Large Deformation Analysis of Rubber using Smoothed Finite Element Method with Tetrahedral Elements

A state-of-the-art tetrahedral smoothed finite element method, F-barES-FEM-T4, is demonstrated on viscoelastic large deformation problems. The stress relaxation of viscoelastic materials brings near incompressibility when the long-term Poisson’s ratio is close to 0.5. The conventional hybrid 4-node tetrahedral (T4) elements cannot avoid the shear locking and pressure checkerboarding issues, meanwhile F-barES-FEM-T4 can suppress these issues successfully by adopting the edge-based smoothed finite element method (ES-FEM) with the aid of the F-bar method and the cyclic smoothing procedure. A few examples of analyses verify that F-barES-FEM-T4 is locking-free and pressure oscillation-free in viscoelastic analyses as well as in nearly incompressible hyperelastic or elastoplastic analyses.

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F-Bar Aided Edge-Based Smoothed Finite Element Method with 4-Node Tetrahedral Elements for Static Large Deformation Elastoplastic Problems

International Journal of Computational Methods ◽

10.1142/s0219876218400108 ◽

2019 ◽

Vol 16 (05) ◽

pp. 1840010 ◽

Cited By ~ 2

Author(s):

Yuki Onishi

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Large Deformation ◽

Element Formulation ◽

Tetrahedral Elements ◽

Smoothed Finite Element Method ◽

New Type ◽

Displacement Based ◽

Edge Based ◽

Element Method

A new type of smoothed finite element method (S-FEM), F-barES-FEM-T4, is demonstrated in static large deformation elastoplastic cases. F-barES-FEM-T4 combines the edge-based S-FEM (ES-FEM) and the node-based S-FEM (NS-FEM) for 4-node tetrahedral (T4) elements with the aid of the F-bar method in order to resolve the major issues of Selective ES/NS-FEM-T4. As well as most of the other S-FEMs, F-barES-FEM-T4 inherits pure displacement-based formulation and thus has no increase in DOF. Moreover, the cyclic smoothing procedure introduced in F-barES-FEM-T4 is effective to adjust the smoothing level so that pressure checkerboarding (oscillation) is suppressed reasonably. Some examples of static large deformation analyses for elastoplastic materials proof the excellent performance of F-barES-FEM-T4 in contrast to the conventional hybrid T4 element formulation.

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Hexahedral-Based Smoothed Finite Element Method Using Volumetric-Deviatoric Split for Contact Problem

Materials Science Forum ◽

10.4028/www.scientific.net/msf.940.84 ◽

2018 ◽

Vol 940 ◽

pp. 84-88 ◽

Cited By ~ 1

Author(s):

Kai Oshiro ◽

Hiroka Miyakubo ◽

Masaki Fujikawa ◽

Chobin Makabe

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Contact Problem ◽

Large Strain ◽

Deformation Gradient ◽

Deformation Analysis ◽

Tetrahedral Elements ◽

Incompressible Materials ◽

Smoothed Finite Element Method ◽

Element Method

A first-order hexahedral (H8)-element-based smoothed finite element method (S-FEM) with a volumetric-deviatoric split for nearly incompressible materials was developed for highly accurate deformation analysis of large-strain problems. In the proposed method, the isovolumetric part of the deformation gradient at the integration point is derived from F based on the beta finite element method (i.e., an S-FEM), whereas the volumetric part of the deformation gradient is derived from F on the basis of the standard FEM with reduced integration elements. This method targets H8 elements that are automatically generated from tetrahedral elements, which makes it quite practical. This is because the FE mesh can be created automatically even if the targeted object has a complex shape. This method eliminates the phenomena of volumetric and shear locking, and reduces pressure oscillations. The proposed method was implemented in the commercial FE software Abaqus and applied to the large-deformation contact problem to verify its effectiveness.

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