A sharp-interface immersed smoothed finite element method for interactions between incompressible flows and large deformation solids

2018 ◽  
Vol 340 ◽  
pp. 24-53 ◽  
Author(s):  
Chen Jiang ◽  
Jian-Yao Yao ◽  
Zhi-Qian Zhang ◽  
Guang-Jun Gao ◽  
G.R. Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Deformation ◽  
Incompressible Flows ◽  
Sharp Interface ◽  
Smoothed Finite Element Method ◽  
Element Method

Accurate Viscoelastic Large Deformation Analysis Using F-Bar Aided Edge-Based Smoothed Finite Element Method for 4-Node Tetrahedral Meshes (F-BarES-FEM-T4)

2019 ◽  
Vol 17 (02) ◽  
pp. 1845003 ◽  
Author(s):  
Yuki Onishi ◽  
Ryoya Iida ◽  
Kenji Amaya
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Deformation ◽  
Pressure Oscillation ◽  
Deformation Analysis ◽  
Smoothed Finite Element Method ◽  
Edge Based ◽  
Smoothing Procedure ◽  
Element Method

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.

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

2019 ◽  
Vol 16 (05) ◽  
pp. 1840010 ◽  
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.

A Concept of Cell-Based Smoothed Finite Element Method Using 10-Node Tetrahedral Elements (CS-FEM-T10) for Large Deformation Problems of Nearly Incompressible Solids

2019 ◽  
Vol 17 (02) ◽  
pp. 1845009
Author(s):  
Yuki Onishi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Deformation ◽  
Hydrostatic Stress ◽  
Reaction Force ◽  
Strain Smoothing ◽  
Smoothed Finite Element Method ◽  
Incompressible Solids ◽  
Large Deformation Problems ◽  
Element Method

A new concept of smoothed finite element method (S-FEM) using 10-node tetrahedral (T10) elements, CS-FEM-T10, is proposed. CS-FEM-T10 is a kind of cell-based S-FEM (CS-FEM) and thus it smooths the strain only within each T10 element. Unlike the other types of S-FEMs [node-based S-FEM (NS-FEM), edge-based S-FEM (ES-FEM), and face-based S-FEM (FS-FEM)], CS-FEM can be implemented in general finite element (FE) codes as a piece of the element library. Therefore, CS-FEM-T10 is also compatible with general FE codes as a T10 element. A concrete example of CS-FEM-T10 named SelectiveCS-FEM-T10 is introduced for large deformation problems of nearly incompressible solids. SelectiveCS-FEM-T10 subdivides each T10 element into 12 four-node tetrahedral (T4) subelements with an additional dummy node at the element center. Two types of strain smoothing are conducted for the deviatoric and hydrostatic stress evaluations and the selective reduced integration (SRI) technique is utilized for the stress integration. As a result, SelectiveCS-FEM-T10 avoids the shear/volumetric locking, pressure checkerboarding, and reaction force oscillation in nearly incompressible solids. In addition, SelectiveCS-FEM-T10 has a relatively long-lasting property in large deformation problems. A few examples of large deformation analyses of a hyperelastic material confirm the good accuracy and robustness of SelectiveCS-FEM-T10. Moreover, an implementation of SelectiveCS-FEM-T10 in the FE code ABAQUS as a user-defined element (UEL) is conducted and its capability is discussed.

A Smoothed Finite Element Method (S-FEM) for Large-Deformation Elastoplastic Analysis

2015 ◽  
Vol 12 (04) ◽  
pp. 1540011 ◽  
Author(s):  
Jun Liu ◽  
Zhi-Qian Zhang ◽  
Guiyong Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Deformation ◽  
Computational Efficiency ◽  
Triangular Element ◽  
Fem Method ◽  
Deformation Plasticity ◽  
Smoothed Finite Element Method ◽  
Edge Based ◽  
Element Method

An edge-based smoothed finite element method (ES-FEM) using 3-node triangular element was recently proposed to improve the accuracy and convergence rate of the standard finite element method (FEM) for 2D elastic solid mechanics problems. In this research, ES-FEM is extended to large-deformation plasticity analysis, and a selective edge-based/node-based smoothed finite element (selective ES/NS-FEM) method using 3-node triangular elements is adopted to address volumetric locking problem. Validity of ES-FEM for large-deformation plasticity problem is proved by benchmarks, and numerical examples demonstrate that, the proposed ES-FEM and selective ES/NS-FEM method possess (1) superior accuracy and convergence properties for strain energy solutions comparing to the standard FEM using 3-node triangular element (FEM-T3), (2) better computational efficiency than FEM-T3 and similar computational efficiency as FEM using 4-node quadrilateral element and 6-node quadratic triangular element, (3) a selective ES/NS-FEM method can successfully simulate problems with severe element distortion, and address volumetric locking problem in large-deformation plasticity analysis.

SMOOTHED FINITE ELEMENTS LARGE DEFORMATION ANALYSIS

2010 ◽  
Vol 07 (03) ◽  
pp. 513-524 ◽  
Author(s):  
S. J. LIU ◽  
H. WANG ◽  
H. ZHANG
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Large Deformation ◽  
Large Deformations ◽  
Meshfree Methods ◽  
Deformation Analysis ◽  
The Finite Element Method ◽  
Smoothed Finite Element Method ◽  
First Time ◽  
Element Method

The smoothed finite element method (SFEM) was developed in order to eliminate certain shortcomings of the finite element method (FEM). SFEM enjoys some of the flexibilities of meshfree methods. One advantage of SFEM is its applicability to modeling large deformations. Due to the absence of volume integration and parametric mapping, issues such as negative volumes and singular Jacobi matrix do not occur. However, despite these advantages, SFEM has never been applied to problems with extreme large deformation. For the first time, we apply SFEM to extreme large deformations. For two numerical problems, we demonstrate the advantages of SFEM over FEM. We also show that SFEM can compete with the flexibility of meshfree methods.

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