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A large deformation tetrahedral smoothed finite element formulation for nearly incompressible solids based on the strain smoothed element (SSE) technique
Last modified: 2022-05-30
Abstract
Large deformation finite element (FE) analyses are still difficult to analyze accurately and robustly even today.
In practical problems, the geometries are usually complex, and it is almost impossible to generate low-skew hexahedral meshes.
Therefore, accurate and robust FE formulations using tetrahedral meshes are still highly desired in industry circles.
The smoothed finite element methods (S-FEMs) are being widely used to avoid locking even using tetrahedral meshes. The authors have developed several advanced S-FEMs for nearly incompressible solids using 4-node tetrahedral meshes (SelectiveES/NS-FEM-T4, F-barES-FEM-T4, etc.) or using 10-node tetrahedral meshes (SelectiveCS-FEM-T10). These methods avoid shear and volumetric locking, but they suffer from pressure or deviatoric stress oscillations (checkerboarding) in some cases.
Meanwhile, Lee et al. recently proposed the strain smoothed element (SSE) using tetrahedral meshes as an improved S-FEM formulation. Besides, Jinsong also proposed the edge-center-based SSE (EC-SSE) tetrahedral meshes as an advanced SSE formulation. The SSE assumes a linear strain/stress distribution in each smoothing domain, whereas the classical S-FEMs assume a constant strain/stress distribution in each smoothing domain. Accordingly, the mesh convergence rate of strain/stress in SSE is faster than that in classical S-FEMs. This advantage of SSE is also attractive for nearly incompressible large deformation analyses.
This study proposes a new S-FEM formulation for nearly incompressible large deformation analyses that incorporates the SSE approach using tetrahedral meshes.
In practical problems, the geometries are usually complex, and it is almost impossible to generate low-skew hexahedral meshes.
Therefore, accurate and robust FE formulations using tetrahedral meshes are still highly desired in industry circles.
The smoothed finite element methods (S-FEMs) are being widely used to avoid locking even using tetrahedral meshes. The authors have developed several advanced S-FEMs for nearly incompressible solids using 4-node tetrahedral meshes (SelectiveES/NS-FEM-T4, F-barES-FEM-T4, etc.) or using 10-node tetrahedral meshes (SelectiveCS-FEM-T10). These methods avoid shear and volumetric locking, but they suffer from pressure or deviatoric stress oscillations (checkerboarding) in some cases.
Meanwhile, Lee et al. recently proposed the strain smoothed element (SSE) using tetrahedral meshes as an improved S-FEM formulation. Besides, Jinsong also proposed the edge-center-based SSE (EC-SSE) tetrahedral meshes as an advanced SSE formulation. The SSE assumes a linear strain/stress distribution in each smoothing domain, whereas the classical S-FEMs assume a constant strain/stress distribution in each smoothing domain. Accordingly, the mesh convergence rate of strain/stress in SSE is faster than that in classical S-FEMs. This advantage of SSE is also attractive for nearly incompressible large deformation analyses.
This study proposes a new S-FEM formulation for nearly incompressible large deformation analyses that incorporates the SSE approach using tetrahedral meshes.
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