Immersed smoothed finite element method for fluid–structure interaction simulation of aortic valves

Yao, Jianyao; Liu, G. R.; Narmoneva, Daria A.; Hinton, Robert B.; Zhang, Zhi‐Qian

doi:10.1007/s00466-012-0781-z

Cited by 74 publications

(23 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We choose lumped mass for simplicity, which is also proven with good accuracy. (–)Matrix B I is the link between the strain rate and velocities of node I , whose 2‐dimensional form is given as

B_{I} = ([], \begin{array}{c} \frac{\partial Φ_{I}}{\partial x} & 0 \\ 0 & \frac{\partial Φ_{I}}{\partial y} \\ \frac{\partial Φ_{I}}{\partial y} & \frac{\partial Φ_{I}}{\partial x} \end{array}) .

…”

Section: Cbp Methodsmentioning

confidence: 99%

A quasi‐implicit characteristic–based penalty finite‐element method for incompressible laminar viscous flows

Jiang

Zhang

Han

et al. 2018

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

Summary In this paper, a novel characteristic–based penalty (CBP) scheme for the finite‐element method (FEM) is proposed to solve 2‐dimensional incompressible laminar flow. This new CBP scheme employs the characteristic‐Galerkin method to stabilize the convective oscillation. To mitigate the incompressible constraint, the selective reduced integration (SRI) and the recently proposed selective node–based smoothed FEM (SNS‐FEM) are used for the 4‐node quadrilateral element (CBP‐Q4SRI) and the 3‐node triangular element (CBP‐T3SNS), respectively. Meanwhile, the reduced integration (RI) for Q4 element (CBP‐Q4RI) and NS‐FEM for T3 element (CBP‐T3NS) with CBP scheme are also investigated. The quasi‐implicit CBP scheme is applied to allow a large time step for sufficient large penalty parameters. Due to the absences of pressure degree of freedoms, the quasi‐implicit CBP‐FEM has higher efficiency than quasi‐implicit CBS‐FEM. In this paper, the CBP‐Q4SRI has been verified and validated with high accuracy, stability, and fast convergence. Unexpectedly, CBP‐Q4RI is of no instability, high accuracy, and even slightly faster convergence than CBP‐Q4SRI. For unstructured T3 elements, CBP‐T3SNS also shows high accuracy and good convergence but with pressure oscillation using a large penalty parameter; CBP‐T3NS produces oscillated wrong velocity and pressure results. In addition, the applicable ranges of penalty parameter for different proposed methods have been investigated.

show abstract

B_{I} = ([], \begin{array}{c} \frac{\partial Φ_{I}}{\partial x} & 0 \\ 0 & \frac{\partial Φ_{I}}{\partial y} \\ \frac{\partial Φ_{I}}{\partial y} & \frac{\partial Φ_{I}}{\partial x} \end{array}) .

…”

Section: Cbp Methodsmentioning

confidence: 99%

A quasi‐implicit characteristic–based penalty finite‐element method for incompressible laminar viscous flows

Jiang

Zhang

Han

et al. 2018

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…Although special efforts [18][19][20] to cure the volumetric locking are also proposed in the frame of FEM using T4 element, it must use the pressure as an extra unknown, in addition to its poor accuracy. Because of these advantages of FS/NS-FEM-T4, it has been applied into the analysis of rubber-like materials [17,21,22], hemodynamics [23], opening of aortal valves [24], and tissues of arterial wall [25]. What is worth to be mentioned is that selective FS/NS-FEM-T4 performs well only for nearly incompressible material and shows slight oscillation of hydrostatic pressure field just like the selective integration technique in FEM.…”

Section: Introductionmentioning

confidence: 97%

“…It was then further developed for linear static problems [31], structural dynamic problems [32] and fracture mechanics [33,34]. In these previous works, 3D-ES-FEM using T4 element has been found with several interesting merits than other S-FEMs and FEMs, including the nearly-quadratic accuracy and the least time consuming to reach a high accuracy using T4 meshes [24,25]. Hence, applying the 3D-ES-FEM to replace the FS-FEM in Selective S-FEM should develop a more accurate selective S-FEM.…”

Section: Introductionmentioning

confidence: 98%

An edge-based/node-based selective smoothed finite element method using tetrahedrons for cardiovascular tissues

Jiang

Zhang

Liu

et al. 2015

Engineering Analysis with Boundary Elements

Self Cite

View full text Add to dashboard Cite

“…It conducts the node‐based gradient smoothing operation for volumetric part, which is soft and volumetric locking free; and conducts edge‐based gradient smoothing operation for deviatoric part, which is more stiff and temporal stable than NS‐FEM. This selective FS/NS‐FEM‐TET4 has been applied recently in rubber‐like problems , fluid‐structure interaction problems and aortic valves motion and deformation .…”

Section: Introductionmentioning

confidence: 99%

“…It conducts the nodebased gradient smoothing operation [31] for volumetric part, which is soft and volumetric locking free; and conducts edge-based gradient smoothing operation [47] for deviatoric part, which is more stiff and temporal stable than NS-FEM. This selective FS/NS-FEM-TET4 has been applied recently in rubber-like problems [32], fluid-structure interaction problems [48][49][50] and aortic valves motion and deformation [51].Although the FS/NS-FEM-TET4 has already been proposed and applied to analyze a few different problems [32,42], it has not been extended in biomechanics study with anisotropic material yet. In this work, we explore the FS/NS-FEM-TET4 method and modified it partly so that it can deal e02697 (2 of 25) C. JIANG ET AL.…”

mentioning

confidence: 99%

A smoothed finite element method for analysis of anisotropic large deformation of passive rabbit ventricles in diastole

Jiang

Liu

Han

et al. 2015

Numer Methods Biomed Eng

Self Cite

View full text Add to dashboard Cite

The smoothed FEM (S-FEM) is firstly extended to explore the behavior of 3D anisotropic large deformation of rabbit ventricles during the passive filling process in diastole. Because of the incompressibility of myocardium, a special method called selective face-based/node-based S-FEM using four-node tetrahedral elements (FS/NS-FEM-TET4) is adopted in order to avoid volumetric locking. To validate the proposed algorithms of FS/NS-FEM-TET4, the 3D Lame problem is implemented. The performance contest results show that our FS/NS-FEM-TET4 is accurate, volumetric locking-free and insensitive to mesh distortion than standard linear FEM because of absence of isoparametric mapping. Actually, the efficiency of FS/NS-FEM-TET4 is comparable with higher-order FEM, such as 10-node tetrahedral elements. The proposed method for Holzapfel myocardium hyperelastic strain energy is also validated by simple shear tests through the comparison outcomes reported in available references. Finally, the FS/NS-FEM-TET4 is applied in the example of the passive filling of MRI-based rabbit ventricles with fiber architecture derived from rule-based algorithm to demonstrate its efficiency. Hence, we conclude that FS/NS-FEM-TET4 is a promising alternative other than FEM in passive cardiac mechanics.

show abstract

Immersed smoothed finite element method for fluid–structure interaction simulation of aortic valves

Cited by 74 publications

References 49 publications

A quasi‐implicit characteristic–based penalty finite‐element method for incompressible laminar viscous flows

A quasi‐implicit characteristic–based penalty finite‐element method for incompressible laminar viscous flows

An edge-based/node-based selective smoothed finite element method using tetrahedrons for cardiovascular tissues

A smoothed finite element method for analysis of anisotropic large deformation of passive rabbit ventricles in diastole

Contact Info

Product

Resources

About