relaxation. Furthermore, upper and lower energetic bounds are compared between unweighted and nonlinearly weighted averages of order distributions, where the weighted case is shown to yield an improved effective energy description.
Towards modelling of energy storages for use in an intelligent energy management system
Authors: Kappertz Lars , Büskens Christof
Published: March 2023

With the transition towards renewable energy underway, demand‐side management together with the local generation of renewable energy is receiving growing attention. Optimizing the self‐consumption of locally produced renewable energy can not only have financial benefits for the respective household or business (and improve their autarky from increasingly unstable energy markets), but also help improve grid stability against the volatility of some sources of renewable energy. In order to optimize the self‐consumption of a given household or enterprise with an energy management system, the energy demand and generation, as well as the behaviour of all controlled devices have to be forecast. There are many different methods of mathematically modelling these different properties, but the task becomes especially challenging for dynamic systems like energy storage systems. Here, the state of charge at a specific time point depends on both external influences and the previous time point's state of charge, thus modelling errors quickly accumulate. In the context of small and medium agricultural enterprises, examples of such dynamic systems can be electrical storages, like a battery, or thermal storages like a milk cooling tank or a heat pump.

In this work, a common way for the modelling of these systems is explored, namely parameter identification. Here, the parameters of an ordinary differential equation representing the assumed physical behaviour of the system are identified from measured data of states and controls in an optimization problem. The success of this approach, and with it the performance of the derived model depends on how well the physical equations actually describe the system, but also on the quality, quantity and content of the measurement data used. In the case of a household battery storage already a simple physical model with parameters identified from measurement data of state of charge and battery power provides useful results. The example of a milk cooling tank provides a situation where external forcing has an important influence on the system's state of charge, its temperature. The cleaning of the tank generates a large heat influx, and raises the temperature, while the filling and emptying of milk influences the heat capacity. While these influences are shown to also be representable by equations based on the physical processes, parameter identification becomes difficult when they are not included in the measurement data. Thus, different approaches to derive these external forcings from the available data are outlined.
Analysis of GMRES for Low‐Rank and Small‐Norm Perturbations of the Identity Matrix
Authors: Carr Arielle K. , de Sturler Eric , Embree Mark
Published: March 2023

In many applications, linear systems arise where the coefficient matrix takes the special form I + K + E, where I is the identity matrix of dimension n, rank(K) = p ≪ n, and ∥E∥ ≤ ϵ < 1. GMRES convergence rates for linear systems with coefficient matrices of the forms I+K and I+E are guaranteed by well‐known theory, but only relatively weak convergence bounds specific to matrices of the form I + K + E currently exist. In this paper, we explore the convergence properties of linear systems with such coefficient matrices by considering the pseudospectrum of I + K. We derive a bound for the GMRES residual in terms of ϵ when approximately solving the linear system (I + K + E)x = b and identify the eigenvalues of I + K that are sensitive to perturbation. In particular, while a clustered spectrum away from the origin is often a good indicator of fast GMRES convergence, that convergence may be slow when some of those eigenvalues are ill‐conditioned. We show there can be at most 2p eigenvalues of I + K that are sensitive to small perturbations. We present numerical results when using GMRES to solve a sequence of linear systems of the form (I + Kj + Ej)xj = bj that arise from the application of Broyden's method to solve a nonlinear partial differential equation.
Implementation of a surrogate model for a novel path‐based finite element simulation for additive manufacturing processes in construction
Authors: Ekanayaka Virama , Hürkamp André
Published: March 2023

Additive manufacturing in large‐scale construction is an ongoing research topic that shows significant potential to overcome the challenges in terms of efficient material usage and process automation in construction. A large challenge in deposition based additive manufacturing processes of concrete material is to ensure the structural stability while printing. Due to the weak material properties of the fresh concrete, it has to be ensured that during the printing process the not fully cured printed structure is able to carry its own weight. This requires process stabilization and a proper process control to prevent a collapse of the structure. Therefore, a numerical model of the printing process that takes into account the time dependent material behavior of the applied concrete as well as the printing path and the process parameters is necessary to support the process planning. Within the framework of project B04 of the collaborative research center TRR277 – Additive Manufacturing in Construction, a novel path‐based finite element simulation was developed in which the simulated geometry is constructed directly from the printing trajectory. Additionally, this approach allows the time‐dependent material properties of fresh concrete to be modeled directly and efficiently into the mesh of the printed structure. Since the computation of large scale printing processes with finite element simulations is quite expensive, there exists a need for a much faster computational model. In this contribution, the implementation of a surrogate model based on a neural network and its deployment to optimize the interlayer waiting time is presented.
Optimization of Mirror Positioning for Single‐Camera 3D Displacement Measurements
Authors: Gille Max , Maierhofer Johannes , Rixen Daniel J.
Published: March 2023

Camera‐based 3D displacement measurements are only possible when two different viewing angles of the respective measurement point are available. We earlier introduced a simplified 3D reconstruction algorithm for camera‐mirror measurements where the mirror reflects the second view onto the camera sensor to eliminate the need for a second (costly) high speed camera. In this study, we concentrate on formulating guidelines on how to position the mirror with respect to the camera and the measured structure, the goal being to minimize errors arising in the 3D reconstruction procedure. The focus lies on the angle between the optical axes of both camera views. We hereby also take into account limitations in the experimental setup that the special camera‐mirror‐setup brings with it. This study is conducted in terms of simulations using the animation software BLENDER as well as real experiments on a simple vibrating structure.
A procedure for determination of the microstructural probabilistic characteristics from micrographs and their impact on subsequent results
Authors: Klatt Eduard , Widera Ilona M. , Rauter Natalie
Published: March 2023

In this study a methodology for the experimental determination of the probabilistic characteristics induced by injection molding of short‐fibre reinforced composites is presented. This approach is based on a pattern recognition algorithm for the fibre detection on the two‐dimensional micrograph. Since the fibres are of elliptic shape when dealing with a two‐dimensional arbitrary oriented cross‐section, the method of ellipses is used. The stochastic characteristics of the microstructure are described by probability density functions of the fibre length, diameter, and orientation, which are extracted from the two‐dimensional micrograph. For accurate results, sample preparation is of major significance, otherwise the microstructural characteristics are not captured correctly. The result of the fibre orientation over the cross‐section shows a typical layered structure of the microstructure. Furthermore, the extracted probability density function of the fibre diameter present as expected a normal distribution. In general, the results are in good agreement with literature and other scientific works.
Coupled thermo‐viscoplastic fracture model for ductile‐brittle failure of amorphous glassy polymers with phase‐field approach
Authors: Başdemir Selçuk , Gültekin Osman , Dal Hüsnü
Published: March 2023

Amorphous glassy polymers have an extensive use in the industrial sectors including micro‐electronics, medical industry and aerospace, therefore their design and usage have become a significant task nowadays. The fracture response of these polymers may vary from ductile to brittle depending on several factors such as entanglement density, temperature level and external loading rate. The ductile response is driven by diffuse shear zones exhibiting volume–preserving inelastic deformations while the brittle response is manifested by very small crack‐like defects composed of a sequence of fibrillar bridges separated by micro‐voids, thereby connotating void formation consisting of nucleation and propagation steps. The presents study is focused on the description of shear yielding and crazing phenomenon in terms of their respective evolution equations. In addition, an extension towards the modelling of the fracture is employed via the crack phase–field approach, considering ductile and brittle failure simultaneously. This is provided by the novel failure criterion that features a critical amount of plastic strain and void volume fraction. Since the proposed approach unitedly models the macroscopic crack initiation and propagation for ductile or brittle failure, it is asserted to be more physically grounded compared to present models in the literature. Constitutive formulations for shear yielding, crazing, and void volume fraction are derived with their specific forms starting with the local and conductive component of the dissipation inequality. The performance of model is evaluated after developing the local and global Newton–type update algorithms for the dissipative internal and primary field variables, respectively and it has been analysed by fitting of several experimental data of homogeneous and inhomogeneous tests. The findings reveal the remarkable temperature dependency on the type of failure as well as the interaction between loading rate and temperature change owing to dissipative heating in the solid.