bluuebunny/crossref_metadata_2025_split huggingface dataset:
Ray tracing in thermally loaded optical systems
Authors: Rall Phillip Lino , Pflaum Christoph 
Published: December 2021

AbstractHigh‐power laser beams are usually imaged with the help of suitable optics. The propagation of such beams, through optical systems, often result in a focus shift. This is mainly due to the deposited power in the beam acting as a heat source in the optical elements. Finally, the resulting change in temperature leads to both, a deformation of the lens surface, and a change of the refractive index in the lens. Ray tracing and the finite element method are needed in order to analyze the above effects. The accuracy and the computational time of focus shift calculations, in both simulation techniques, are strongly influenced by the interpolation of the data. This paper will present, a newly proposed interpolation method, allowing a fast and accurate interpolation of data using an unstructured finite element grid. This method will specifically focus on the accurate calculation of laser beam thermal load inside an optical lens.
Freezing of sea ice with an inhomogeneous material distribution using the Theory of Porous Media
Authors: Schwarz Alexander , Bluhm Joachim , Schröder Jörg , Skatulla Sebastian 
Published: December 2021

AbstractIn this paper, we present results of a four‐field finite element formulation in the context of the Theory of Porous Media for the modeling of freezing processes. The primary solution variables are ice displacements, fluid pressure, temperature, and volume fraction ice. In detail, we show results on ice formation (mass transfer from liquid to solid constitutents) and temperature distribution. Special attention is given to the modeling of the heat of solidification. A thermodynamically consistent approach is used for the energetic effects to characterize and control the phase transition, see [1]. Finally, a numerical example of a freezing process with an inhomogeneous material distribution is shown.
Reduced integration‐based solid and solid‐shell finite elements for gradient‐extended damage
Authors: Barfusz Oliver , van der Velden Tim , Brepols Tim , Reese Stefanie 
Published: December 2021

AbstractThe present contribution is concerned with the incorporation of gradient‐extended damage into reduced integration‐based continuum finite elements. To this end, the purely mechanical low‐order solid and solid‐shell elements based on the isoparametric concept are combined with a gradient extended two‐surface damage plasticity model. Due to a tailored combination of reduced integration with hourglass stabilization, the enhanced assumed strain (EAS) method and in case of the solid‐shell the assumed natural strain (ANS) method, the most dominant locking phenomena are eliminated. A polynomial approximation of the strain‐like as well as the stress‐like quantities within the weak forms enables the definition of a suitable hourglass stabilization. In this way, the element stiffness contributions coming from the hourglass stabilization can be determined analytically, since they represent polynomials with respect to Cartesian coordinates. Two representative numerical examples of an elasto‐plastic asymmetrically notched specimen as well as an elastic thin annular plate reveal the accuracy and efficiency of the proposed methodology. Besides the ability to deliver mesh independent results, the framework is especially suitable for constrained situations in which conventional low‐order finite elements suffer from well‐known locking phenomena.
Optimal sensor placement for stochastic sources in machine tools
Authors: Herzog Roland , Naumann Andreas 
Published: December 2021

AbstractAccuracy requirements for machine tools demand an accurate positioning of the tool center point. Due to the heat sources, for example the friction and heat loss of motors, a machine can undergo complicated deformations during operation. While the location of mounted sources are known in advance, there are also process dependent sources, like hot chips after chip off. Furthermore many material parameters and most coupling parameters are not known exactly, or have an unknown temperature dependency. We consider a coupled thermo‐elastic finite element model of a simplified machine tool. We include uncertain heat sources and exchange parameters and present an optimal sensor placement approach to capture the sources.
A Proof of Concept for Very Fast Finite Element Poisson Solvers on Accelerator Hardware
Authors: Ruda Dustin , Turek Stefan , Ribbrock Dirk , Zajac Peter 
Published: December 2021

AbstractIt is demonstrated that modern accelerator hardware specialized in AI, e.g., “next gen GPUs” equipped with Tensor Cores, can be profitably used in finite element simulations by means of a new hardware‐oriented method to solve linear systems arising from Poisson's equation in 2D. We consider the NVIDIA Tesla V100 Tensor Core GPU with a peak performance of 125 TFLOP/s, that is only achievable in half precision and if operations with high arithmetic intensity, such as dense matrix multiplications, are executed, though. Its computing power can be exploited to a great extent by the new method based on “prehandling” without loss of accuracy. We obtain a significant reduction of computing time compared to a standard geometric multigrid solver on standard x64 hardware.
A NURBS enhanced polygonal element formulation based on the scaled boundary method for the analysis of solids in boundary representation
Authors: Reichel Rainer , Klarmann Simon , Klinkel Sven 
Published: December 2021

AbstractThe contribution is concerned with a numerical element formulation for the nonlinear analysis of solid in boundary representation. Its results in a polygonal element with an arbitrary number of sides. Straight edges are possible as well as curved edges, which are described by e.g. Non‐Uniform Rational B‐Splines (NURBS). The element formulation is based on the so‐called scaled boundary finite element method (SBFEM). The basic idea is to scale the domain's boundary with respect to a scaling center in order to describe the interior domain. In contrast to SBFEM, the proposed method makes use of a numerical aproximation for the displacement response in scaling direction. This enables the analysis of geometrically and physically nonlinear problems in solid mechanics. The interpolation at the boundary in circumferential direction is independent of the interpolation in scaling direction. So, different basis functions can be used for each direction, e.g. NURBS basis functions in circumferential and Lagrange basis functions in radial direction. The advantage of the presented element formulation is the flexibility in mesh generation. The avoidance of so‐called hanging node problems as arbitrary element geometries are possible. For example, using Quadtree algorithms, a fast and reliable mesh generation can be achieved. Furthermore, in connection with trimming algorithms, the element formulation allows a precise representation of the geometry even with coarse meshes. Some benchmark tests are presented to evaluate the accuracy of the proposed numerical method against analytical solutions.
Estimation of unordered core size using a robustness measure for topological defects in discretized orientation and vector fields
Authors: Hoffmann Karl B. , Sbalzarini Ivo F. 
Published: December 2021

AbstractWe show how the finite sizes of unordered defect cores in discretized orientation and vector fields can reliably be estimated using a robustness measure for topological defects. Topological defects, or singular points, in vector and orientation fields are considered in applications from material science to life sciences to fingerprint recognition. Their identification from discretized two‐dimensional fields must deal with discontinuities, since the estimated topological charge jumps in (half‐)integer steps upon orientation changes above a certain threshold. We use a recently proposed robustness measure [Hoffmann & Sbalzarini, Phys. Rev. E 103(1), 012602 (2021)] that exploits this effect to quantify the influence of noise in a vector field, and of the path chosen for defect estimation, on the detection reliability in two‐dimensional discrete domains. Here, we show how this robustness measure can be used to quantify the sizes of unordered regions surrounding a defect, which are known as unordered cores. We suggest that the size of an unordered core can be identified as the smallest path radius of sufficient robustness. The resulting robust core‐size estimation complements singular point and index estimation and may serve as uncertainty quantification of defect localization, or as an additional feature for defect characterization.
Phase field modeling with deformation‐dependent interface energies
Authors: Wilbuer Hendrik , Lammen Henning , Mosler Jörn 
Published: December 2021

AbstractIn the last years, the phase field method has established itself for the simulation of various problem types, especially in the fields of microstructure evolution and phase transformations as well as in fluid dynamics. Concerning the first two cases, usually a constant, deformation‐independent, surface energy is considered. In this work, however, deformation‐dependent surface elasticity according to [5] will be incorporated into phase field theory. In line with [4], a finite element framework for an Allen‐Cahn type phase field model coupled to continuum mechanics is presented, which is solved in a monolithic manner by means of Newton's method. The resulting model also accounts for a spatial evolution of the diffuse interface by a functional of Ginzburg–Landau type. The implemented model is employed in numerical simulations. These will be used to study the behavior of the phase field model.
Geometric and finite element modeling of biopolymer aerogels to characterize their microstructural and mechanical properties
Authors: Chandrasekaran Rajesh , Hillgärtner Markus , Rege Ameya , Milow Barbara , Itskov Mikhail 
Published: December 2021

AbstractBiopolymer aerogels belong to a class of highly open‐porous cellular materials. Their macroscopic mechanical properties (such as elasticity or thermal conductivity) depend on microstructural features (namely pore size distribution (PSD), fiber diameter and solid fraction), which can be tailored by different synthesis and drying routes. The design of modern aerogel materials requires a better perception into the microstructure and its influence on the mechanical properties. To predict the material properties using simulation, it is significant to construct a geometric model which is sufficiently precise to represent the microstructure of real materials. A tessellation approach based on Voronoi diagrams is a powerful tool to model such cellular‐like materials. In this contribution, the diversified cellular morphology of aerogels is described computationally using a Voronoi tessellation‐based approach [1]. Accordingly, Voronoi tessellations are generated to create periodic representative volume elements (RVEs) resembling the microstructural properties of the cellular network. Stress‐strain curves resulting from finite element simulations of these RVEs and experiments of the aerogels under compression are compared. This work is an extension of our previous Voronoi tessellation‐based on the 2‐d description of biopolymer aerogels [2].
The First Stage of Firn Densification ‐ An Evaluation of Grain Boundary Sliding
Authors: Schultz Timm , Müller Ralf , Gross Dietmar , Humbert Angelika 
Published: December 2021

AbstractFirn describes the interstage product between snow and ice in cold regions of the earth, where annual snow fall exceeds the amount of snow melting. The continuing accumulation of snow leads to its densificiation due to overburden stress until it becomes ice. In the field of glaciology various attempts on simulating firn densification have been made and new models are still developed, as the knowledge of the firn column's density structure allows important derivations.The presented study reassesses a model description for low density firn based on the process of grain boundary sliding presented by Alley in 1987 [1] using an optimisation approach. By comparing simulation results to 159 measured firn density profiles from Greenland and Antarctica it finds a possible additional dependency of the constitutive relation on the mean surface mass balance. This result is interpreted as an insufficient description of the stress regime.
Parameter‐robust preconditioning for unsteady Stokes control problems
Authors: Leveque Santolo , Pearson John W. 
Published: December 2021

AbstractWe propose a saddle‐point preconditioner for an optimization problem constrained by the time‐dependent Stokes equations, discretized using the backward Euler method in time. The key ingredients are an inner iteration for the (1, 1)‐block, accelerated by a known preconditioner for the heat control problem, and an approximation of the Schur complement involving a commutator argument applied to a block matrix. Numerical results demonstrate the efficacy and robustness of this approach.
Numerical modeling of the receptor driven endocytosis
Authors: Klinge Sandra , Wiegold Tillmann , Aygün Serhat , Gilbert Robert P. , Holzapfel Gerhard A. 
Published: December 2021

AbstractThe present contribution focuses on the receptor driven endocytosis typical of viral entry into a cell. The process is characterized by a local increase in receptor density necessary to establish contact between the cell and the virus. While the receptors of the virus are fixed on its surface, the receptors of the cell are able to move over its membrane, which leads to a local change in their concentration. In the model developed, the receptor motion is described by the diffusion equation along with two boundary conditions. The boundary conditions represent the balance of fluxes at the front of the contact area, where the velocity is assumed to be proportional to the gradient of the chemical potential, and the energy balance behind and before the front, causing the fronts movement. The model provides a basis to incorporate different phenomena such as for example cooperativity. This property strongly influences the effective binder density necessary to establish contact. The moving boundary problem describing the process is numerically solved by using the finite difference method and applied to study the change of receptor density over the membrane as well as the motion of the adhesion front. Two features are investigated in particular: The process initiation is analyzed in order to obtain information on possibilities for inhibiting the viral entry, and the non‐dimensional analysis is performed to minimize the number of necessary process parameters and to check their priority.
Investigation of copper lattice structures using a Split Hopkinson Pressure Bar
Authors: Bieler Sören , Kang Sung Gyu , Heußen Daniel , Ramachandramoorthy Rajaprakash , Dehm Gerhard , Weinberg Kerstin 
Published: December 2021

AbstractThe paper deals with experiments on 3D printed lattices in a Split Hopkinson Pressure Bar. An energy‐based evaluation of the measured wave signals enables us to compare the damping properties of two different copper lattice structures.
Improving energy efficiency of bipedal walking using nonlinear compliant mechanisms
Authors: Luo Yinnan , Zirkel Marten , Römer Ulrich J. , Zentner Lena , Fidlin Alexander 
Published: December 2021

AbstractA method to improve the energy efficiency of a bipedal robot by coupling its thighs with compliant smart mechanisms is introduced. The walking gaits are driven by electric motors in its revolute joints, whose reference trajectories are generated via numerical optimization. The optimized nonlinear characteristic of the compliant mechanism modifies the free oscillation frequency of the system that matches the current double step frequency even under different conditions, which results in a very high energy efficiency.
A mixed finite element formulation for energy‐momentum time integrations of composites with fiber bending stiffness
Authors: Dietzsch Julian , Gross Michael , Kalaimani Iniyan 
Published: December 2021

AbstractWe aim at dynamic simulations of 3D‐fiber‐reinforced materials in light‐weight structures, which are reinforced by fiber rovings comprised of thousands of filaments. Each roving possesses a separate bending stiffness, which has a large influence on the material behaviour on the macro scale. For the description of this material behavior, we extend a hyperelastic anisotropic Cauchy continuum formulation, which models only the macro‐scopic behaviour of a reinforcement by filaments, by a higher‐order gradient of the deformation mapping as an independent field. The new mixed finite element formulation is based on well‐known mixed finite elements for anisotropic polyconvex material formulations, but include new additional mixed fields concernd with the fiber bending stiffness. As we aim at dynamic long‐term simulations, we apply higher‐order accurate time integrators. Here, we include the new mixed finite element formulation in a variational‐based time finite element method. As numerical examples serve a simple cantilever beam. Here, we first analyze the influence of the fiber bending stiffness.
On the impact of the jerk on structural dynamics
Authors: Steiner Wolfgang 
Published: December 2021

AbstractIn mechanics, the term jerk, which is usually defined as the time derivative of acceleration, is often used incorrectly to interpret shock loads. Unfortunately, it is often very difficult to convince technicians with less insight into the basic laws of mechanics that their views are invalid, since jerky motions undoubtedly have certain effects on the dynamics of mechatronic systems. The fact is, however, that according to Newton the magnitude of the force acting on a body is determined exclusively by the acceleration itself and not by its derivative. From Newton's law follows only the trivial statement that the change of force is proportional to the change of acceleration. The effects of the jerk only become apparent in structural‐dynamic applications, such as in robotics or in biomechanics. In this presentation, such effects are discussed for a simple mechanical model to make fundamental phenomena such as component vibrations, which are related to the jerk, understandable. Quantitative relations between the jerk and the amplitude of such vibrations are derived analytically.
Existence of weak solutions of diffuse interface models for magnetic fluids
Authors: Kalousek Martin , Mitra Sourav , Schlömerkemper Anja 
Published: December 2021

AbstractIn this article we collect some recent results on the global existence of weak solutions for diffuse interface models involving incompressible magnetic fluids. We consider both the cases of matched and unmatched specific densities. For the model involving fluids with identical densities we consider the free energy density to be a double well potential whereas for the unmatched density case it is crucial to work with a singular free energy density.
Modeling of wear processes by a regularized damage‐plasticity model based on the emulated RVE
Authors: Hoormazdi Golnaz , Hackl Klaus 
Published: December 2021

AbstractWear is defined as damage to the surface of a solid body, involving progressive material removal, due to relative motion and frictional contact with another surface. This process is usually slow but is considered as one of the major factors causing damage and consequently failure of component parts during the lifetime of tools or machines in different applications such as tunneling.The implementation of conventional local material models in finite element simulations involving softening behavior (e.g., softening plasticity or damage) tends toward an ill‐posed boundary value problem after the onset of softening due to non‐convex and non‐coercive energy functions and suffers from strongly mesh‐dependent results. Therefore, different regularization strategies are developed to overcome the mentioned problem, such as integral or gradient enhancement, introducing an internal length scale and subsequently increasing computation effort.In this study, we present a variational approach for regularization of damage material model coupled with local plasticity based on emulated representative volume element (ERVE). This model shall be applied for the numerical investigation of wear processes, where a fine resolution of the involved constituents (cut sheet and abrasive particles in the soil) are required. We start with the theoretical derivation of material model, briefly present the numerical treatment, and prove the efficiency of this new approach via some numerical examples. Furthermore, results to the simulation of different wear modes in single scratch tests are presented.
On the orbital stability of periodic trajectories of a class of discontinuous systems
Authors: Zuyev Alexander , Benner Peter , Seidel-Morgenstern Andreas 
Published: December 2021

AbstractThis paper focuses on the stability analysis of periodic trajectories for non‐autonomous systems whose right‐hand sides are time‐periodic discontinuous functions. Such systems arise, in particular, in optimal control problems for nonlinear control systems with periodic bang‐bang inputs. We obtain sufficient orbital stability conditions of the Andronov–Witt type for this class of systems. The proposed stability conditions are applied to the analysis of periodic extremal trajectories of the controlled nonlinear chemical reaction model.
Efficient computation of coupled bending and torsion vibrations of slender structures with an axially moving eccentric load
Authors: Holl Helmut J. , Keplinger Lukas 
Published: December 2021

AbstractFrequently slender structures are excited by moving loads and show the corresponding transient vibrations. A model is derived using a simply supported Bernoulli‐Euler beam and the coupled bending and torsion vibration equations are derived. An analytical solution of the decoupled partial differential equations is derived based on the eigenmode expansion considering the boundary and initial conditions. For the pure bending and the pure Saint‐Venant torsion the analysis is performed and the beam vibrations are calculated. The coupled bending and torsion deformations are computed using a modal transformation, where it is essential that the eigenmodes are the same for both kinds of vibrations. The resulting modal decoupling yields two separated ordinary differential equations in time with the assumed constant velocity of the axially moving excitation load. Closed form solutions are used which show a very good convergence. A transformation into the original coordinates results in the solutions of the coupled equations. The results are plotted in a dimensionless form. The evaluation and comparison with a suitable numerical calculation using a finite element model shows a good agreement of the results. It turns out that a fine discretization is necessary and the computation effort for computing the transient dynamic solution is very much higher.
Efficient surrogate strategy for investigating stick‐slip instability
Authors: Fau Amelie , Fuhg Jan N. 
Published: December 2021

AbstractAn innovative sampling strategy called MiVor coupled with kriging metamodeling is employed for detecting stick‐slip instabilities within a parametric domain based on very few simulations. The interest of the approach is here exposed on an oscillator of Duffing's type in combination with an elasto‐plastic friction force model, more details can be found in [3].