bluuebunny/crossref_metadata_2025_split huggingface dataset:
External problems of steady vibrations in the theory of elastic materials with a triple porosity structure
Authors: Svanadze Merab 
Published: March 2023

AbstractIn this paper, the linear theory of elasticity for materials with a triple porosity (macro, meso and micro levels of porosities) structure based on the volume fraction concept is considered. The external boundary value problems (BVPs) of steady vibrations of this theory are investigated. Namely, the uniqueness theorem for classical solutions of these BVPs is established. Then, the basic properties of the surface (single‐layer and double‐layer) potentials are given. Finally, on the basis of the properties of potentials, the existence theorems for classical solutions of the above mentioned BVPs of steady vibrations are proved by means of the potential method (boundary integral equation method) and the theory of singular integral equations.
A novel anisotropic stress‐driven model for bioengineered tissues accounting for remodeling and reorientation based on homeostatic surfaces
Authors: Holthusen Hagen , Rothkranz Christiane , Lamm Lukas , Brepols Tim , Reese Stefanie 
Published: March 2023

AbstractA co‐rotated formulation of the intermediate configuration is derived in a thermodynamically consistent manner. As a result of this formulation, algorithmic differentiation (AD) and the equations of the material model can be combined directly, i.e., the equations can be implemented into the AD tool and the corresponding derivatives can be calculated using AD. This is not possible when the equations are given in terms of the intermediate configuration, since the multiplicative decomposition suffers from an inherent rotational non‐uniqueness. Moreover, a novel stress‐driven kinematic growth model is presented that takes homeostasis and fiber reorientation into account and is based on the co‐rotated formulation. A numerical example reveals the promising potential of both the co‐rotated formulation and the stress‐driven growth model.
Core thickness optimization of buckling‐endangered sandwich columns under compressive loads
Authors: Nuño Miguel , Schröder Kai-Uwe 
Published: March 2023

AbstractOptimizing the core thickness of a sandwich structure can be a computationally expensive task. In this work, an optimization approach for slender columns is presented. The approach iteratively determines the optimal thickness distribution using the second derivative of the eigenmodes as an input for the shape function. To demonstrate its capabilities, it is applied to simple columns constrained according to Euler's buckling cases. The optimization results are validated with detailed finite element models and compared to those from a nonlinear least squares‐based optimization.
Two‐dimensional meso‐structural simulation of concrete fracture by the implementation of zero‐thickness cohesive interface elements
Authors: Najafi Koopas Rasoul , Rauter Natalie , Lammering Rolf 
Published: March 2023

AbstractConcrete is considered as a non‐homogeneous material and from a mesoscopic point of view is constituted of three main phases, namely aggregates, mortar matrix and interfacial transition zone (ITZ). To investigate the damage process of concrete materials at the mesoscale due to mechanical loading, an explicit numerical model with full representation of the three mesoscopic phases is required. To this end, in this work, a Python code is developed to generate zero‐thickness cohesive interface elements in two‐dimensions (2D). The generated code is capable of generating two‐dimensional quadratic cohesive interface elements (i) within the mortar elements, (ii) within the aggregates elements and (iii) at interfaces between mortar and aggregates. To simulate the crack propagation, the generated zero thickness‐cohesive elements are preinserted at the interface of solid elements and different traction‐separation laws are assigned to them to simulate all potential crack paths. The implemented algorithms to generate the cohesive elements are discussed in detail and numerical examples of crack propagation in concrete is presented using Abaqus/CAE. The numerical results are compared with those in the literature qualitatively to validate the performance of the model. The developed method provides the possibility to investigate the damage processes in meso‐and micro‐scales underlying the macroscopic behavior of the semi‐brittle materials.
Modeling the size‐effect of metamaterial beams under bending via the relaxed micromorphic continuum
Authors: Sarhil Mohammad , Scheunemann Lisa , Schröder Jörg , Neff Patrizio 
Published: March 2023

AbstractMechanical metamaterials are media with periodic unit cells comprised of tailored geometry in order to accomplish extraordinary bulk mechanical properties which can not be found in conventional materials. However, metamaterials exhibit size‐effect phenomena which can be captured by enriched continua. In this work, the relaxed micromorphic model will be used to reproduce the mechanical response of an assumed metamaterial. The solution of the fully discretized metamaterial is used as a reference that the homogeneous relaxed micromorphic model should meet. We discuss the parameters identification and boundary conditions. Our analysis indicates that the relaxed micromorphic model faithfully reproduces the size‐effect.
Approaches for optimizing surrogate models considering uncertain parameters
Authors: Oberleiter Thomas , Willner Kai 
Published: March 2023

AbstractSurrogate models are a common tool to perform expensive optimization or uncertainty analysis in a cost‐effective way. The structure and the application of surrogate models is well known, but there is still potential for improvement. The structure of the surrogate model can be divided into three parts, which can be considered separately. The sampling plan, the black box and the selection of the model itself. The optimization of the surrogate models in the sampling plan and the black box is presented on the basis of two case studies. In the sampling plans, the example of the FOSS method is used to show how sampling points are found for an optimized uncertainty analysis with a low number of sampling points. It is taken into account that the result space is not uniformly relevant for the uncertainty consideration with fuzzy parameters. If the black box is a problem from mechanics, known information can be used for an optimized surrogate modeling. For a Finite‐Element‐Method (FEM) black box, it makes sense to consider the maximum possible number of sampling points and maximum accuracy of the FEM‐black box with regard to the surrogate modeling. As the case study shows, a reduction of the accuracy in the FEM calculation, by using a lower mesh density, can lead to an increasing accuracy of the surrogate model.
Curved, linear Kirchhoff beams formulated using tangential differential calculus and Lagrange multipliers
Authors: Kaiser Michael Wolfgang , Fries Thomas-Peter 
Published: March 2023

AbstractLinear Kirchhoff beams, also known as curved Euler‐Bernoulli beams, are reformulated using tangential differential calculus (TDC). The model is formulated in a two dimensional Cartesian coordinate system. Isogeometric analysis (IGA) is employed, hence, NURBS are used for the geometry definition and generation of sufficiently smooth shape functions. Dirichlet boundary conditions are enforced weakly using Lagrange multipliers. As a post‐processing step, the obtained FE solution is inserted into the strong form of the governing equations and this residual error is integrated over the domain in an L2‐sense. For sufficiently smooth physical fields, higher‐order convergence rates are achieved in the residual errors. For classical benchmark test cases with known analytical solutions, we also confirm optimal convergence rates in the displacements.
An Inverse Neural Particle Method for Flow Field Reconstruction
Authors: Wessels Henning 
Published: March 2023

AbstractPhysics‐Informed Neural Networks (PINNs) are a novel discretization scheme for the solution of partial differential equations (PDEs), where a neural network is chosen as global ansatz function. The problem of solving the PDE is then cast as an optimization problem and addressed by training the neural network. PINNs have been promoted to perform particularly well in inverse problems. This contribution presents recent advances of the Neural Particle Method, an updated Lagrangian Physics‐Informed Neural Network, in the inverse problem of reconstructing flow fields from sparse data.
Numerical comparison of biofilm growth models using prominent modeling approaches
Authors: Klempt Felix , Soleimani Meisam , Junker Philipp 
Published: March 2023

AbstractTo make implants, especially oral implants, safer and more durable in patients bodies, in silico models proof to be a useful tool to investigate the growth behavior of harmful biofilms causing implant loss. In literature, most growth models fall into one of two categories: either the growth is calculated volumetricly or by adjusting the density of the growing biological body. The volumetric models perform a kinematic split F = FeFg in which the growth part of the deformation tensor is a direct function of the nutrient concentration Fg = Fg(c). The density based models, on the other hand, develop the density variable φ via an evolution equation. To make existing models more accurate and increase the predictability of those models, a combination of the existing growth models is presented. The model combines the volumetric growth model implemented by a kinematic split of the deformation tensor as a function of a growth parameter Fg(α). The numerical example presented here shows sensible growing behaviour. The combined model thus makes a very promising approach in simulating growth more accurately.
A detailed surface reaction mechanism to investigate oxidation of methane over nickel catalyst
Authors: Rakhi  , Günther Vivien , Mauss Fabian 
Published: March 2023

AbstractWe have developed a kinetically consistent detailed surface reaction mechanism for modeling the oxidation of methane over a nickel‐based catalyst. A one‐dimensional model, LOGEcat based on the single‐channel 1D catalyst model, is used to perform the simulations. The original multi‐step reaction mechanism is thermodynamically consistent and consists of 52 reactions. By thermodynamic consistency, we mean that the equilibrium is achieved with the support of the Arrhenius parameters and does not depend on the thermochemistry of the species involved in the considered reactions. The detailed mechanism developed in this investigation contains 26 reversible reactions. These reactions are obtained with the use of the thermochemistry of the species. The study focuses on ensuring kinetic consistency and this is done with the help of thermodynamic analysis by bringing the thermochemistry of the species in play in order to develop a surface reaction mechanism. The new mechanism can be used to understand the other processes, for example, steam‐ and dry‐reforming of methane over nickel, however, the main focus of the paper is to check the performance of the detailed mechanism for catalytic partial oxidation of methane. The applicability of the mechanism is checked for various reactor conditions in terms of parameters such as temperature and pressure by comparing the results with the available reference data. The detailed mechanism developed in this study is able to accurately express oxidation of methane over the nickel catalyst for the considered reactor conditions.
A Continuous Model for Demand‐Side Management in an Aggregator Model in Electricity Markets
Authors: Thünen Anna , Ulke Alena 
Published: March 2023

AbstractWe develop a novel time continuous Stackelberg game to model the interaction of costumers and aggregators in electricity markets. It features time dependent pricing policies that aim to align electricity consumption with its availability. Furthermore the model has the special potential of scalability with respect to the amount of costumers. We illustrate that in fact the aggregator can create an incentive to the costumer that is then changing its consumption behavior.
Adaptive methods for MOR in non‐linear FE simulations of unit cells
Authors: Özmen Yasemin , Scheunemann Lisa , Nigro Paulo S. B. , Schröder Jörg 
Published: March 2023

AbstractIn this contribution, an adaptive method for Model Order Reduction (MOR) is presented for simulating physically non‐linear material behavior of micro‐heterogeneous structures. The method is purely online and includes a Galerkin projection, which is performed using a projection operator initially gained by a Proper Orthogonal Decomposition (POD). By this projection, the number of degrees of freedom to solve for is decreased drastically and can be projected back to the vector space of the high fidelity problem after the solution process. The composition of the projection operator follows an adaptive algorithm, which evaluates an update of the operator if convergence is not ensured during the Newton Raphson scheme. Later on, during the simulation, the number of degrees of freedom to solve is controlled using a POD‐based control criterion for sorting out non‐relevant basis vectors from previous updates. This results in an efficient method and leads to a satisfying speedup of the simulation process. The performance and efficiency of the presented adaptive MOR scheme is investigated in numerical simulations of a hexagon‐shaped unit cell.
Growth of green wood based on a phase field model
Authors: Wulf Jan Bernd , Muench Ingo 
Published: March 2023

AbstractTree engineering is a young discipline utilizing trees as structural elements, where the determination of limit loads in tree trunks is of great importance. Simple numerical models underestimate the load‐bearing capacity of green wood in contrast to experimental bending tests. A well‐known reason for this is the residual stress state of the living tree lowering compressive stress towards the trunks surface. This results in an overall stress state, which increases the load capacity, since the tensile strength of wood is commonly higher than its compressive strength. By determining the residual growth stress, a more accurate evaluation of the load‐bearing capacity of a living tree is possible. The residual stress state is a non‐linear and time dependent function in thickness direction of the trunk. In order to simulate growth and growth stress, a phase field model is employed.The morphology of a tree is the result of innumerable and often temporary environmental stimuli, which also change and interact with the genetically predisposed growth tropisms. Therefore, we use image processing to capture the individual tree morphology of an existing tree, which is based within the phase field model as predefined growth direction. This is the basis for primary growth in the model. Additionally the model simulates the secondary growth, which corresponds to the thickness of the trunk. Except in tropical areas, this growth is associated with growth rings, which we assign as an attribute to the modelled material. While in the branch structure several tropisms (e.g. gravitropism) are responsible for the off‐centre accumulation of woody material, in the stem region we only follow the stress‐induced growth. This mechanism can respond to either the principal tensile stress or the principal compressive stress in our model, as this difference is observed in hardwoods and softwoods.Since the wood matrix represents an anisotropic material with a distinct fiber direction, we approach it in our model by a transversely isotropic constitutive law, whose principal direction coincides with the growth direction.
Factors influencing the dynamic stiffness in short‐fiber reinforced polymers
Authors: Magino Nicola , Köbler Jonathan , Andrä Heiko , Welschinger Fabian , Müller Ralf , Schneider Matti 
Published: March 2023

AbstractIn short‐fiber reinforced polymers, fatigue damage is typically characterized by measuring the dynamic stiffness and its degradation under cyclic loading. Computational homogenization methods may be used to characterize the fatigue behavior of the composite via numerical predictions. Such an approach may reduce the experimental effort significantly. In the previous works, the authors proposed an elastic fatigue damage model for predicting the relative stiffness degradation of short‐fiber reinforced materials. However, the absolute value of the dynamic stiffness within the first cycle showed deviations from the expected elastic material behavior. Thus, the effect of viscoelastic polymer behavior as well as different microstructure descriptors on the dynamic stiffness is studied in the work at hand.
Data‐based prediction of the viscoelastic behavior of short fiber reinforced composites
Authors: Marr Julian , Zartmann Lukas , Reinel-Bitzer Doris , Andrä Heiko , Müller Ralf 
Published: March 2023

AbstractThe viscoelastic behavior of short fiber reinforced polymers (SFRPs) partly depends on different microstructural parameters such as the local fiber orientation distribution. To account for this by simulation on component level, two‐scale methods couple simulations on the micro‐ and macroscale, which involve considerable computational costs. To circumvent this problem, the generation of a viscoelastic surrogate model is presented here. For that purpose, an adaptive sampling technique is investigated and data are obtained by creep simulations of representative volume elements (RVEs) using a fast Fourier transform (FFT) based homogenization method. Numerical tests confirm the high accuracy of the surrogate model. The possibility of using that model for efficient material optimization is shown.
Artefact Indicator for Flow‐based Temporal Interpolation of Power Doppler Ultrasound
Authors: Biberger Simon , Mercier Gwenael , Wallinger Christian , Buckton Daniel , Scherzer Otmar 
Published: March 2023

AbstractPower Doppler ultrasound is a sonography technique to detect and visualise blood circulation. Its acquired image sequences suffer from poor temporal resolution and artefacts caused by aliasing, noise, large displacements, shearings or out‐of‐plane movements. These pitfalls distort flow fields and have unforeseen consequences on flow‐based temporal interpolations. We propose a method to detect artefacts caused by such distorted flow fields and to improve the visual quality by replacing regions with detected artefacts by locally better results. This is demonstrated on real data.
Model‐free data‐driven inelasticity in Haigh‐Westergaard space ‐ a study how to obtain data points from measurements
Authors: Ciftci Kerem , Hackl Klaus 
Published: March 2023

AbstractModel‐free data‐driven computational mechanics replace phenomenological models with numerical simulations in strain‐stress space based on sample data sets. The approach has recently been extended to inelasticity problems employing structured data sets, tangent space information, and transition rules. Coverage of qualified data states and calculation of the related tangent space is critical from the standpoint of actual application. This study applies the data‐driven paradigm to elasto‐plasticity with isotropic hardening. We develop our method using Haigh‐Westergaard coordinates, which provide information on the underlying material yield surface. Based on this, we employ a combined tension‐torsion test to cover the yield surface knowledge and a single tensile test to determine the tangent space. Under compatibility and equilibrium requirements, the resulting data‐driven technique minimizes the distance over the Haigh‐Westergaard space augmented by directions in the tangent space.
Solving phase‐field fracture problems in the tensor train format
Authors: Risthaus Lennart , Schneider Matti 
Published: March 2023

AbstractPhase‐field models for the quasi‐static simulation of brittle fracture where the crack is approximated by a damage phase‐field are limited by the necessary memory and computation time. In this contribution, we study the applicability of low‐rank methods to phase‐field fracture models, specifically the tensor train (TT) format. To this end, we investigate the low‐rank structure of the crack phase‐field. Additionally, we present an implementation of an alternating minimization scheme to solve the coupled displacement and damage problem in the TT format. We show the evolution of the TT ranks of the displacement and damage fields for a specific example.
Weak solutions to gradient flows in metric measure spaces
Authors: Górny Wojciech , Mazón José M. 
Published: March 2023

AbstractDue to the fact that in a metric space there is (in general) no notion of directional derivatives, the definition of solutions to gradient flows in metric measure spaces necessarily avoid their direct use. The most classical example is the heat flow, or more generally the p‐Laplacian evolution equation, which has been studied as the gradient flow in L2 of the p‐Cheeger energy. Typically, solutions are defined using the semigroup theory through a subdifferential of the energy. Other popular approaches include variational solutions and the weighted energy‐dissipation formalism. In this paper, using the first‐order differential structure on a metric measure space introduced by Gigli, we characterize the subdifferential in L2 of the p‐Cheeger energy. This gives rise to a new notion of solutions to the p‐Laplacian evolution equation in metric measure spaces. In the case p = 1, we introduce a metric analogue of the Anzellotti pairing and obtain a Green‐Gauss formula, which is then used in place of Gigli's structure to characterise the 1‐Laplacian operator and study the total variation flow.
Investigation of a Realistic Flap Modeling Using a Combination of Chimera Method and Grid Deformation on a Wing Fuselage Configuration
Authors: Hillebrand Marco , Müller Jens , Ullah Junaid , Lutz Thorsten 
Published: March 2023

AbstractFlap deflections of an aircraft wing for active load alleviation within CFD simulations are realized using pure grid deformation due to time saving and low modeling complexity. In this case, spanwise gaps are neglected, which are present in reality during a flap deflection. Another possibility to realize the deflections is the combination of pure grid deformation and Chimera method, which allows the modeling of the gap between flap and wing or consecutive flaps. The overall aim of this work is the analysis of the aerodynamic effects caused by the different modeling approaches realizing leading and trailing edge flap deflections. The comparison of the modeling methods is investigated on the DLR LEISA configuration, which is a generic wing‐fuselage configuration. For active gust load alleviation, the leading edge flaps are deflected downward and the trailing edge flaps are deflected upward. Due to the downward deflection of the leading edge flaps, vortices are formed using the combined Chimera method as a result of the gap consideration. These vortices lead to a local drag increase resulting in a difference between both modeling methods in the spanwise as well as global drag coefficient. With the pure grid deformation these vortices do not occur. Due to the upward trailing edge deflection, the combined Chimera method leads to a pressure compensation via the effective gap enlargement, which is not present in the pure grid deformation. Overall, the combined Chimera method offers a good possibility to model the induced drag as well as the pressure compensation at a large flap deflection.