Three-dimensional variable-node elements based upon CS-FEM for elastic–plastic analysis

Lee, Kyehyung; Kim, Yong-Gun; Im, Seyoung

doi:10.1016/j.compstruc.2015.06.005

Cited by 19 publications

(2 citation statements)

References 78 publications

(135 reference statements)

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“…A solution to this problem, the smoothed finite element method (S‐FEM) based on generalized smoothed Galerkin (GS‐Galerkin) weak form, was proposed by Liu et al 26‐29 The strain smoothing technique 30 is used to convert the element‐based calculations of standard FEM into different smoothing domain calculations. According to the way to construct smooth domains in element, smoothed finite elements are classified into node‐based smoothed FEM (NS‐FEM), 31‐38 Cell‐based smoothed FEM (CS‐FEM), 39‐43 edge‐based smoothed FEM (ES‐FEM), 44‐49 and face‐based smoothed FEM (FS‐FEM), 50‐53 etc. A large number of numerical experiments show that ES‐FEM and FS‐FEM have excellent h‐convergence characteristics, accuracy and temporal and spatial stability, which can greatly improve the performance of tetrahedral elements 53 .…”

Section: Introductionmentioning

confidence: 99%

A selective smoothed finite element method with visco‐hyperelastic constitutive model for analysis of biomechanical responses of brain tissues

Jiang

et al. 2020

Numerical Meth Engineering

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Brain tissues are known for exhibiting complex nonlinear and time-dependent properties, which require visco-hyperelastic constitutive models for proper simulation. In this paper, a Total Lagrangian Explicit Selective Smoothed Finite Element Method (Selective S-FEM) is formulated to analyze the dynamic behavior of incompressible brain tissues undergoing extremely large deformation. The proposed Selective S-FEM deals with three-dimensional problems using four-node tetrahedron elements that can be automatically generated for geometrically complex soft tissues. It consists of the three key ingredients. (i) A visco-hyperelastic constitutive model is developed within the framework of S-FEM in the first time, allowing adequate modeling of the dynamic brain tissue behavior. (ii) Selective S-FEM strategy is used for overcome the mesh distortion and the volumetric locking that often occurs in soft tissues. (iii) Total Lagrangian formulation is used in an explicit algorithm allowing rigorous simulation of extreme large deformation. (iv) A combined implementation of Selective S-FEM with the visco-hyperelastic constitutive model for dynamic simulations. The shear deformation is calculated by Face/Edge-based S-FEM, and the volume deformation is calculated by NS-FEM. Numerical experiments show that Selective S-FEM is a robust solver with good accuracy, and excellent ability to reduce element distortion effects in simulate time-dependence behavior of bio-tissues.

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Section: Introductionmentioning

confidence: 99%

A selective smoothed finite element method with visco‐hyperelastic constitutive model for analysis of biomechanical responses of brain tissues

Jiang

et al. 2020

Numerical Meth Engineering

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“…Problems such as vibration and dynamic analysis [12,13], elastic-plastic analysis [14,15], fracture mechanics [16,17,18], heat transfer [19,20], structural acoustics [21,22,23], contact problems [24], adaptive analysis [25,26], impact problem [27] and many more. These researches show that compared with the FEM, SFEMs have many advantages in treating different problems, specifically when there are large deformations and nonlinear material behavior.…”

Section: Introductionmentioning

confidence: 99%

Application of smoothed finite element method in coupled hydro-mechanical analyses

Karimian

Oliaei

2017

Scientia Iranica

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Smoothed finite element method (SFEM) was introduced by application of the stabilized conforming nodal integration in the conventional finite element method. In this method, integration is performed on "smoothing domains" rather than elements. Smoothing domains are created based on cells, nodes or edges for two dimensional problems. Based on the smoothing domain creation method, different types of SFEM are developed that have different properties. It has been shown that these methods are insensitive to mesh distortion and are generally more computationally efficient than mesh-free and finite element methods for the same accuracy level. Because of their interesting features, they have been used to solve different problems. This paper investigates the performance of these methods in coupled hydro-mechanical (consolidation) analysis, by solution of some problems using a developed SFEM/FEM code. Biot's consolidation theory is reviewed, and after introduction of the idea and formulation of SFEMs, discretized form of equations is given. Requirements for creation of stable coupled hydro-mechanical models are discussed and based on them, two methods for creation of stable SFEM models are introduced. To investigate the effectiveness of the methods, a number of examples are solved and results are compared with the finite element and analytical ones.

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Polyhedral elements using an edge-based smoothed finite element method for nonlinear elastic deformations of compressible and nearly incompressible materials

Lee

Kim

et al. 2017

Comput Mech

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Three-dimensional variable-node elements based upon CS-FEM for elastic–plastic analysis

Cited by 19 publications

References 78 publications

A selective smoothed finite element method with visco‐hyperelastic constitutive model for analysis of biomechanical responses of brain tissues

A selective smoothed finite element method with visco‐hyperelastic constitutive model for analysis of biomechanical responses of brain tissues

Application of smoothed finite element method in coupled hydro-mechanical analyses

Polyhedral elements using an edge-based smoothed finite element method for nonlinear elastic deformations of compressible and nearly incompressible materials

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