A remeshing strategy for large deformations in the finite cell method

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

doi:10.1016/j.camwa.2020.03.020

Cited by 17 publications

(17 citation statements)

References 35 publications

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“…In this section, we investigate two numerical examples using a hyperelastic material model [2] to demonstrate the performance of the presented method. In the first example, we consider a plate with a cylindrical hole.…”

Section: Numerical Examplesmentioning

confidence: 99%

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

Garhuom

Hubrich

Radtke

et al. 2021

Proc Appl Math & Mech

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The finite cell method (FCM) is based on an immersed boundary concept with high‐order finite elements. When solving nonlinear problems using the FCM, it is often difficult to reach to the desired load step because of the large distortion of the mesh, particularly when badly broken cells are existing in the mesh. To overcome this problem, a global remeshing strategy is proposed to allow the nonlinear computation to proceed even for very large deformations where the distortion of the cells becomes significant. The core concept is to perform a computation up to a specific deformation state where the distortion of the cells becomes significant. Then, to continue the analysis, a new mesh is introduced. The performance of the proposed method is illustrated using two numerical examples of hyperelasticity.

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Section: Numerical Examplesmentioning

confidence: 99%

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

Garhuom

Hubrich

Radtke

et al. 2021

Proc Appl Math & Mech

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“…To overcome the problem of severely distorted cells in the FCM for structures undergoing large deformations, this chapter serves to present a remeshing strategy with respect to the total Lagrangian formulation [161]. The main idea of the proposed remeshing strategy is based on a decomposition of the deformation gradient.…”

Section: Finite Strain Elastoplasticitymentioning

confidence: 99%

“…In the following, we present a remeshing strategy suited for the FCM [161]. The motivation for this remeshing strategy is to improve the robustness of the FCM considering problems in finite strain.…”

Section: Remeshing Proceduresmentioning

confidence: 99%

The hierarchical finite cell method for nonlinear problems: Moment fitting quadratures, basis function removel, and remeshing

Hubrich¹

2021

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In this thesis, several approaches are discussed in order to further enhance the performance of the finite cell method (FCM). Thereby, novel moment fitting quadrature schemes are introduced that allow to reduce the effort of the numerical integration process significantly. Further, a basis function removal scheme is proposed to improve the conditioning behavior of the resulting equation system. Finally, an innovative remeshing strategy is presented that overcomes the problem of severely distorted elements for simulations with large deformations. Contents 1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Goal and scope of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Basic elements of continuum mechanics 6 2.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.1 Motion and deformation . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.2 Strain measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Equilibrium and stress measures . . . . . . . . ....

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“…Additionally, for the analysis using high-order shape functions, degrees of freedom that have a small support in the physical domain tend to increase the condition number and decrease the robustness of the FCM. To this end, [15,17,42] proposed a basis function removal (BFR) strategy to improve the condition number by removing shape functions that do not contribute much to the global stiffness matrix. Thereby, a global criterion was developed based on the energy contribution of each degree of freedom -allowing to determine which shape function needs to be removed.…”

Section: Introductionmentioning

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%

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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A remeshing strategy for large deformations in the finite cell method

Cited by 17 publications

References 35 publications

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

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

The hierarchical finite cell method for nonlinear problems: Moment fitting quadratures, basis function removel, and remeshing

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

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