A remeshing approach for the finite cell method applied to problems with large deformations

Garhuom, Wadhah; Hubrich, Simeon; Radtke, Lars; Düster, Alexander

doi:10.1002/pamm.202100047

Cited by 6 publications

(5 citation statements)

References 4 publications

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“…To this end, hierarchic shape functions based on integrated Legendre polynomials are utilized [38,39]. The FCM was successfully applied to a variety of problems in solid mechanics such as thermoelasticity [44], geometrical nonlinearities [18,37], explicit and implicit elastodynamics [16,24], biomechanics [35,42], elastoplasticity [3,26,40], and microstructured materials [20,21,27]. Figure 1 illustrates the basic concept of the method using a twodimensional geometry of solid mechanics.…”

Section: The Finite Cell Methodsmentioning

confidence: 99%

“…Moreover, the severe distortion of the mesh in nonlinear finite strain problems can cause the analysis to terminate before reaching the desired deformation state. To this end, a remeshing strategy proposed in [17,18] can improve the robustness of the FCM by creating a new mesh whenever the old mesh cannot take any more deformations. Starting with an initial mesh, the structure is deformed until the remeshing criteria indicate that a remeshing step is required because the mesh is strongly distorted.…”

Section: Introductionmentioning

confidence: 99%

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An eigenvalue stabilization technique to increase the robustness of the finite cell method for finite strain problems

2022

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Broken cells in the finite cell method—especially those with a small volume fraction—lead to a high condition number of the global system of equations. To overcome this problem, in this paper, we apply and adapt an eigenvalue stabilization technique to improve the ill-conditioned matrices of the finite cells and to enhance the robustness for large deformation analysis. In this approach, the modes causing high condition numbers are identified for each cell, based on the eigenvalues of the cell stiffness matrix. Then, those modes are supported directly by adding extra stiffness to the cell stiffness matrix in order to improve the condition number. Furthermore, the same extra stiffness is considered on the right-hand side of the system—which leads to a stabilization scheme that does not modify the solution. The performance of the eigenvalue stabilization technique is demonstrated using different numerical examples.

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Section: The Finite Cell Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An eigenvalue stabilization technique to increase the robustness of the finite cell method for finite strain problems

2022

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“…One possibility to perform the data interpolation is the usage of RBFs, similar to references [2,7]. There exist different RBFs, see, for example, [14].…”

Section: Radial Basis Function Interpolationmentioning

confidence: 99%

“…Thus, the values at new integration points need to be interpolated from the old values. To this end, radial basis functions (RBFs) are used for the interpolation and have successfully been applied in [2,7].…”

Section: Introductionmentioning

confidence: 99%

Remeshing and data transfer in the finite cell method for problems with large deformations

Sartorti,

Düster

2023

Proc Appl Math and Mech

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The simulation of complex structures using standard finite element discretization techniques can be challenging because the creation of the boundary conforming meshes for such structures can be time‐consuming. Therefore, fictitious domain methods are attractive alternatives because the underlying mesh does not have to conform to the boundary. One fictitious domain method is the finite cell method where a structured non‐geometry conforming Cartesian grid is created and the geometry is then described by a simple indicator function. When solving non‐linear problems, for example, if large deformations are taken into account, broken cells are typically heavily distorted and may lead to failure of the overall solution procedure. To tackle this issue remeshing is applied to proceed with the simulation. In previous publications, radial basis functions (RBFs) were applied to map the deformation gradient between the different meshes. However, it is not clear whether this is the best way to transfer data during the remeshing procedure. Therefore, we investigate whether there are alternative methods that can be used instead. This is then compared to the RBF interpolation and applied to different numerical examples with hyperelastic materials.

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“…For smooth problems, the FCM exhibits high convergence rates and hence, can compete with the p-FEM [28,71]. The FCM is used in a wide range of application-including geometric nonlinearities [81], hyperelasticity and elastoplasticity at small and finite strains [32][33][34][35]53], structural dynamics [9,23,51,69,76], acoustics [73,77], fracture mechanics [47,70], biomechanics [27,31], homogenization [29,40,60], and Isogeometric Analysis (IGA) [80,81,90].…”

Section: Introductionmentioning

confidence: 99%

Geometry smoothing and local enrichment of the finite cell method with application to cemented granular materials

Gorji,

Komodromos,

Garhuom

et al. 2024

Comput Mech

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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 L$$^2$$ 2 -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.

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A remeshing approach for the finite cell method applied to problems with large deformations

Cited by 6 publications

References 4 publications

An eigenvalue stabilization technique to increase the robustness of the finite cell method for finite strain problems

An eigenvalue stabilization technique to increase the robustness of the finite cell method for finite strain problems

Remeshing and data transfer in the finite cell method for problems with large deformations

Geometry smoothing and local enrichment of the finite cell method with application to cemented granular materials

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