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Item type:Publication, Access status: without files , Application of the Non-Negative Moment Fitting Approach in the Finite Cell Analysis of Brittle Phase-Field Fracture(World Scientific Publishing (WSPC), 2025-04-21); ; ; ; This paper addresses the prediction of fracture processes in complex geometries. In this approach, phase-field modeling is integrated into the finite cell method to have an efficient and robust simulation tool for brittle fracture. The non-negative moment fitting approach is employed as an integration scheme to reduce the number of integration points, which leads to shorter simulation times as well as lower memory requirements for history variables. Two 3D benchmark examples are provided to demonstrate the performance of the implemented approach compared to the standard quadrature based on the space-tree approach. Finally, the proposed method is applied to predict the sequence of strut fractures in brittle foams.Publicationtype: Journal Article132 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Stabilization techniques and adaptive conjugate gradient solver tolerances for the finite cell method(2025-03); ; ; Immersed boundary methods such as the finite cell method provide a versatile tool for the analysis of structures, which are difficult to discretize in a boundary conforming manner due to their complex geometries. Using Cartesian grids and a fictitious domain approach, the effort is shifted from meshing toward the quadrature, which needs to be adapted to discontinuous integrands for cut cells, i.e., elements cut by the immersed boundary. Further, the condition number of the stiffness matrix of such discretizations is typically much larger compared to boundary fitted discretizations, making the use of iterative solvers challenging. In order to restore the performance of iterative solvers, i.e., lower the condition number of the stiffness matrix, several stabilization methods are available. In this work, we compare the performance of two stabilization methods. The classical -stabilization method uses a material with low (but non-zero) stiffness in the fictitious domain. The so called eigenvalue- or -stabilization is based on an eigendecomposition of the stiffness matrix and selectively stabilizes modes, which are associated with very low eigenvalues. Generally, both stabilization methods introduce an error, which, however, can be corrected. This work includes an investigation of such correction mechanisms for linear and nonlinear problems.Publicationtype: Journal Article33 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , On the efficiency of explicit and semi-explicit immersed boundary finite element methods for wave propagation problems(American Institute of Mathematical Sciences, 2025-03-01); ; ; ; Immersed boundary methods have attracted substantial interest in the last decades due to their potential for computations involving complex geometries. Often these cannot be efficiently discretized using boundary-fitted finite elements. Immersed boundary methods provide a simple and fully automatic discretization based on Cartesian grids and tailored quadrature schemes that account for the geometric model. It can thus be described independently of the grid, e.g., by image data obtained from computed tomography scans. The drawback of such a discretization lies in the potentially small overlap between certain elements in the grid and the geometry. These badly cut elements with small physical support pose a particular challenge for nonlinear and/or dynamic simulations. In this work, we focus on problems in structural dynamics and acoustics and concentrate on solving them with explicit time-marching schemes. In this context, badly cut elements can lead to unfeasibly small critical time step sizes. We investigate the performance of implicit-explicit time marching schemes and two stabilization methods developed in previous works as potential remedies. While these have been studied before with regard to their effectiveness in in-creasing the critical time step size, their numerical efficiency has only been considered in terms of accuracy per degree of freedom. In this paper, we eval-uate the computation time required for a given accuracy, which depends not only on the number of degrees of freedom but also on the selected spatial dis-cretization, the sparsity patterns of the system matrices, and the employed time-marching scheme.Publicationtype: Journal Article15 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Hemodynamics in arterial bypass graft anastomoses with varying cuff sizes and proximal flow paths: a fluid–structure interaction studyThis article investigates the effect of the cuff size of arterial bypass grafts and the flow conditions on the hemodynamics in the anastomosis (connection) to the artery, using numerical simulations. We consider a fluid-structure interaction problem which is solved based on a partitioned scheme. Additionally, we employ computational fluid dynamics to investigate the effect of a rigid wall assumption. The work focuses on clinically relevant hemodynamic quantities associated with the development of intimal hyperplasia. We also include a model for the prediction of hemolysis into the simulation. The results show that even minor changes of the cuff size can result into significant differences in the corresponding quantities of interest. The importance of the inflow path is shown to be lower than that of the cuff size. The usually employed rigid wall assumption is found to be adequate to address wall shear stress oscillations but falls short on predicting maximum and minimum wall shear stress-related quantities of interest.Publicationtype: Journal Article30 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Vibroacoustic simulations of acoustic damping materials using a fictitious domain approach(Elsevier, 2024-01-06); ; ; The numerical investigation of acoustic damping materials, such as foams, constitutes a valuable enhancement to experimental testing. Typically, such materials are modeled in a homogenized way in order to reduce the computational effort and to circumvent the need for a computational mesh that resolves the complex micro-structure. However, to gain detailed insight into the acoustic behavior, e.g., the transmittance of noise, such fully resolved models are mandatory. The meshing process can still be drastically simplified by using a fictitious domain approach. We propose the finite cell method, which combines the fictitious domain approach with high-order finite elements and resolves the complex geometry using special quadrature rules. In order to take into account the fluid-filled pores of a typical damping material, a coupled vibroacoustic problem needs to be solved. To this end, we construct two separate finite cell discretizations and prescribe coupling conditions at the interface in the usual manner. The only difference to a classical boundary fitted approach to vibroacoustics is that the fluid-solid interface is immersed into the respective discretization and does not correspond to the element boundaries. The proposed enhancement of the finite cell method for vibroacoustics is verified based on a comparison with commercial software and used within an exemplary application.Publicationtype: Journal Article13 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Immersed IGA and mass lumping for explicit dynamics of 1D structural elements(2024-01-01); 50 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Performance of acceleration techniques for staggered phase-field solutions(2023-05-15); ; ; The staggered phase field formulation has proved to be a robust formulation for the modeling of crack nucleation and propagation, but it suffers from a very slow convergence rate. Here, we summarize some of the methods that were proposed in the literature to accelerate staggered schemes and numerically investigate their performances in staggered hybrid quasi-static phase field modeling. Between the studied methods, we found that Anderson's method was the most robust in terms of the mean number of iterations that were required for convergence and the stability of the solution.Publicationtype: Journal Article38 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , A fluid-structure interaction study of hemodynamics in arterial bypass-graft anastomoses(2022-06); ; ; This paper reports on numerical experiments on arterial bypass-graft anastomoses. Bypass-grafts are oftentimes used in surgical procedures to divert blood around narrowed or occluded parts of an artery. The diverted blood flow is crucial to the success of the operation as it may lead to undesirable peculiarities that can result to a renewed occlusion in the distal connection of the graft. However, an a priori prediction of detrimental hemodynamic aspects due to undesirable flow properties is difficult to perform in vitro or in vivo conditions. To this end, this work targets to enhance our understanding of harming mechanisms through in silico experiments using computational fluid dynamics (CFD) and fluid-structure interaction (FSI) simulations. The latter are realized through a partitioned coupled approach which is verified for a 2D benchmark case against literature-reported results. Finally, we present numerical results on grafts with different cuff sizes. Wall shear stress (WSS), oscillatory shear index (OSI) and hemolysis are monitored and compared in the context of either rigid or elastic walls and cuff sizes. Special interest is given to the prediction of hemolysis induction which is often not considered in such studies. We show that wall elasticity is the key parameter in terms of WSS prediction while cuff size mainly affects the estimation of OSI.Publicationtype: Conference Paper49 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Adaptive Quadrature and Remeshing Strategies for the Finite Cell Method at Large DeformationsNumerical methods based on a fictitious domain approach, such as the finite cell method, simplify the meshing process significantly as the mesh does not need to conform to the geometry of the underlying problem. However, such methods result in elements/cells which are intersected by the domain boundary. Consequently, special integration methods have to be applied for the broken elements/cells to achieve accurate results. One of the methods that is commonly used in the finite cell method is an adaptive scheme based on a spacetree decomposition. Unfortunately, it results in a large number of integration points which makes the method quite expensive. In the first part of this contribution, we try to overcome this problem by introducing an adaptive scheme for the moment fitting to be able to integrate broken cells efficiently and robustly for nonlinear problems. Furthermore, a remeshing strategy for the finite cell method will be introduced to improve the solution quality and overcome the large distortion of the mesh during the simulation which can cause the analysis to fail. To this end, a new mesh with a good quality is created whenever the old mesh is no longer capable of taking any further deformations. Afterwards, a data transfer between the old and the new meshes is performed with the help of a local radial basis function interpolation. Different numerical examples are presented to study the performance of the proposed methods.Publicationtype: Journal Article50 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Optimally blended spectral elements in structural dynamics: Selective integration and mesh distortion(2021-12-01); ; In the field of structural dynamics, spectral finite elements are well known for their appealing approximation properties. Based on a special combination of shape functions and quadrature points, a diagonal mass matrix is obtained. More recently, the so-called optimally blended spectral element method was introduced, which further improves the accuracy but comes at the cost of a non-diagonal mass matrix. In this work, we study and compare the approximation properties of the different spectral and finite element methods. For each method, an h-version (fine meshes and low-order shape functions) as well as a p-version (coarse meshes and high-order shape functions) are considered. Special attention is paid to the influence of the quadrature rule used to compute the stiffness matrix and the element distortion on the convergence behavior. The investigations reveal the importance of a correct (full) integration of the stiffness matrix in order to achieve the theoretically predicted convergence rates. However, looking at the full spectrum, novel variants of the method that apply only a single (reduced) quadrature rule for mass and stiffness matrix show a higher accuracy.Publicationtype: Journal Article73