bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the evolution of residual stresses due to cooling considering martensitic phase transformation
Authors: Uebing Sonja , Brands Dominik , Scheunemann Lisa , Schröder Jörg 
Published: December 2021

AbstractThe direct consideration of residual stresses can positively influence the properties of a component and offers a new perspective compared to the typical strategy of avoiding residual stresses. Instead of minimizing residual stresses in forming processes, their consideration can positively influence the properties of the final component. For instance, the targeted adjustment of residual stresses can extend the service life or durability and improve the manufacturability of metal components. This is investigated in current research using experimental and numerical analyses on a cylindrical component with eccentric hole made of steel 100Cr6. Here, the cooling process after hot bulk forming is simulated to analyze the influence of microscopic phase evolution on the macroscopic stress distribution. For this purpose, different variants of the microstructural evolution described by a random process are compared.
An extended Hamilton functional for the thermodynamic topology optimization of hyperelastic structures
Authors: Junker Philipp , Balzani Daniel 
Published: December 2021

AbstractWe present our work on a new variational approach for thermodynamic topology optimization of hyperelastic structures: building upon our previous works, we follow a thermodynamic approach for deriving a field equation that describes the evolution of the density. The problem of topology optimization is consequently solved without the need of expensive optimization routines. Furthermore, our new formulation can also be applied to hyperelastic structures which show a remarkable difference to structures optimized for small deformations. Important aspects like tension/compression asymmetry and buckling are inherently included in the topology optimization approach due to the large deformation formulation.
Prediction of missing values. Comparison of approaches
Authors: Litvinenko Alexander , Kriemann Ronald , Berikov Vladimir 
Published: December 2021

AbstractWe compare four numerical methods for the prediction of missing values in four different datasets [1]. These methods are 1) the hierarchical maximum likelihood estimation (ℋ‐MLE), and three machine learning (ML) methods, which include 2) k‐nearest neighbors (kNN), 3) random forest, and 4) Deep Neural Network (DNN). From the ML methods, the best results (for considered datasets) were obtained by the kNN method with three (or seven) neighbors. On one dataset, the MLE method showed a smaller error than the kNN method, whereas, on another, the kNN method was better. The MLE method requires a lot of linear algebra computations and works fine on almost all datasets. Its result can be improved by taking a smaller threshold and more accurate hierarchical matrix arithmetics. To our surprise, the well‐known kNN method produces similar results as ℋ‐MLE and worked much faster.
Modeling the Evolution of a cluster of gravitating bodies taking into account their absolutely inelastic collisions
Authors: Kiryan Dmitry , Kiryan George 
Published: December 2021

AbstractNumerical simulation of evolution of a cluster of a finite number of gravitating bodies interacting only by their intrinsic gravity has been carried out. The goal of the study was to reveal the main characteristic phases of the spatial distribution of material bodies constituting the cluster. In solving the problem, the possibility of interbody collisions was taken into account, the collisions being assumed to be absolutely inelastic. Forces external to the body cluster under consideration were ignored. Among all the internal force factors acting within the cluster, only the gravitational interaction was taken into account. The total mass of all the gravitating bodies of the cluster was assumed to remain constant during the entire evolution. The Cauchy problem with natural initial conditions was considered. To check the process of solution, the so‐called rotation curve was used which represents the current radial distribution of orbital velocities of the cluster bodies. The numerical analysis showed time variations of the model cluster rotation curve and, particularly, the fact that the rotation curve horizontal section is only a short moment in evolution of the gravitating bodies cluster. The results obtained within the scope of classical mechanics show that it is possible to represent all the rotation curve variations for the observed galaxies without appealing to the hypothesis of non‐observable gravitating “dark matter”.
Phase Field Modeling of Dynamic Surface Wetting informed by Molecular Simulations
Authors: Diewald Felix , Wolf Jana , Heier Michaela , Lautenschläger Martin , Stephan Simon , Kuhn Charlotte , Langenbach Kai , Hasse Hans , Müller Ralf 
Published: December 2021

AbstractWetting scenarios on the micro scale are becoming more important for a variety of engineering applications. The development of manufacturing techniques that can produce surfaces with a defined microstructure is in the scope of current research efforts. This allows to directly manipulate the wetting properties of a surface. Hence, a need for numerical models that can predict the wetting properties of microstructured surfaces arises. Phase field (PF) models can be applied for this purpose. The present PF model for wetting is informed by molecular dynamics (MD) simulations. It uses the MD based perturbed Lennard‐Jones truncated and shifted (PeTS) equation of state and an MD based viscosity correlation. This approach ensures a sound physical foundation of the model.
Variational based effective models for inelastic materials
Authors: Jezdan Ghina , Govindjee Sanjay , Hackl Klaus 
Published: December 2021

AbstractMechanical systems with inelastic materials and given boundary conditions can be generally defined and solved. However, for large systems, this problem becomes non trivial and computationally costly, especially when microstructures occure. Therefore, multi‐scale modeling is used to capture the behavior of the system.In this study, we present a methodology to provide such models for inelastic materials starting from the variational scheme. Using the variational principle we define the material strain energy and dissipation potential at the coarse scale (macro scale) starting from their counterparts on the fine scale, through the homogenization scheme. Then we solve the material model at the macro level instead of solving the fine scale model or the whole combination of scales. This multi‐scale model offers a reduced number of degrees of freedom and can generally provide the behavior of the system. Moreover, the macro scale model preserves the mathematical structure of the micro scale one. Nevertheless, for this effective model, special care needs to be given to the selection of the inelastic variables solved on the macro scale. This model is illustrated by the application to problems in classical plasticity.
On temporal homogenization in the numerical simulation of atherosclerotic plaque growth
Authors: Frei Stefan , Heinlein Alexander , Richter Thomas 
Published: December 2021

AbstractA temporal homogenization approach for the numerical simulation of atherosclerotic plaque growth is extended to fully coupled fluid‐structure interaction (FSI) simulations. The numerical results indicate that the two‐scale approach yields significantly different results compared to a simple heuristic averaging, where only stationary long‐scale FSI problems are solved, confirming the importance of incorporating stress variations on small time‐scales. In the homogenization approach, a periodic fine‐scale problem, which is periodic with respect to the heart beat, has to be solved for each long‐scale time step. Even if no exact initial conditions are available, periodicity can be achieved within only 2–3 heart beats by simple time‐stepping.
Modelling the dynamic contact forces during orthogonal turn‐milling
Authors: Knape Katharina , Nitzschke Steffen , Woschke Elmar 
Published: December 2021

AbstractThe aim of this work is to numerically calculate the effective cutting forces during orthogonal turn‐milling using the well‐known analytical approach introduced by Victor/Kienzle in connection with a multi‐body system. Starting with a routine that numerically computes the mill's infeed with the implemented dexel model, it is possible to reconstruct and follow the tool's outline and track caused by its rotation. Hence, the acting cutting forces can be determined.
A general sandwich‐type model for delamination failure in angle‐ply laminates under thermo‐mechanical loading
Authors: Frey Christopher , Dölling Sebastian , Becker Wilfried 
Published: December 2021

AbstractWe propose a highly efficient analytical closed‐form approach to assess the interlaminar stresses at the free edge in symmetric angle‐ply laminates under uniform axial extension and homogeneous thermal loading. The model is based on a two‐dimensional generalized plane strain representation of the structural situation – a so‐called general sandwich‐type model. Using the results of this approach we predict the delamination onset by means of a coupled stress and energy criterion within the framework of finite fracture mechanics. For comparative purposes we use numerical results from a cohesive zone model as well as experimental findings from the literature.
Lattice Boltzmann Method for Antiplane Shear with Non‐Mesh Conforming Boundary Conditions
Authors: Müller Henning , Schlüter Alexander , Müller Ralf 
Published: December 2021

AbstractLattice Boltzmann methods [1] have been extended beyond their initial usage in transport problems, and can be used to solve a broader range of partial differential equations, e.g. the wave equation [2]. Thereby they can be utilized for fracture mechanics [3]. In the context of antiplane shear deformation we previously examined a stationary crack [4, 5] with a finite width. In this work we present two implementation strategies for non‐mesh conforming boundary conditions, for which the bounding geometry does not need to adhere to the underlying lattice. This rectifies problems in modeling the crack. A numerical example shows the improvement compared to the previous results.
A novel approach for the consideration of plastic material behavior in thermodynamic topology optimization
Authors: Kick Miriam , Junker Philipp 
Published: December 2021

AbstractIn order to find optimal structures for realistic applications, it is essential to include the real material behavior in the optimization process. For this purpose, this research focuses on thermodynamic topology optimization accounting for plasticity for which a surrogate material model is developed. Characteristically, the stress/strain diagram resulting from physical loading and unloading shows a hysteresis for classical plasticity models. Our material model takes only the physical loading during the optimization process into account. To this end, during a virtual unloading in the optimization process, the dissipation of energy is suppressed which yields the same elasto/plastic deformation state as for physical loading. By using this novel material model, optimized structures can be computed without resourceful classical path‐dependent plasticity computation.
Semi‐analytical assessment of free‐edge stress fields in circular cylindrical cross‐ply laminated shells subjected to transverse loads
Authors: Kappel Andreas , Mittelstedt Christian 
Published: December 2021

AbstractThe present work deals with the semi‐analytical assessment of the three‐dimensional stress fields in circular cylindrical symmetrically and unsymmetrically laminated cross‐ply shells undergoing different transverse loads. Starting from a closed‐form plane‐strain analysis in the innermost regions of the laminated shell, the elasticity solution is upgraded by a higher‐order displacement‐based approach which enables the developed method to capture the three‐dimensional stress state due to the free‐edge effect in thick, finite‐length composite laminated shells. In order to realize this, the shell panel is discretized into a number of numerical layers with respect to the thickness direction. By introducing a priori unknown displacement functions in the interfaces of those numerical plies and by making use of the principle of minimum elastic potential, a system of coupled ordinary differential equations is obtained, which, however, can be solved by utilizing the state‐space approach. The results of the developed analysis method are verified through comparison with existing analytical approaches in the literature and finite element simulations and it can be noted that the semi‐analytical approach works with comparable accuracy, however, only at a fraction of the computational effort coming with full‐scale three‐dimensional finite element computations.
Modeling the Mullins effect of rubbers used in constrained‐layer damping applications
Authors: Jackstadt Alexander , Frölich Felix , Weidenmann Kay , Kärger Luise 
Published: December 2021

AbstractThe benefits of incorporating rubber interlayers in lightweight laminates, such as fiber‐metal laminates, in order to compensate for their usually undesirable dynamic behavior have been studied in previous works [1,2]. In such constrained‐layer damping laminates, the rubber layers undergo large deformations due to their comparably low stiffness. This motivates the consideration of large strain phenomena commonly found in rubbers even when global laminate deformations are small such as in linear dynamic analysis. This work specifically addresses the cyclic softening of filled rubbers commonly known as the Mullins effect. As this effect significantly influences the elastic properties of the material, a change in the dynamic behavior of the laminate is to be expected. A constitutive model based on the work of Dorfmann and Ogden [3] for the prediction of the cyclic softening as well as residual strains upon unloading is presented in this study. Special consideration is given to the implementation of the model for use in a commercial implicit finite element solver by building on the work of Connolly et al. [4]. The model is validated against experimental data and compared to a current state‐of‐the‐art model with regard to its predictive quality and computational efficiency. Furthermore, the experimental identification of material parameters for said model is addressed.
Computing the effective crack energy of microstructures via quadratic cone solvers
Authors: Ernesti Felix , Schneider Matti , Böhlke Thomas 
Published: December 2021

AbstractRecently, mathematically well‐defined homogenization results for the Francfort‐Marigo fracture model were established. To solve the resulting cell formula, efficient computational methods were developed and improvements on solver and discretization techniques were investigated.We discuss an approach for solving the governing cell formula based on a rewriting as a second order cone problem, a specific normal form for optimization problems. For such a formulation, potent high‐accuracy optimization solvers are available. We demonstrate our approach on heterogeneous two‐dimensional microstructures.
MSM building and projection for the analysis of time‐resolved spectra
Authors: Sechi Renata , Weber Marcus , Heyne Karsten 
Published: December 2021

AbstractUnderstanding the kinetics between the components of time‐resolved spectra is a crucial step in the study of photo‐activated processes. However, modeling the kinetics requires usually some a priori knowledge about the system. In our approach, we build a Markov State Model (MSM) from the spectral data, and obtain a Koopman transition matrixK(τ). With genPCCA, an invariant subspace projection, we project the process into its metastable components. The result of the application of gen‐PCCA is a transition matrixKc(τ), from which we can read the transition probability between the metastable components of the reaction. We discuss the application of this analysis method to the transient absorption spectrum of brominated Al‐corrole.
Phase‐field modelling and simulation of fracture in viscoelastic materials
Authors: Dammaß Franz , Ambati Marreddy , Kästner Markus 
Published: December 2021

AbstractHerein, a unified phase‐field formulation of fracture in viscoelastic materials is presented. The model is characterised by a pseudo‐energy functional from which the governing equations for the phase‐field and the viscous internal variables are derived. Depending on the specific choice of the parameters, the formulation has flexibility in capturing the coupling between viscous mechanisms and fracture. By means of a numerical study, different assumptions on the coupling are compared.
Pressure‐robustness for the Stokes equations on anisotropic meshes
Authors: Kempf Volker 
Published: December 2021

AbstractPressure‐robustness has been widely studied since the conception of the notion and the introduction of the reconstruction approach for classical mixed methods in [1]. Using discretizations capable of yielding velocity solutions that are independent of the pressure approximation has been recognized as essential, and a large number of recent articles attest to this fact, e.g., [2, 3]. Apart from the pressure‐robustness aspect, incompressible flows exhibit anisotropic phenomena in the solutions which can be dealt with by using anisotropic mesh grading. The recent publications [4,5] deal with the combination of both challenges. We briefly revisit the results from [4] and provide an insightful new numerical example.
Semi‐analytical method for the stress analysis of transverse cracks in composite structures
Authors: Peiler Clemens , Kappel Andreas , Mittelstedt Christian 
Published: December 2021

AbstractIn this paper a semi‐analytical approach is developed which enables the computation of the stress field in the vicinity of a transverse crack in symmetric cross‐ply laminated plates subjected to an in‐plane tensile load. Due to the assumption of a plane state of strain, the analytical model can be reduced to a two‐dimensional plate strip. After a discretization of the considered laminate into mathematical layers with respect to the thickness direction, the displacements for the undamaged part are derived by making use of the classical laminate plate theory. To incorporate transverse cracks into the formulation, the closed‐form analytical solution is upgraded by a so‐called ‘local solution’ that incorporates unknown displacement functions, specified in the interfaces of the numerical layers, as well Lagrangian interpolation functions of different order. The governing equations are determined by means of the principle of minimum elastic potential and eventually yield a quadratic eigenvalue problem which requires numerical evaluation. The obtained formulation of the previously defined interface displacements includes unknown ‘weight factors' which have to be characterized by adequate boundary and continuity conditions. Consequently, by solving the resulting linear system of equations, a full‐scale representation of the displacement‐, strain‐ and stress field within the damaged laminate is obtained. The semi‐analytical method is verified by comparison with numerical results of detailed finite element simulations. Using only a fraction of the computational effort, the results of the semi‐analytical approach show comparable accuracy to the finite element method.
Simulating sea ice drift in the Southern Ocean incorporating real wind data using the LSFEM
Authors: Schwarz Carina , Schröder Jörg 
Published: December 2021

AbstractThe viscous‐plastic sea ice model of [2] describes the motion of sea ice on large scales. The numerical model of the sea ice drift considers velocities and stresses and is coupled with the field quantities ice thickness and ice concentration, which are modeled by transient advection equations. Here, the viscosity in sense of a non‐Newtonian fluid depends on velocity gradients, as well as on ice concentration and ice thickness. This leads to a strong nonlinearity of the constitutive model.In [8], we discussed the hurdles of large scale sea ice models and possible solutions of an implementation within a least‐squares finite element method (LSFEM). Previous studies on sea ice model implementations have shown that the LSFEM is a promising solution to the numerically difficult problem, cf. [9] and [7]. In this work, another essential aspect of sea ice research comes into play: embedding real data into the numerical solution is an important field of research in sea ice and ocean modeling. Here, we show a 2D boundary value problem for simulating sea ice drift in the Southern Ocean incorporating real wind data from the ERA‐5 project [1].
PDE Constrained Inverse Problems arising from Turbulence Modeling
Authors: Pochampalli Rohit , Gauger Nicolas R. 
Published: December 2021

AbstractTurbulence models, which are a means to fix the closure problem arising from Reynolds averaging of Navier‐Stokes equations, are economical stop‐gaps but suffer from accuracy issues. Modifying turbulence models by incorporating corrections in their functional form is one approach to improve their accuracy. We estimate correction functionals for the Spalart ‐ Allmaras turbulence model, based on an inverse problem with PDE constraints emphasizing the issue of regularization.
An enhanced algorithmic scheme for relaxed incremental variational damage formulations at finite strains
Authors: Köhler Maximilian , Neumeier Timo , Peterseim Daniel , Peter Malte A. , Balzani Daniel 
Published: December 2021

AbstractRelaxed damage formulations enable to overcome the mesh dependency induced by a loss of ellipticity. However, such approaches require the construction of a convex hull of the associated energy potential. Within this contribution, an improved one‐dimensional, relaxed damage formulation of [1] with a successive, computationally optimal convexification scheme, see [2], is presented. Instead of solving a non‐convex optimization problem at the material point level, we iterate over a discrete grid and build consecutively linear Taylor expansions to construct the convex hull. Due to the reduced computational effort, integration of the one‐dimensional mechanical model over orientation distributions to obtain the three‐dimensional response as proposed in [3] becomes more feasible.
IMEX‐DG Schemes for Advection‐Diffusion Problems using Term‐based or Domain‐based IMEX Splitting
Authors: Ortleb Sigrun 
Published: December 2021

AbstractIMEX partitioning may be based on a decomposition of the computational domain into two subgrids by implicitly discretizing the unknowns on the smallest cells while explicit time stepping is applied to moderately sized elements. Alternatively, advection‐diffusion IMEX splitting applies implicit time discretization only to the viscous terms while inviscid terms are discretized explicitly. Analytical investigations have shown that a careful choice of both the specific IMEX scheme and the particular DG approach yield an additional stability property of such schemes resulting in time step restrictions independent of grid refinement. In this contribution, we will compare the domain‐based IMEX partitioning to advection‐diffusion splitting with respect to time step restrictions and efficiency.