Second-invariant-preserving Remap of the 2D deviatoric stress tensor in ALE methods

For numerical simulations of impact problems or fluid–solid interactions, the ALE (Arbitrary Lagrangian–Eulerian) approach is a useful tool due to its ability to keep the computational mesh smooth and moving with the fluid. The elastic–plastic extension of the compressible fluid model requires tenso...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2019-07, Vol.78 (2), p.654-669
Main Authors: Klíma, Matěj, Kuchařík, Milan, Velechovský, Jan, Shashkov, Mikhail
Format: Article
Language:English
Subjects:
ALE
Compressible fluids
Computational grids
Computer simulation
Eigenvalues
Finite element method
Invariants
Limiter
Numerical methods
Remapping
Stress tensor
Symmetry preservation
Tensors
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Summary:For numerical simulations of impact problems or fluid–solid interactions, the ALE (Arbitrary Lagrangian–Eulerian) approach is a useful tool due to its ability to keep the computational mesh smooth and moving with the fluid. The elastic–plastic extension of the compressible fluid model requires tensor variables for the description of non-volumetric (deviatoric) mechanical stress. While Lagrangian numerical schemes based on the evolution equation of the stress tensor are well developed, tensor remap is still a relatively unexplored territory. We propose a new approach to deviatoric stress remapping, where the second invariant J2 (a conservative scalar quantity related to the strain energy) is remapped independently of the tensor components. These are re-scaled to match the remapped invariant value, effectively using only the principal directions and eigenvalue ratio from the component-wise remap. This approach is frame invariant, preserves J2 invariant bounds and conserves the total invariant. We compare our method with component-based remapping using a simple synchronized limiter or a specialized stress tensor limiter described in the literature.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2018.06.012