A regularization technique for the XFEM: extension to finite deformations, inelastic material behaviour and multifield problems

Löhnert, Stefan; Beese, Steffen

doi:10.1002/pamm.201610065

Cited by 1 publication

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“…This means that some of the modes will tend to have linear dependencies which result in an increasing condition number. To overcome this problem, following the ideas of Loehnert [29,30] and Loehnert and Beese [31], we can compute the eigenvalues and eigenmodes of each broken cell by factorizing the cell stiffness matrix k c using the eigenvalue decomposition…”

Section: Eigenvalue Stabilization Techniquementioning

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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Section: Eigenvalue Stabilization Techniquementioning

confidence: 99%