bluuebunny/crossref_metadata_2025 huggingface dataset:
Optimal tax policy of a one‐predator–two‐prey system with a marine protected area
Authors: Huang Lirong , Cai Donghan , Liu Weiyi
Published: January 2021

This paper is devoted to handle a dynamic one‐predator–two‐prey model. In order to protect fish population from over exploitation, we assume that marine protected area (MPA) is established and the fisherman only harvest the prey in the unreserved area, the predator consumes the prey in both the MPA and the unreserved area. And a tax is imposed in the process of harvesting. To begin with, boundeness of the system is discussed. Following this, we studied the existence of the possible equilibrium along with their local stability for both of the unexploited system (8) and exploited system (5). After that, we analyzed the global stability of the positive equilibrium of the exploited system and how the tax τ affects the positive equilibrium. Then, the optimal tax policy is obtained by using the Pontryagin's maximum principle. Finally, some numerical simulations are given to support the analytical findings.
Miniaturized single‐/dual‐band bandpass filters based on grounded square patch resonator with controllable passbands
Authors: Fei Huihui , Wang Yangyang , Zhang Qiao , Zhou Lingyun , Chen Weidong , Chen Chang
Published: January 2021

Miniaturized single‐/dual‐band bandpass filters (BPFs) are proposed in this paper based on one single grounded square patch (GSP) resonator. The GSP resonator is realized by introducing ring‐shaped metallic vias at the center of a patch. Owing to this specific geometry, an additional mode nominated as LC mode is generated, which makes the proposed GSP resonator operate below the fundamental resonate frequency of the non‐grounded patch, thus miniaturization has been achieved. In addition, several slots are etched on the GSP resonator to serve as perturbations and control bandwidths (BWs) and center frequencies of the filter. As a result, the designed filters have featured both compact size and independent controllability. Moreover, single‐ or dual‐band BPF can be realized by changing the location of the input/output feedlines. For demonstration, the proposed filters have been fabricated, and the measured results agree with predicted responses.
Effect of Aerobic Exercise Intensity on Energy Expenditure and Weight Loss in Severe Obesity—A Randomized Controlled Trial
Authors: Berge Jarle , Hjelmesæth Jøran , Hertel Jens K. , Gjevestad Espen , Småstuen Milada Cvancarova , Johnson Line Kristin , Martins Catia , Andersen Eivind , Helgerud Jan , Støren Øyvind
Published: January 2021

Objective

This study aimed to compare the effects of two aerobic exercise programs of different intensities on energy expenditure.

Methods

This was a single‐center randomized controlled trial of patients with severe obesity allocated to a 24‐week moderate‐intensity continuous training (MICT) program or a combined MICT with high‐intensity interval training (HIIT/MICT) program. The primary outcome was energy expenditure during exercise (EEDE). Secondary outcomes included resting metabolic rate, cardiorespiratory fitness, and body composition.

Results

A total of 82 (56% females) patients were screened, and 71 (55% females) patients were allocated to HIIT/MICT (n = 37) or MICT (n = 34). Per‐protocol analysis showed that EEDE increased by 10% (95% CI: 3%‐17%) in the HIIT/MICT group (n = 16) and 7.5% (95% CI: 4%‐10%) in the MICT group (n = 24), with no differences between groups. In the 8‐ to 16‐ week per‐protocol analysis, the HIIT/MICT group had a significantly larger increase in EEDE compared with the MICT group. Resting metabolic rate remained unchanged in both groups. HIIT/MICT and MICT were associated with significant weight loss of 5 kg and 2 kg, respectively.

Conclusions

Patients completing a 24‐week combined HIIT/MICT program did not achieve a higher EEDE compared with those who completed a 24‐week MICT program. The HIIT/MICT group experienced, on average, a 3‐kg‐larger weight loss than the MICT group.
Evidence of a Role for the Hippocampus in Food‐Cue Processing and the Association with Body Weight and Dietary Added Sugar
Authors: Jones Sabrina , Luo Shan , Dorton Hilary M. , Angelo Brendan , Yunker Alexandra G. , Monterosso John R. , Page Kathleen A.
Published: January 2021

Objective

The current analysis used functional magnetic resonance imaging (fMRI) to explore a model of energy regulation postulating that the hippocampus integrates interoceptive signals and environmental stimuli to suppress responding to food cues. It was hypothesized that hippocampal activity would increase in response to food cues under postnutritive relative to fasted conditions, given the role of the hippocampus in integrating postnutritive signals with food cues, and that obesity, added sugar intake, or a combination of these factors would alter this response.

Methods

Data were analyzed on 65 participants (29 males). Participants consumed drinks containing 75 g of glucose or water and underwent an fMRI‐based food‐cue task. Blood‐oxygen‐level‐dependent (BOLD) fMRI was used to examine hippocampal responses to food and nonfood cues.

Results

In lean participants, the hippocampal BOLD signal was higher following glucose compared with water, but participants with obesity showed the opposite pattern. BMI interacted with added sugar intake such that BMI was more negatively correlated with hippocampal food‐cue reactivity after glucose ingestion in individuals who consumed high levels of added sugar. Hippocampal BOLD was negatively correlated with prospective food intake.

Conclusions

The findings are consistent with the view that energy regulation involves hippocampal processes in humans and that added sugar and excess weight may impair this function.
MBS model for control and optimization of a hydrofoil boat
Authors: Graf Matthias
Published: January 2021

The most efficient hull concept for racing boats is a hull completely lifted out of the water by a configuration of hydrodynamic foils. Due to its similarity to an inverted pendulum, the system is intrinsically unstable and requires control mechanisms. This paper describes a typical configuration of a hull and the hydrofoils and the corresponding MBS model. The MBS‐model allows studying parameters for control and hydrofoil positions and is coupled with a global optimizer to choose the most beneficial set of parameters.
Measuring the Time Discretization Error in Linear Elasticity
Authors: Schröder Bettina , Kuhl Detlef
Published: January 2021

The present paper considers the spread of longitudinal waves in an elastic rod. On the one hand an analytical solution is presented, on the other hand a spatially and temporally discretized continuum formulation of this problem is treated. With these approaches at hand the appearing time discretization error is analyzed using various quantities.
A hybrid model for the electrothermal behavior of semiconductor devices
Authors: Glitzky Annegret , Liero Matthias , Nika Grigor
Published: January 2021

We introduce a hybrid model for the electro‐thermal behavior of semiconductor heterostructures. It combines a model based on drift‐diffusion with thermistor type models in different subregions of the semiconductor device. The aim of this hybrid modeling approach is to be physically as accurate as necessary and at the same time as computationally efficient as possible. Our existence proof uses a regularization method, a priori estimates, and Schauder's fixed point theorem.
Phase field modeling of fatigue crack initiation and growth under various loading situations
Authors: Schreiber Christoph , Kuhn Charlotte , Müller Ralf
Published: January 2021

In this work we illustrate the ability of a phase field model for fatigue crack growth in terms of extension capability to various amplitude loading and mean stress effects. The additional energy density contribution accounting for the energy associated with fatigue is modified in order to provide a more general model. Results obtained from numerical fatigue crack growth simulations are briefly presented and discussed.
Modelling fluid‐driven fractures for partially saturated porous materials
Authors: Sonntag Alixa , Wagner Arndt , Ehlers Wolfgang
Published: January 2021

This contribution aims to study the influence of the saturation degree on the fracturing process. Therefore, a continuum‐mechanical model for fluid‐driven fracturing in partially saturated porous material is presented on the basis of the Theory of Porous Media and the phase‐field approach to fracture. The material is described on the macroscopic scale as an immiscible mixture of three phases, i.e. a solid phase, representing the solid skeleton, and two fluid phases percolating the pore space. Hereby, capillarity effects between the fluid phases are taken into account. The fracturing process is modelled with a phase‐field approach, characterising a diffuse crack pattern. The crack propagation in the solid skeleton is driven by the pressure field of the injected fluid. Finally, a numerical example showing the coupled process of crack propagation in partially saturated porous materials is discussed.
A higher order fictitious domain method for the Navier–Stokes equations
Authors: Bause Markus , Anselmann Mathias
Published: January 2021

We present a higher order approach for the numerical approximation of the Navier–Stokes equations of incompressible viscous flow on time‐dependent domains. A fictitious domain method using non body‐fitted finite element meshes for immersed and moving boundaries along with cut cell techniques is applied. Higher order discontinuous Galerkin time discretization schemes and inf‐sup stable pairs of finite elements for the discretization in space are further ingredients of the approach.
Experimental Investigation of non‐periodic oscillations in a surface tension driven flow around a bubble
Authors: Tadrous Ebram , Wozniak Günter
Published: January 2021

Thermocapillary convection around an air bubble under a heated wall is experimentally investigated under gravitational conditions. The flow is basically studied through temperature fluctuation plots near the bubble periphery, which is subjected to an upward flow driving temperature gradient. This study illuminates the thermocapillary‐buoyancy convective flow behaviour within the regime of non‐periodic oscillations. Moreover, the fluid flow is qualitatively categorized according to the transient behaviour of the thermocapillary vortex boundary line around the bubble using the shadowgraph technique. A low viscous silicone oil as test fluid restricts reaching higher temperature gradients to avoid the formation of undesired vapour bubbles. However, pursuing the experiments under high pressures allowed reaching higher temperature gradients in order to achieve the non‐periodic flow regime. Both periodic and chaotic oscillations of the liquid flow around the bubble were recorded. They were distinguished from each other through the periodicity of the visualized thermocapillary vortex boundary line movements. The recording of temperature fluctuations at positions near the bubble during a time period Δt demonstrated the thermocapillary fluid flow behaviour at different Marangoni‐numbers Mg.
Integral jump conditions for singular problems – applied to Debye‐layer phenomena
Authors: Marthaler Philipp G. , Class Andreas G.
Published: January 2021

In numerical simulations boundary layers can be treated as jump conditions inheriting detailed physical effects that emerge inside the thin layer. The presented approach, first applied by Class et al. [3], is used to determine such jump conditions in integral form. It is applied to an electro‐hydrodynamic problem with a Debye‐layer in direct vicinity to a charged solid wall.
Substructured Model Order Reduction for Simple Exchange of Subsystems
Authors: Walker Nadine , Eberhard Peter
Published: January 2021

This contribution deals with substrucutured model order reduction for simple exchange of substructures. It is shown, that the Krylov‐Subspace‐Method is well suited in this context and a numerical example is presented.
Inverse Identification of Material Properties of the Human Eye Using Optical Deformation Measurements
Authors: Muench Stefan , Roellig Mike , Balzani Daniel
Published: January 2021

The aim of the study presented here is the non‐invasive and in‐vivo measurement of material parameters of the eye. For this purpose, we propose a method for the construction of full‐field displacements from 2D deformation contours to enable a fast identification of material parameters, which could be used as advanced diagnostic tool for a broad range of diseases of the human eye. First results are presented here based on virtual test setups which should be confirmed through the use of real medical data in the future.
Influence of lubricant film cavitation on the rotor dynamic system behaviour of an exhaust gas turbocharger rotor
Authors: Ziese Christian , Irmscher Cornelius , Woschke Elmar
Published: January 2021

The vibration behaviour of fast rotating rotors is significantly influenced by the bearing properties. Lubricant film induced excitations can cause sub‐synchronous rotor oscillations known as oil‐whirl and oil‐whip phenomena. The non‐linear bearing properties depend primarily on the lubricant properties, kinematics of bearing partners and especially on the occurrence of cavitation. Outgassing processes lead to a two‐phase flow consisting of gas and oil, which can influence the bearing stiffness and damping respectively and consequently the rotor response behaviour. In this contribution, the oscillations of a semi‐floating ring supported turbocharger rotor are investigated under the influence of lubricant film cavitation. For this purpose, run‐up simulations are carried out under the assumption of mass‐conserving cavitation according to the two‐phase model and compared with measurements. In order to illustrate the influence of outgassing processes, a comparison is made with non‐mass‐conserving cavitation theory according to the assumptions of Half‐Sommerfeld.
Modelling stress‐state dependent nonlocal damage and failure of ductile metals
Authors: Nahrmann Marvin , Matzenmiller Anton
Published: January 2021

Damage and failure of ductile metals is highly influenced by the stress state. In fact, void growth takes place under hydrostatic tensile loading and void coalescence leads eventually to ductile failure. A completely different damage mechanism occurs for shear dominated loading that results in void elongation within a narrow shear band. In order to account for both failure mechanisms, a stress state dependent damage model is proposed. The model is based on a continuum damage mechanics approach, whereby nonlinear damage evolution is taken into account. The influence of the stress triaxiality and the LODE parameter on damage initiation and failure is considered by the Hosford‐Coulomb model. Pathological mesh sensitivity is prevented by an integral type nonlocal formulation. Finally, the proposed stress‐state dependent nonlocal damage model is verified by test data for the microalloyed high strength steel HX340LAD for a wide range of stress states.
Statistical Analysis of Missile's Trajectory Deviation Due to Production Errors
Authors: Trzun Zvonko , Vrdoljak Milan , Cajner Hrvoje
Published: January 2021

The paper describes the model for assessing the effect that manufacturing errors have on the missile's trajectory and the position of its impact point. Manufacturing errors are considered to be non‐deterministic variables. One typical error is analyzed: the erroneously manufactured missile's warhead. To test the resulting trajectory deviation, a realistic 3D CAD model of a missile is built and linked to the improved 6DOF model. A simulation using the Monte‐Carlo method shows the resulting dispersion of missile's impact points.
The legacy of Coulomb and generalized laws of friction
Authors: Popova Elena , Popov Valentin L.
Published: January 2021

The simple formulation of “Coulomb's law of friction” which can be found in most textbooks—the force of friction is proportional to the normal force and does not depend on the contact area and velocity—has little to do with the real work of Coulomb. On the contrary, Coulomb found that Amontons' law, as well as the independence of the coefficient of friction on velocity, normal force, contact area and roughness are only a first, very rough approximation. He differentiated between material couples (e.g. metal‐metal), where Amontons' law is a good approximation, and other (wood on metal or wood on wood), where there are significant deviations from Amontons' law. In all cases, however, the dependencies are relatively weak. In contemporary language, we would say they are of logarithmic character: the geometric and loading parameters have to be changed by several orders of magnitude to achieve a change in the coefficient of friction by a factor of two. Coulomb also gives simple two‐term relations, which empirically summarize these experimental findings.
MLMC method to estimate propagation of uncertainties in electromagnetic fields scattered from objects of uncertain shapes
Authors: Litvinenko Alexander , Yucel Abdulkadir , Bagci Hakan , Oppelstrup Jesper , Michielssen Eric , Tempone Raúl
Published: January 2021

We estimate the propagation of uncertainties in electromagnetic wave scattering problems. The computational domain is a dielectric object with uncertain shape. Since classical Monte Carlo (MC) method is too expensive, we suggest to use a modified multilevel Monte Carlo (MLMC) method. This method uses a hierarchy of spatial meshes and optimally balances the statistical and discretisation errors. MLMC performs most of the simulations using low‐fidelity models and only a few simulations using high‐fidelity models. As a result, the final computational cost is becoming significantly smaller.
Simulation of absorption processes in nanoparticle catalysts
Authors: Köhler Maximilian , Junker Philipp , Balzani Daniel
Published: January 2021

In this contribution, we present a novel modeling approach for mass transport problems that connects the microscale with the macroscale. It is based on a proper investigation of the diffusion process in the catalytic pellets from which, after semi‐analytic considerations, a source term for the macroscopic advection‐diffusion process can be identified. For the special case of a spherical catalyst pellet, the parabolic partial differential equation at the microscale can be reduced to a single ordinary differential equation in time through the proposed semi‐analytic approach. After the presentation of our model, we show results for its calibration against the macroscopic response of a mass transport experiment. Based thereon, the effective diffusion parameters of the catalyst pellet can be identified. Furthermore, we test the model's robustness by applying significant noise to virtual experimental datasets.
Analysis of model and data uncertainties for the failure of adhesive bonds in composite materials
Authors: Drieschner Martin , Gruhlke Robert , Petryna Yuri , Eigel Martin , Hömberg Dietmar
Published: January 2021

This study has been performed within the research project MuScaBlaDes “Multi‐scale failure analysis with polymorphic uncertainties for optimal design of rotor blades" as part of the DFG Priority Programme (SPP 1886) “Polymorphic Uncertainty Modelling for the Numerical Design of Structures" started in 2016. Stress concentrations in adhesive bonds of a composite structure influence the structural integrity and can initiate the overall failure. Their numerical prediction always depends on present model and data uncertainties. For that, the development of an efficient numerical model and the role of the quality of data is presented. The assessment of the numerical models is shown by comparing predicted strains to measured ones.
Influence of the geometric nonlinearity on the wave propagation properties of periodic lattice frame structures
Authors: Mellmann Marius , Zhang Chuanzeng
Published: January 2021

The elastic wave propagation and vibration characteristics of periodic lattice frame structures can be tuned by changing the density or the stiffness of the structural components, adding certain local resonators or pre‐deforming some structural members [1, 2]. In this way, it is possible to generate the so‐called band‐gaps, which are certain frequency ranges, in which the propagation of elastic or acoustic waves is prohibited. In this paper, the influence of the geometric nonlinearity on the wave propagation properties of two‐dimensional (2D) periodic lattice frame structures is analyzed.
Analysis of the remote laser cutting process induced damage in carbon fibre reinforced polymers with cutting process simulations
Authors: Schmidt Benjamin , Rose Michael , Zimmermann Martina , Kästner Markus
Published: January 2021

Remote laser cutting in carbon fibre reinforced polymers is a promising machining technology, which can reduce the main drawback in laser cutting, the heat affected zone. As the heat affected zone has a strong influence on the mechanical behaviour of the composite, an exact characterisation is a key challenge for the simulation and design of fibre reinforced polymers. In order to reach this goal, a laser cutting process model is introduced. Based on the finite difference method, the heat transport is modelled on a macroscopic scale. The macroscopic material parameters are calculated with a rule of mixture. Matrix and fibre evaporation, which cause the formation of the matrix evaporation zone and the gap, are modelled with phase transitions and an adaption in the rule of mixture.

The simulation results are validated with micro‐sections of the cutting gap.
The Virtual Element Method for the numerical homogenization of electro‐mechanical responses
Authors: Böhm Christoph , Hudobivnik Blaž , Marino Michele , Wriggers Peter
Published: January 2021

The virtual element method (VEM) has been attracting interest for applications in micromechanical homogenization. This work aims to introduce and analyze multiphysical formulations in a VEM‐based numerical homogenization scheme. Addressing electromechanical polycrystalline materials, the performance of a VEM‐based approach with respect to FEM‐based approaches is investigated. Results show the outperformance of VEM with respect to FEM models (with the same number of degrees of freedom) on the obtained value of homogenized quantities. The coarse mesh permitted by the VEM rationale, where each grain might represent one element, allows to maintain a low computational cost with a high accuracy.
A Scaled Boundary Approach for Inelasticity of Fibre‐Reinforced Composites
Authors: Eisenträger Johanna , Zhang Junqi , Song Chongmin
Published: January 2021

As versatile materials with elevated mechanical properties, short fibre reinforced composites (SFRCs) are currently used in many applications. To enhance the mechanical properties, e.g. the ductility, or to reduce crack propagation, short fibres are added to a matrix material, such as polymers or concrete. In the case of concrete, for example, the composite might contain additional aggregates as well. Although the addition of fibres improves the mechanical properties in general, it is well‐known that many matrix materials exhibit creep deformations under constant long‐term loads.

The contribution at hand discusses a scaled boundary approach to model the inelastic behaviour of SFRCs. To allow for an efficient and automated mesh generation, the scaled boundary finite element method (SBFEM) is used in conjunction with the quadtree/octree decomposition algorithm. Within this framework, the fibres are modelled in a discrete manner, and the mesh of the matrix is generated independently of the fibres. Applying a novel embedding method, the meshes of the matrix and the fibres are combined, which results in a compatible mesh without requiring additional constraints. Furthermore, it is straightforward to combine the discussed techniques with image‐based mesh generation, e.g. based on computed tomography scans. The current contribution presents various 2D and 3D examples illustrating the efficiency and adaptability of the proposed framework.

In addition, we present a methodology to incorporate non‐linear constitutive models into the SBFEM. Separate constitutive equations are formulated for the matrix, aggregates, and fibres. Whereas the mechanical behaviour of the aggregates and the fibres can be modelled within the framework of elasticity, one must make use of non‐linear approaches to account for the rate‐dependent inelastic deformation of the matrix under multiaxial stress and deformation states. Overall, this method allows for the simulation of creep in SFRCs, while considering the complex microstructure of these materials in detail. This provides the basis for a realistic estimation of the effect of long‐term loading on SFRC components.
About the influence of neglecting locking effects on the failure behavior at the interface
Authors: Bayat Hamid Reza , Rezaei Shahed , Rajaei Harandi Ali , Brepols Tim , Reese Stefanie
Published: January 2021

In the present work, a novel cohesive discontinuous Galerkin (CDG) method is proposed to model interfacial failure of brittle materials. Before the failure, an incomplete interior penalty Galerkin (IIPG) variant of discontinuous Galerkin (DG) family is applied for the linear elasticity. Once the failure criterion is met, an extrinsic cohesive zone (CZ) model captures the failure behavior of the interface. Through application of the DG method in combination with reduced integration on the boundary terms, the locking problem of the bulk elements is solved as well as a realistic propagation of the crack is obtained. In addition, due to the presence of the DG elements prior to failure, remeshing of the interface during crack propagation is not required for the proposed extrinsic CZ model. Delamination of a composite structure is simulated in a numerical example. Furthermore, the performance of the CDG element formulation in comparison to a conventional intrinsic CZ element is discussed and conclusions are drawn.
Tensile Strength Simulations of Nonwoven Fiber Materials
Authors: Harmening Marc , Marheineke Nicole , Wegener Raimund
Published: January 2021

For airlay manufactured nonwoven materials we present a model which enables efficient tensile strength simulations using virtually generated fiber structure samples. Therefore, we model the fiber structures as truss which yields a family of large‐scale, non‐linear equation systems that has to be solved in order to simulate the elastic material behavior. The assembly and regularization of these non‐linear systems are discussed in this paper.
The maximal angle condition on finite elements: useful or not?
Authors: Apel Thomas , Eckardt Leon , Haubner Christof , Kempf Volker
Published: January 2021

The finite element method may converge in situations where the interpolation error does not; in particular meshes violating the maximal angle condition were discussed in the literature recently. However, there is also an example where the finite element method does not converge to the exact solution of the problem on these types of meshes. With a numerical study we stress that the finite element method converges; it converges to a function which is not the exact solution. A carefully designed a posteriori error estimator indicates this behavior. But a numerical test with the error measure as the difference to a solution on a very fine mesh of the same family leads to completely wrong conclusions: one observes a convergence order.
A first Model of Fatigue Corrosion of a Metal through Hydrogen Embrittlement
Authors: Hofmann Martin , Shi Yuhao , Wallmersperger Thomas
Published: January 2021

Predicting the durability of components under mechanical loading combined with environmental conditions leading to corrosion is one of the most challenging tasks in mechanical engineering. Precise predictions are neccesary for lightweight design in transportation due to environmental protection. During corrosion often hydrogen is produced by electrochemical reactions. Hydrogen embrittlement is one of the most feared damage mechanisms for metal constructions leading to early and unexpected failure. Until now predictions are mostly done through costly experiments. In the present research, a first simple simulation model based on the fundamentals of electrochemistry and continuum damage mechanics is developed to couple the damage induced by the mechanical stress with the hydrogen embrittlement. Results of the durability are presented for the case of uniaxial cyclic loading for varying testing frequency.
Electrohydrodynamic‐enhanced internal pipe flows from a One‐Dimensional Turbulence perspective
Authors: Medina Méndez Juan A. , Schmidt Heiko , Bacher Christian , Riebel Ulrich
Published: January 2021

The One‐Dimensional Turbulence (ODT) model is applied for the evaluation of internal pipe flows subject to electrohydrodynamic (EHD) forces. The ODT formulation presented here incorporates the effects of the electrostatic potential energy transfer to the kinetic energy of the flow due to EHD instabilities in the presence of a corona discharge. Results for integral quantities such as the skin friction coefficient Cf and the Nusselt number Nu are obtained from ODT simulations and compared to available experimental data [1,2]. The results demonstrate the capabilities of ODT for simulating EHD flows.
Combined continuum mechanics and molecular dynamics approach for uniaxial deformation of a thermoplastic polymer
Authors: Bauer Christof , Pfaller Sebastian
Published: January 2021

A hybrid molecular dynamics (MD)‐continuum mechanics (CM) method for calculating a molecular system of an amorphous polymer under uniaxial tensile load was developed. In this contribution, the operating principle of this method is introduced and applied to a sample system. Furthermore, the practicability of the hybrid MD‐CM approach is examined.
Predeformed geometrically exact beam model for a dynamic‐response prosthesis
Authors: Scheiterer Eduard S. , Leyendecker Sigrid
Published: January 2021

Clinical trials have shown that the storage and release of energy in prosthetic feet plays a major role in the resulting walking comfort for the patient. In comparison to rigid multi‐axis prosthetic feet, dynamic‐response prosthetic feet show good energy storage and release capabilities and thereby increase the walking comfort of the patient. To accurately simulate such a prosthesis in a gait cycle simulation, its model has to represent the deformation energy as accurately as possible.

Based on the theory of predeformed geometrically exact beams [1], this work proposes a model for a carbon spring foot prosthesis, continuing the work from [3]. The model is based on the Össur Vari‐Flex®, which has been non destructively reverse engineered resulting in a CAD representation and various parameters. Additionally, the parameters for density and elasticity and shear modulus were refined with parameter optimisation [4]. The geometrically exact beam model of the prosthesis offers a good representation of the deformation energy for large deformations occurring during the gait cycle while reducing the computational cost. The model's implementation is validated numerically and a brief mesh study is performed.

The next step is the consideration of epistemic uncertainty and to investigate its influence on the prediction of the energy storage and release capabilities of the prosthesis.
3D Virtual Elements for Elastodynamic Problems
Authors: Cihan Mertcan , Aldakheel Fadi , Hudobivnik Blaž , Wriggers Peter
Published: January 2021

A virtual element framework for nonlinear elastodynamics is outlined within this work. The virtual element method (VEM) can be considered as an extension of the classical finite element method. While the finite element method (FEM) is restricted to the usage of regular shaped elements, VEM allows to use non‐convex shaped elements for the spatial discretization [1]. It has been applied to various engineering problems in elasticity and other areas, such as plasticity or fracture mechanics as outlined in [3, 4]. This work deals with the extension of VEM to dynamic problems. Low‐order ansatz functions in two and three dimensions, with elements being arbitrary shaped, are used in this contribution. The formulations considered in this framework are based on minimization of energy, where a pseudo potential is used for the dynamic behavior. While the stiffness‐matrix needs a suitable stabilization, the mass‐matrix can be calculated fully through the projection part. For the implicit time integration, Newmark‐Method is used. To show the performance of the method, various numerical examples in 2D and 3D are presented.
Model order reduction for small strain elasto‐plasticity based on an adaptive strategy
Authors: Özmen Yasemin , Nigro Paulo S. B. , Scheunemann Lisa , Schröder Jörg
Published: January 2021

In this contribution, an online adaptive reduced order model is presented for small‐strain elasto‐plasticity. Using the GALERKIN method, the problem is projected to a lower subspace giving a reduced problem based on the displacement field snapshots. The adaptivity lies in the update of the projection operator, which is carried out in different parts of the simulation if certain criteria related to the convergence behavior are not fulfilled. With a relative POD analysis called Proper Snapshot Selection (PSS), the new basis is chosen and the simulation is proceeded.
A comparison of different approaches to enforce lattice symmetry in two‐dimensional crystals
Authors: Backofen Rainer , Sahlmann Lisa , Willmann Anna , Voigt Axel
Published: January 2021

The phase‐field crystal (PFC) model allows for the resolution of atomic‐scale structures on diffusive time scales. It is based on an approximation of the two‐particle direct correlation function in the free energy, which provides the symmetry of the lattice structure. Various approaches have been proposed to model common lattices. We here only focus on two‐dimensional crystals, review the different approaches and demonstrate that one, which is based on affine linear deformations, violates rotational invariance. The consequences of this physical inconsistency are shown numerically using a pseudospectral algorithm for the higher order equations.
Lagrangian transport in two‐dimensional time‐periodic cavity flow
Authors: Babor Lukas , Kuhlmann Hendrik C.
Published: January 2021

The Lagrangian transport in a laminar incompressible flow in a two‐dimensional square cavity driven by a harmonic tangential oscillation of a single cavity wall is investigated numerically for a range of Reynolds (Re) and Strouhal (Str) numbers. The topology of fluid trajectories is described by means of stroboscopic projections, which reveal the co‐existence of chaotic trajectories and regular Kolmogorov‐Arnold‐Moser (KAM) tori. The higher the frequency of the lid oscillation the more regular the fluid motion becomes and the size of the KAM tori increases. For low frequencies the KAM tori are strongly stretched along instantaneous streamlines of the flow, while for high frequencies they resemble streamlines of a mean flow.
Influence of Micro‐Inertia on the Macroscale ‐ A Fully‐Coupled Direct Homogenization Framework for Dynamics
Authors: Tamsen Erik , Balzani Daniel
Published: January 2021

This contribution presents a numerical example of a locally‐resonant microstructure, analyzed using a fully‐coupled large strain homogenization framework including dynamics at both scales. The fundamental assumptions the framework is based on are summarized and results showcasing the ability of the proposed homogenization method are given.
Algorithm‐Driven Optimization of Support‐Free Truss‐like Structures in Early‐Stage Design for Additive Manufacturing
Authors: Reintjes Christian , Lorenz Ulf
Published: January 2021

Material extrusion processes require internal or external or both support structures to support the printing process. These support structures generate costs due to additional material, printing time and energy. Contrary to the optimization strategy to minimize the need for additional support by optimizing the support structure itself and keeping the original part, we focus on designing a new part in a single step by optimizing the topology towards a support‐free lattice structure. Assuming that the support structures cannot be removed by non‐destructive post‐processing this optimization approach becomes necessary, since the force distribution in a lattice structure is manipulated by the additional support structures. We extend the work by [1] to model support‐free lattice structures considering a positioning of a static area load. We show how integer dependent constraints can be used to implement design standards for support‐free and extrusion‐based additive manufacturing.
Nonlinear computation of cables with high order solid elements using an anisotropic material model
Authors: Hildebrandt André , Sharma Prateek , Diebels Stefan , Düster Alexander
Published: January 2021

Due to their complex structure cables exhibit an anisotropic behaviour and undergo large deformations in various applications. The large deformations are simulated using blended high order solid elements that can represent large deformations efficiently. To reduce the computational complexity the cross section consisting of many single wires and different layers of material is homogenized and represented by a transversely isotropic material model. Frictional effects and possible reordering of the parts are modelled through elastoplastic material behaviour with an anisotropic yield function. The simulations show that for a simple tension test and a free torsion test the material parameters can be satisfactorily identified.
An Adaptive Isogeometric Phase‐Field Model for Topology Optimization
Authors: Hennig Paul , Heindel Leonhard , Kästner Markus
Published: January 2021

In this contribution, we apply adaptive isogeometric analysis to a phase‐field model for topology optimization. To increase the efficiency of the computation, we perform local mesh refinement and coarsening between the time increments of the simulation. To provide a trial solution for the iterative solver of the next increment, state variables are projected from the old to the new mesh. The quality and efficiency of the approach are tested in a two‐dimensional benchmark.
Micromechanical analysis of failure in fiber reinforced polymer‐metal structures
Authors: Hirsch Franz , Natkowski Erik , Kästner Markus
Published: January 2021

In this contribution, the interface region of a fiber reinforced polymer and a metal component is considered within a representative volume element. The connecting surface exhibits a random height distribution with a defined roughness. Under shear loading, different failure mechanisms are studied with respect to the local interface roughness. Furthermore, adhesive failure of the interface and cohesive failure of the polymer are distinguished. The results show an enhanced bonding strength with increasing interface roughness.
Neural Networks for Structural Optimisation of Mechanical Metamaterials
Authors: Bronder Stefan , Diebels Stefan , Jung Anne
Published: January 2021

Mechanical metamaterials are man‐made designer materials with unusual properties, which are derived from the micro‐structure rather than the base material. Thus, metamaterials are suitable for tailoring and structural optimisation to enhance certain properties. A widely known example for this class of materials are auxetics with a negative Poisson's ratio. In this work an auxetic unit cell is modified with an additional half strut.During the deformation this half strut will get into contact with the unit cell and provide additional stability. This leads to a higher plateau stress and consequently to a higher energy absorption capacity. To achieve the maximum energy absorption capacity, a structural optimisation is carried out. But an optimisation exclusively based on finite element simulations is computationally costly and takes a lot of time. Therefore, in this contribution neural networks are used as a tool to speed up the optimisation. Neural networks are one of many machine learning methods and are able to approximate any arbitrary function on a highly abstract level. So the stress‐strain behaviour and its dependency from the geometry parameters of a type of microstructure can be learned by the neural network with only a few finite element simulations of varying geometry parameters. The modified auxetic structure is optimised with respect to the mass specific energy absorption capacity. As a result a qualitative trend for the optimal geometry parameters is obtained. However, the Poisson's ratio for this optimisation is close to zero.
Simulation of nonequilibrium effects in quantum cascade lasers
Authors: Jirauschek Christian
Published: January 2021

Quantum cascade lasers exploit optical transitions between quantized electronic energy levels in multi‐quantum‐well structures for light generation and detection. This design principle enables the realization of compact, semiconductor‐based lasers in the mid‐infrared and terahertz spectral regions. In this contribution, the modeling of such devices is discussed based on an ensemble Monte Carlo approach, enhanced by modifications obtained from the density matrix formalism. A special emphasis is put on the inclusion of nonequilibrium electron and phonon effects. The simulations are validated against available experimental data for a terahertz quantum cascade laser.
A hybrid approach for the multi‐scale simulation of irreversible material behavior incorporating neural networks
Authors: Hütter Geralf , Settgast Christoph , Lange Nils , Abendroth Martin , Kiefer Björn
Published: January 2021

The present contribution presents a hybrid approach for the multi‐scale modeling where the yield surface and evolution equations are represented by neural networks, for which micro‐scale simulations are used as training data. The approach and its implementation into a commercial finite element code are demonstrated for a ductile foam material. The results are verified by comparison with an FE2 simulation.
Investigations on modeling of freezing processes within the framework of the Theory of Porous Media
Authors: Schwarz Alexander , Bluhm Joachim , Schröder Jörg
Published: January 2021

In this contribution we present investigations on modeling of freezing processes between two ice floes. In detail we show results on the ice formation (mass exchange between the constituents) and the temperature distribution under calm sea conditions. For the detection of energetic effects regarding the characterization and the control of the phase transition, a thermodynamical consistent approach is presented, see [1]. In the later contribution the resulting finite element is a four field formulation in terms of ice displacements, liquid pressure, temperature and volume fraction of ice and is used in the present paper. An advanced numerical example show that the simplified model is capable of simulating the temperature development and phase change.
Mixed finite element formulations and energy‐momentum time integrators for thermo‐viscoelastic fiber‐reinforced continua
Authors: Dietzsch Julian , Groß Michael , Schuffenhauer Richard Friedrich
Published: January 2021

Today, fiber‐reinforced materials and their exact dynamic simulation play a significant role in the construction of lightweight structures. These materials are used in aircraft, automobiles and wind turbines, for instance. The low density and the high modulus of elasticity play a major role, but also the thermal properties should not be neglected. First of all, the thermal expansion of the matrix part and the ability to conduct the heat in a directional way with the fibers. For these materials, volumetric locking effects of an incompressible matrix material as well as locking effects due to stiff fibers can occur. On the one hand, there are combinations of well known mixed elements with an independent approximation of the volume dilatation and an independent approximation of the right Cauchy‐Green tensor for the anisotropic part of the strain energy function to reduce these effects. On the other hand, we have developed mixed elements where fields for the fourth and fifth invariants are added, as well as a version with the corresponding tensor fields. For long‐term simulations it is necessary to use higher order time integrators to perform an accurate dynamic simulation. Galerkin‐based time integrators offer a good option for this application. To eliminate a huge energy error these have to be extended to an energy‐momentum time integration scheme. It is logical to combine these methods and thus combine the advantages of these methods. We formulate the mixed elements using Hu‐Washizu functionals and combine this with the mixed principle of virtual power. By adding a thermo‐mechanical coupling part in the strain energy and introducing Fourier's heat conduction we obtain a thermo‐mechanical formulation for the different mixed elements and a higher order Galerkin‐based time integrator. Dirichlet boundary conditions in the form of Lagrange multiplier methods as well as Neumann boundary conditions in the mechanical and thermal context are also provided. In addition, we extend the continuum so that we can model different fiber families and the directional heat conduction of the fibers. As numerical examples serve cook's cantilever beam as well as a rotating heat pipe. We primarily analyze the spatial and time convergence, the conservation properties as well as the effect of the heat conduction of the fibers.
Variational Methods and Parallel Solvers in Chemo‐Mechanics
Authors: Kiefer Björn , Rheinbach Oliver , Roth Stephan , Röver Friederike
Published: January 2021

This study represents a first step towards tailored solvers for chemo‐mechanical multi‐field problems in a variational setting.
Modeling of the Bayliss‐Effect in Vascular Smooth Muscles
Authors: Uhlmann Klemens , Balzani Daniel
Published: January 2021

This contribution presents a model for the smooth muscle contraction embracing a stretch‐dependent calcium function. It enables the coupling of the mechanical material answer with the chemical reactions on cellular level. Based thereon, simulation results of arteries under time‐dependent intravascular pressure, mimicking the scenario during heart‐beat, are analyzed.
Microstructure‐related modeling of timber constructions
Authors: Wiese Sandra , Dinkler Dieter
Published: January 2021

Wood is an organic porous material of cellulose fibers, which consist of a cell wall and a lumen. In this paper a microstructure‐related model utilizing the polygonal finite element method (PFEM) is presented. The PFEM enables the discrete modeling of the wooden cellular structure under application of shape functions based on mean value coordinates. The numerical integration scheme is based on the triangulation of the elements. In the scope of this framework the transverse compression behavior of wood is simulated. The deformation is presented and compared to the macrostructure‐related result.
Modelling basal‐cell carcinoma behaviour in avascular skin
Authors: Suditsch M. , Schröder P. , Lambers L. , Ricken T. , Ehlers W. , Wagner A.
Published: January 2021

Malignant neoplasms are one of the most dangerous diseases. Within the framework of the well‐established Theory of Porous Media (TPM), a multi‐constituent model is derived. The model is mathematically formulated by a set of coupled partial differential equations which are solved within the well‐known framework of the finite‐element method. The general TPM model is applied to basal‐cell carcinoma in the avascular skin and representative numerical examples show the capabilities of the model.