bluuebunny/crossref_metadata_2025_split huggingface dataset:
A finite element formulation in boundary representation for the analysis of nonlinear problems in solid mechanics
Authors: Klinkel Sven , Reichel Rainer 
Published: December 2018

AbstractThe contribution is concerned with a numerical element formulation for the analysis of the nonlinear behavior in solid mechanics. It is based on the so‐called scaled boundary finite element method (SB‐FEM). The SB‐FEM is as a semi‐analytical formulation to analyze problems of linear elasticity. The basic idea is to scale the boundary with respect to a scaling center. Hence, the boundary denoted as circumferential direction and the scaling direction span the parameter space. The original SB‐FEM approach is based on an analytical ansatz for the displacement response preserving equilibrium in scaling direction. In the present approach, an interpolation in scaling direction is introduced to account for nonlinear problems. Lagrange interpolations with different polynomial order are therefore discussed. The interpolation in circumferential direction is independent of the scaling direction and is defined by independent Lagrange functions. The displacement degrees of freedom are located at the nodes on the boundary and in the interior element domain. The degrees of freedom located in the interior of the domain are eliminated by static condensation, which leads to a polygonal finite element formulation with an arbitrary number of nodes on the boundary. The element formulation allows a priori for Voronoi meshes and quadtree mesh generation. Numerical examples give rise to the performance of the present approach in comparison to other element formulations, like mixed formulations.
Implicit time discretization schemes for least‐squares finite element formulations to model incompressible flows
Authors: Averweg Solveigh , Schwarz Alexander , Nisters Carina , Schröder Jörg 
Published: December 2018

AbstractIn the present contribution different implicit time integration schemes to model incompressible flow problems are investigated. Amongst the tested methods are the fully implicit Newmark, Houbolt and Crank‐Nicolson schemes.The first‐order system for the proposed formulation is given in terms of stresses and velocities as introduced in [1]. Raviart‐Thomas and standard Lagrange interpolation functions are used to approximate the stresses and velocities, respectively.For the comparison of all time discretization schemes, the unsteady two‐dimensional laminar flow around a cylinder at Reynolds number Re = 100 is chosen. For a rating on the accuracy, the obtained results for the drag coefficient are benchmarked against reference solutions by [2].
Region‐ and loading‐specific finite viscoelasticity of human brain tissue
Authors: Budday S. , Sommer G. , Paulsen F. , Holzapfel G. A. , Steinmann P. , Kuhl E. 
Published: December 2018

AbstractComputational simulations are a powerful tool to understand the mechanical behavior of our brain in health and disease, with the ultimate goal to prevent pathological conditions. Accurate numerical predictions, however, require the development of appropriate constitutive models and, equally important, the careful calibration of the corresponding constitutive parameters. This has been exceptionally challenging due to the ultrasoft and heterogeneous nature of brain tissue, resulting in a distinctly nonlinear, rate‐dependent, compression‐tension asymmetric, and region‐dependent behavior. Previous constitutive models have been deduced from a single loading mode, but fail to predict the behavior under various loading conditions. Here, we developed a large strain, nonlinear, viscoelastic constitutive model for brain tissue on the basis of cyclic and relaxation experiments under multiple loading modes, simple shear, compression, and tension. We carefully calibrated individual parameter sets for four different regions of the human brain, the cortex, the basal ganglia, the corona radiata, and the corpus callosum. The model captures effects such as nonlinearity and compression‐tension asymmetry, but also time‐dependent effects with substantial pre‐conditionning during the first loading cycle, only minor conditioning effects during subsequent cycles, and successive softening when the applied strain is stepwise increased. With close consideration of the underlying microstructure, we evaluate the physical meaning of viscoelastic material parameters with rate‐dependent regional trends. Our results help to improve the accuracy of human brain simulations during development and disease or to predict outcomes of neurosurgical procedures.
Fully discrete solution for Bean's critical‐state model in type‐II superconductivity
Authors: Winckler Malte , Yousept Irwin 
Published: December 2018

AbstractWe consider a hyperbolic Maxwell‐type variational inequality arising in Bean's critical state model for type‐II superconductivity. Combining the implicit Euler method in time with a mixed Ritz‐Galerkin approximation in space results in a fully discrete scheme for the concerned variational inequality. We present some numerical experiments, which visualize the Meissner‐Ochsenfeld effect in type‐II superconductivity and verify that the proposed approach is physically reasonable.
Numerical models for evaluating the vibro‐acoustic properties of acoustic metamaterials
Authors: Aumann Quirin , Miksch Matthias , Müller Gerhard 
Published: December 2018

AbstractThe demand for lightweight structures in aerospace and automotive is on the rise and so are the requirements regarding the vibro‐acoustic behavior. Materials with a high stiffness‐to‐mass ratio are often used in this field, but these materials typically have an unfavorable vibrational behavior regarding structure‐borne noise. Acoustic metamaterials offer a solution for improving the vibro‐acoustic performance of the structure, while the stiffness‐to‐mass ratio remains nearly constant. Such a metamaterial consists of periodic patterns of microstructures placed on the host structure. They modify the vibrational behavior of the host by adding local resonances and thus minimize vibrations at specific frequencies. Distinct resonances can have a major contribution to the acoustic behavior of a structure, so it is of interest to tailor microstructures, that generate stop bands at certain frequencies. This can be computationally expensive, so efficient numerical models are required for the design of acoustic metamaterials. Initial investigations show, that a parametric model order reduction (PMOR) method based on the Loewner framework can generate such models.
Configurational forces in fracture mechanics: A comprehensive concept of crack initiation and growth
Authors: Judt Paul , Ricoeur Andreas 
Published: December 2018

AbstractIn engineering structures cracks typically initiate at stress raisers such as holes and notches. In terms of a fracture mechanical assessment, it is important to identify the position xk, the angle ϕc and the length Δac of initiating cracks. Classically a stress based criterion is applied to obtain the position of crack initiation. Recently, the finite fracture mechanics approach [1] was presented, combining a stress and energy based criterion to obtain the positions and initiation lengths of cracks. In this approach, the energy states of the uncracked and the cracked specimens are compared, providing the reduction of the elastic potential ΔΠ due to crack initiation. In general, the global solution ΔΠ(xk, ϕ, Δa) is required for accurately predicting new cracks. In this paper, the material or configurational forces [2] at stress raisers are investigated with respect to the initiation of cracks. The material forces are strongly related to path‐independent integrals, e.g. the J‐integral [3] as crack driving quantity or loading quantity at notches [4]. A new criterion based on configurational forces is suggested, efficiently providing all data of the onset of cracks at stress concentrators.
Homogeneous Cauchy stress induced by non‐homogeneous deformations
Authors: Schweickert Eva , Mihai L. Angela , Neff Patrizio 
Published: December 2018

AbstractWe discuss whether homogeneous Cauchy stress implies homogeneous strain in isotropic nonlinear elasticity. While for linear elasticity the positive answer is clear, we exhibit an example with inhomogeneous continuous deformation but constant Cauchy stress. The example is derived from a non rank‐one convex elastic energy.
A numerically efficient phase‐field model for fatigue fracture – 1D analysis
Authors: Seiler Martha , Hantschke Peter , Brosius Alexander , Kästner Markus 
Published: December 2018

AbstractFatigue loads and fatigue failure come along with high numbers of load cycles. This makes the simulation of fatigue fracture computationally very demanding, if each load cycle is simulated comprehensively with its loading and unloading phase. We present a numerically efficient method for the simulation of fatigue fracture, which avoids resolving the loading path and instead requires only one increment per load cycle at most.We combine the phase‐field method for brittle fracture with a classic fatigue concept for lifetime calculation of components, which is applied to the material point here. A local lifetime variable is obtained, which we use to modify the material resistance incrementally in order to consider the progressive weakening of the material. Since we make use of an elasto‐plastic revaluation technique, a linear‐elastic material model is sufficient in the simulations. Furthermore, the phase‐field method allows to describe fatigue crack initiation as well as propagation.In this contribution we describe the method's framework including the mentioned lifetime concept, followed by a proposal for a simulation scheme. Finally, results – for now limited to the one‐dimensional case and constant load amplitudes – are discussed.
A finite strain elasto‐plastic material model incorporating kinematic and isotropic hardening for thermoplastic polymers
Authors: Felder Sebastian , Simon Jaan‐Willem , Reese Stefanie 
Published: December 2018

AbstractSemicrystalline thermoplastic polymers have superior mechanical properties and are thus very important in numerous technically relevant applications. During the thermoforming process of parts made of thermoplastic polymers the “springback effect”, i.e. the undesired distortion of a part after unloading and removal from tooling, depicts a major problem. These shape distortions occur due to the formation of residual stresses. To counteract this effect, time‐consuming and cost‐intensive trial and error approaches are typically conducted to carefully determine the optimal set of process parameters. Hence, a strong demand for computational models, which accurately predict the material and structural response of the part during forming, arises. Therefore, a phenomenological model formulation is proposed in this work, which is valid for large deformations and large deformation rates in the context of isothermal processes. To capture the biphasic nature of the polymer, i.e. to account for the amorphous and semicrystalline regions of the underlying microstructure, a parallel arrangement of both phases is applied. The overall material response is obtained by a rule of mixture. The qualitative validation of the hyperelastic, viscoplastic material model shows the promising potential to predict the formation and relaxation of residual stresses during the forming process of thermoplastic polymers.
Model‐based identification of injector aging in common rail fuel systems
Authors: Hofmann Oliver , Rixen Daniel 
Published: December 2018

AbstractThis paper discusses a strategy for identifying aging phenomena such as coking or erosion damage in the nozzle area of common rail injectors. These phenomena occur when the systems are operated over a longer time and they are known to impair the engine behavior. The method is based on a cycle‐to‐cycle state estimator of the Kalman filter type, which combines characteristic features of both simulated data and measured feedback from either a high‐frequency pressure sensor or an eddy current displacement sensor. The results show the great potential in accurately predicting the injection behavior and the method presented can thus be used to improve performance and emissions over an engine's lifetime.
Modelling and Finite Element Analysis of Viscoelastic Adhesive Joints
Authors: Rehbein Thomas , Matzenmiller Anton 
Published: December 2018

AbstractBesides large nonlinear deformations, polyurethane adhesives exhibit elastic and viscous material behaviour simultaneously. Although the concept of rheological elements is a quite simple method to describe rate effects, the identification of model parameters is a challenging task. Dynamic mechanical analysis provides the experimental database. By using time‐temperature superposition, the experimental frequency range can be extended in order to identify the relaxation times and dimensionless stiffnesses of the rheological network. The simulation results are in good agreement with stress‐strain curves from tests with different strain rates.
Bridging protein rigidity theory and normal modes using kino‐geometric analysis with hierarchical constraint relaxation
Authors: Budday Dominik , Leyendecker Sigrid , van den Bedem Henry 
Published: December 2018

AbstractElastic‐Network Models (ENM) and pebble game based rigidity analysis are two distinct coarse‐grained approaches that have provided tremendous insight into conformational flexibility of proteins. However, the topological nature of the pebble game, and thereby the absence of motion modes have limited its applicability and a detailed comparison to ENM. Here, we present an alternative approach to rigidity analysis which eliminates these drawbacks through detailed kinematic analysis of dihedral degrees of freedom and non‐covalent hydrogen bond constraints, collected in the constraint Jacobian matrix J. Our new procedure reveals a spatial hierarchy of protein motions intrinsic to the hydrogen bonding network, ranked by the singular values of J. This spectrum of J yields a striking, fold‐specific signature, differentiating stiffer α‐helical from more collective β‐sheet proteins, which often goes undetected in similarly coarse‐grained methods. Overall, our results agree with experimental data and more detailed simulations, indicating that hydrogen bond networks have evolved with different protein folds to modulate structural dynamics and molecular mechanisms, with broad implications for protein and drug design.
Residual‐type a posteriori estimator for a viscoelastic contact problem with velocity constraints
Authors: Walloth Mirjam 
Published: December 2018

AbstractWe consider a linear viscoelastic contact problem in which the non‐penetration condition is enforced by constraints in the velocities. We present a residual‐type a posteriori estimator and sketch how upper and lower bounds are derived based on the works [1,4].
A continuum damage based approach for cavitation and shear failure of hyperelastic adhesives for finite element applications
Authors: Nelson Alexander , Matzenmiller Anton 
Published: December 2018

AbstractShip‐ and rail‐vehicle building as well as the automotive industry use rubber‐like adhesives for glazing and joining of structural components. These adhesives are suitable to compensate relative motions of adherends due to their ability to withstand large elastic strains. In service, the adhesive layer exhibits distinct amounts of isochoric and volumetric deformations that decisively effect the occurence of two different failure mechanisms. In this contribution, a material model of a rubber‐like adhesive is proposed, which accounts for cavitation and shear fracture. A polynomial strain energy density function is applied to describe the hyperelastic response. The failure is modelled with a continuum damage based approach using an energy based failure function. Computations of a component‐like specimen are performed to validate the model.
A Numerical Comparison of Consensus‐Based Global Optimization to other Particle‐based Global Optimization Schemes
Authors: Totzeck Claudia , Pinnau René , Blauth Sebastian , Schotthöfer Steffen 
Published: December 2018

AbstractWe compare a first‐order stochastic swarm intelligence model called consensus‐based optimization (CBO), which may be used for the global optimization of a function in multiple dimensions, to other particle swarm algorithms for global optimization. CBO allows for passage to the mean‐field limit resulting in a nonlocal, degenerate, parabolic PDE. Exploiting tools from PDE analysis, it is possible to rigorously prove convergence results for the algorithm (see [3]). In the present article we discuss numerical results obtained with the Particle Swarm Optimization (PSO) [4], Wind‐Driven Optimization (WDO) [6] and CBO and show that CBO leads to very competitive results.
Improving constitutive equations in multiscale modelling by means of the sufficiency criterion using the example of nano wire contraction
Authors: Kurzeja Patrick , Sievers Christian , Mosler Jörn 
Published: December 2018

AbstractWe demonstrate how two concepts from statistical modelling, namely the sufficiency criterion and the Rao‐Blackwell‐Kolmogorov theorem, can improve mechanical models. Applied to the contraction of relaxed nano wires, we start with a rough and simple equation. A set of sufficient parameters is then used to derive an improved equation that resembles the real solution in shape and quantity. The analytical solution and molecular simulations will finally highlight the functionality and the advantages of the scheme.
Objective modeling of multixial softening of concrete
Authors: Kaliske Michael , Zreid Imadeddin 
Published: December 2018

AbstractConcrete in tension and low confined compression is characterized by strain‐softening, which leads to highly localized cracks or shear bands. Attempting to incorporate this response in standard continuum descriptions causes numerical instabilities and mesh sensitive results. This work presents a regularized plasticity‐damage model, which ensures mesh objectivity for general multixial strain softening. Combining plasticity and damage is necessary to describe the cyclic response of concrete. The damage part contains a split to consider the transition between compression and tension. Regularization of the model is achieved by an over‐nonlocal implicit gradient formulation. The model is implemented into a 3D finite element code and its capabilities are illustrated by numerical examples.
Simulation of bone ingrowth into bone substitutes on implant level length scale
Authors: Krüger Ann‐Kathrin , Julmi Stefan , Klose Christian , Besdo Silke , Maier Hans Jürgen , Wriggers Peter 
Published: December 2018

AbstractComputational modelling is a promising and ethical reasonable method in implant development. A computational model for bone ingrowth on implant level length scale has been implemented and applied for an open‐pored space‐filling bone substitute. First numerical simulations showed reasonable results for the average bone density and the effective Young's modulus of the bone‐implant‐compound.
Numerical Simulation of Crack Propagation in an Anisotropic Medium
Authors: Bilgen Carola , Hennig Paul , Kästner Markus , Weinberg Kerstin 
Published: December 2018

AbstractPhase‐field methods have been proven to address the main challenges in fracture mechanics – the identification of crack initiation and the simulation of the unknown crack paths – in an elegant way. This approach has therefore become very popular recently. Our contribution sets the focus on different ways to capture anisotropy in the phase‐field model. In order to deal with the tension‐compression asymmetry in fracture problems, a suitable operator split has to be deduced to take only the tensile deformations, which lead to crack growth, into account. In general, the strain energy function can be written in terms of principal stretches or principal invariants. A comparison of different decompositions is demonstrated in the context of both, finite and linearized strains. Furthermore, energetic and stress based fracture criteria are considered and checked against each other in more detail. Additionally, material anisotropy is examined within the phase‐field approach using an operator‐scaling anisotropic random field to consider the microstructure of the material implicitly.
Remarks on Fluid‐Structure Interaction Simulations in Realistic Arterial Geometries with regard to the Transmural Stress Distribution
Authors: Fausten Simon , Balzani Daniel , Heinlein Alexander , Klawonn Axel , Rheinbach Oliver , Schröder Jörg 
Published: December 2018

AbstractIn this contribution, Fluid‐Structure‐Interaction (FSI) in blood vessels, in detail the simulation of realistic arterial geometries, where the interaction of the blood flow and the vessel wall is of special interest, is considered. Based on pervious research, cf. [1], our existing framework for FSI‐simulations is extended towards realistic arterial geometries. The inflow and outflow boundary conditions for the fluid, as well as the boundary conditions for the structure are enhanced and adjusted to the chosen patient‐specific geometry. In detail, an inflow profile for arbitrary shaped inflow cross‐sections and a zero pressure boundary condition at the outflow are applied. Furthermore, the vessel wall is discretized using realistic material parameters of the media layer. The geometry and material parameters are adopted from [2]. In order to deal with the increasing complexity of the boundary value problem parallel computing and a two‐level overlapping Schwarz method with energy‐minimizing coarse space are applied; cf. [3]. The numerical simulations are performed using the Open‐Source software LifeV, in particular a code which has been developed in cooperation with the group of Prof. Quarteroni from the EPF Lausanne.
Modelling of lung‐metastases apoptosis within brain tissue
Authors: Schröder Patrick , Wagner Arndt , Stöhr Daniela , Rehm Markus , Jensch Antje , Radde Nicole , Ehlers Wolfgang 
Published: December 2018

AbstractApoptosis, a form of programmed cell death, can be induced in lung‐cancer cells by treatment with death‐receptor ligands. In this contribution, the coupled multiphasic process is described using a continuum‐mechanical model based on the Theory of Porous Media. Furthermore, the data‐enriched model incorporates the crucial apoptosis parameters, which are estimated via the maximum likelihood estimation based on cell‐culture experiments.
A mass‐lumped mixed FEM for acoustic wave propagation with inhomogeneous coefficients
Authors: Egger Herbert , Radu Bogdan 
Published: December 2018

AbstractWe consider the numerical approximation of acoustic wave propagation in the time domain by a mixed finite element method based on the BDM1–P0 spaces. In [2], we considered a mass‐lumping strategy for the BDM1 element that allows for efficient time integration. Moreover, we managed to show that while the accuracy of the method is reduced to first order by the quadrature error, the method does still manage to carry second order global information. This allowed us to devise post‐processing strategies for both variables. Here, we consider the case of inhomogeneous coefficients a and b, and show that the same results hold as for the homogeneous case. In addition, we illustrate the results by a numerical test.