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Item type:Publication, Access status: with files , Final report of DFG project 448085183: numerical modelling of partially cemented soils in the stagnation zone(2026-05-20); ; ; This final report summarizes the results of DFG project 448085183, “Numerical Modelling of Partially Cemented Soils in the Stagnation Zone”. The project investigated the micromechanical behaviour of partially cemented sands by combining experimental testing, X-ray micro-computed tomography, image processing, and advanced numerical modelling. In the first project phase, the focus was on the linear-elastic response of cemented sand specimens. CT-based microstructures were converted into numerical models and analysed using the Finite Element Method (FEM) and the Finite Cell Method (FCM), including numerical homogenization to determine effective material properties. In the second project phase, the numerical frameworks were extended towards fracture and failure processes, including matrix cracking, grain-scale stress localization, and phase-field modelling. Additional experimental data were obtained by Digital Volume Correlation (DVC) to support the validation of the simulations. The project contributes to a better understanding of load transfer, stiffness development, and failure mechanisms in cemented granular materials and provides automated CT-based simulation workflows for future applications in geotechnical modelling.Publicationtype: Research Report70 47 - Some of the metrics are blocked by yourconsent settings
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 Article131 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Geometry smoothing and local enrichment of the finite cell method with application to cemented granular materials(Springer, 2025); ; ; ; In recent times, immersed methods such as the finite cell method have been increasingly employed in structural mechanics to address complex-shaped problems. However, when dealing with heterogeneous microstructures, the FCM faces several challenges. Weak discontinuities occur at the interfaces between the different materials, resulting in kinks in the displacements and jumps in the strain and stress fields. Furthermore, the morphology of such composites is often described by 3D images, such as ones derived from X-ray computed tomography. These images lead to a non-smooth geometry description and thus, singularities in the stresses arise. In order to overcome these problems, several strategies are presented in this work. To capture the weak discontinuities at the material interfaces, the FCM is combined with local enrichment. Moreover, the L²-projection is extended and applied to heterogeneous microstructures, transforming the 3D images into smooth level-set functions. All of the proposed approaches are applied to numerical examples. Finally, an application of cemented granular material is investigated using three versions of the FCM and is verified against the finite element method. The results show that the proposed methods are suitable for simulating heterogeneous materials starting from CT scans.Publicationtype: Journal Article43 77 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Implementation of linear strain elements for image-based Finite Element Analysis of cemented natural sandMesoscopic approaches in material science aim to conceive multiphase materials as compositions of constituent phases, rather than homogenized media. X-ray Computed Tomography is a powerful tool that provides full field information of composites’ structure in the form of three-dimensional images. Image analysis combined with computational geometry concepts permit the transition from voxel images to adapted unstructured tetrahedral meshes, a conversion that delivers important computational benefits of image-based numerical simulations. The current article focuses on the case of cemented natural granular material of two cement saturation degrees. Actual cylindrical samples are scanned and reconstructed in the form of digital volumes. Image artefacts impede reliable particle segmentation. A novel image filter based on domain cylindrical decomposition and histogram compatibility enforcement is applied to alleviate the bias. The conversion of voxel images to quadratic tetrahedral meshes is proposed to facilitate accurate image-based numerical analysis. Localization of stresses is evident in the upgraded linear strain element configuration, but missing from that of constant strain element. The display of stress results and supplementary statistical analysis suggest that the granular skeleton sustains the load by forming intergranular stress channeling, while the cement matrix is partially activated at regions of granular contact to aid the stress flow.Publicationtype: Journal Article20 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Code verification of immersed boundary techniques using the method of manufactured solutionsCode verification plays a crucial role for all finite element applications, especially for non-standard ones, such as immersed boundary approaches, which are typically based on novel algorithms and often error-prone in-house implementations. Instead of relying on rarely available analytical solutions or overkill FEM simulations, in this article, the capabilities of the method of manufactured solutions (MoMS) are explored, enabling an easy and straightforward derivation of closed-form reference solutions. The focus is kept on immersed problems, in particular, on the finite cell method (FCM), and manufactured solutions are derived for 2D and 3D problems involving voids and single/multiple inclusions. We propose several approaches for the construction of the manufactured solutions, where zero traction conditions for void regions and continuous normal stresses along material interfaces are directly fulfilled. Thus, no weak boundary conditions are required for reproducing the manufactured solution via FCM. This not only enables code verification for FCM implementations that lack the option of applying weak boundary conditions, but also keeps the simulation complexity low, when testing other relevant features, e.g., different integration schemes or the implementation of enrichment functions. The flexibility and wide application range of the MoMS in the context of immersed boundary simulations is demonstrated using static, quasi-static, and transient problems in the context of linear elasticity. Finally, the analytical derivations of the manufactured solutions used in this paper are provided as supplementary material.Publicationtype: Journal Article31 82 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Acceleration of immersed computations of brittle phase‐field fracture utilizing moment fitting schemes(Wiley, 2024-03); ; ; ; Numerical methods play an important role when predicting structural failure in industrial applications. Among various methods, the phase‐field modeling (PFM) seems to be a very promising approach. By introducing an additional phase‐field variable, it can account for crack initiation, crack propagation, dynamic crack branching and more. However, it needs a very fine mesh especially along the propagating crack path. When utilizing boundary‐fitted methods such as the finite element method, this can lead to a large amount of elements and thus, results in huge systems of equations. In order to overcome this issue, immersed methods like the finite cell method (FCM) have been developed, where the mesh is independent of the geometry, which results in a fast and simple pre‐processing. In this work, the FCM is applied to the PFM in order to simulate quasi‐static brittle fracture of structures with complex geometries. Furthermore, the non‐negative moment fitting (NNMF) is employed in order to accelerate the finite cell computations. The proposed methods are tested on a numerical example in order to demonstrate the strength of the NNMF.Publicationtype: Conference Paper34 40 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Simulating brittle fracture with a robust hybrid explicit–implicit solver for staggered phase‐field problems(Wiley, 2024-03); ; ; ; In this work, the robustness of phase‐field fracture simulations is increased by introducing a new hybrid approach to take advantages of both explicit and implicit solvers. Switching to an explicit solver at critical load cases enables us to define a threshold on the maximum number of staggered iterations per load step. Having this threshold would be very useful in complicated FCM problems since we cannot wait for a full convergence of the implicit solver at critical load steps. With the new hybrid method, the problem is implicit as long as the implicit solver can converge within a specified threshold; otherwise, the failed load step will be solved robustly using an explicit approach. The method can resolve the highly nonlinear part of the global load–displacement curve. The superiority of the approach is shown in different benchmark examples.Publicationtype: Conference Paper11 17 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Adaptive quadrature of trimmed finite elements and cells based on bezier approximation(World Scientific Publishing (WSPC), 2024-02-01); ; ; In this paper, a new boundary-conforming adaptive method for the numerical integration of trimmed elements is presented. The locations and weights of new integration points are determined based on special mapping formulations. The prerequisite of this technique is to describe the trimming curves/surfaces by parametric Bezier curves/surfaces within the parent element domain. The fitting error is under control, therefore the number of quadrature points for exact integration can be adjusted automatically based on the complexity of trimming curve and the corresponding integrand. The proposed method can be easily implemented into fictitious domain approaches. Different integration tasks as well as structural examples reveal that the proposed method delivers accurate and robust solutions for a wide variety of 2D/3D geometries with a rather low number of integration points.Publicationtype: Journal Article48 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Investigation of the load sustaining micro mechanisms of cemented sand using the mesoscale FEM approachWhile the mechanics of cemented granular material have already been approached by means of constitutive modeling, the capacity of introducing the precise internal structure of multiphase media in numerical simulations offers an alternative perspective of investigation. In specific, means of X-ray computed tomography are able to quantify the internal irregular geometry of the composite material in the form of three-dimensional images. Image analysis can be applied in order to distinguish the topology of each material phase and advanced meshing techniques are able to form a twin meshed domain. The current paper deals with the quantitative description of the morphology of small cemented sand samples, the application of developed image analysis algorithms to treat imaging artefacts (mainly due to beam hardening), the equivalent mesh generation via the image adapted meshing technique and the numerical testing using the Finite Element Method. Four samples are imaged, meshed and numerically tested in uniaxial compression; the mesoscale finite element simulations are able to display the intergranular stress transmission chains. A statistical analysis of the load carried by the granular skeleton provides evidence of the influence of the cementation degree and the compaction of the aggregates on the uniformity of the stress distribution.Publicationtype: Journal Article33 100 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , On the load bearing mechanisms of cemented granular material : a mesoscale FE approachThe numerical investigation of cemented granular material (CGM) is a demanding task that requires the combination of various scientific disciplines. At the mesoscale, CGM is decomposed into the constituents of particles, cement matrix and void pores. The combination of these constituents, as found in nature or in civil infrastructure projects, creates a highly heterogeneous structure, whose morphology defines the response of the CGM under mechanical loading. The composite internal structure is quantified by means of x‐ray Computed Tomography, which provides 16‐bit grayscale 3D images of the scanned microsamples. These images are decomposed into the three constituent materials to be investigated and modeled. Still, the ability of simple Cartesian grids to adequately carry information about curved geometries and provide accurate representations is questioned. In order to overcome staircase effect errors, the interfaces of the material inclusions are smoothed and re‐defined, making use of Gaussian blurred signed distance fields (SDF). These level‐set derived interfaces serve as a reference for the volume reconstruction of the image via tetrahedra. The comparison of the raw and the smoothened images to analytical geometry Standards suggests that the above reconstruction alleviates the grid's inherited uncertainities. In addition, a comparison between a non smoothed and a smoothed meshed image is performed in terms of mechanical response, utilizing the Finite Element (FE) Method. The results suggest that even a slight change in the granular contact fabric can alter the unfolding stress transmission mechanisms.Publicationtype: Journal Article41 93