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A new optimal formulation of the selective cell-based smoothed finite element method using 10-node tetrahedral elements (SelectiveCS-FEM-T10) is proposed.
SelectiveCS-FEM-T10 is a generic name for the S-FEM formulations that apply selective reduced integration (SRI) and CS-FEM to each T10 element simultaneously, and thus it has various formulation variations.
The conventional SelectiveCS-FEM-T10 introduces a dummy node at the center of each element and subdivides a T10 element into 12 subelements of 4-node tetrahedra (T4) as usual unstructured T4 mesh generation.
The unstructured-type mesh subdivision has a disadvantage that strain smoothing is not applied to the silhouette edges when we apply edge-based S-FEM (ES-FEM) within a T10 element.
Meanwhile, the new SelectiveCS-FEM-T10 subdivides it into 16 T4 subelements radially around the dummy node.
Owing to the radial-type mesh subdivision, ES-FEM within a T10 element can apply strain smoothing to all edges including the silhouette edges.
The main target of the new SelectiveCS-FEM-T10 is large deformation analyses of nearly incompressible solids such as rubber.
Our demonstrative analysis reveals that the new SelectiveCS-FEM-T10 is more robust than the conventional T10 elements against severely large deformation.
The accuracy of the new SelectiveCS-FEM-T10 is almost equal to the conventional T10 elements as it does not cause shear/volumetric locking and pressure-checkerboarding issues.
Besides, SelectiveCS-FEM-T10 can be implemented into general finite element codes as a T10 element because it is a CS-FEM, which applies strain smoothing only within each element.