Dynamic and fluid–structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material models

Hsu, Ming‐Chen; Kamensky, David; Xu, Fei; Kiendl, Josef; Wang, Chenglong; Wu, Mike; Mineroff, Joshua; Reali, Alessandro; Bazilevs, Yuri; Sacks, Michael S.

doi:10.1007/s00466-015-1166-x

Cited by 226 publications

(180 citation statements)

References 104 publications

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“…This combination enables application of IGA to trimmed, coupled and overlapping domains in Computer Aided Design (CAD) [32,25,26], topologically complex structures such as porous materials, composites and scanned data [27,33], and problems with moving boundaries such as Fluid Structure Interactions [3,18,14], without laborious (re-)meshing procedures.…”

Section: Introductionmentioning

confidence: 99%

Condition number analysis and preconditioning of the finite cell method

Prenter

Verhoosel

Zwieten

et al. 2017

Computer Methods in Applied Mechanics and Engineering

139

179

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The (Isogeometric) Finite Cell Method -in which a domain is immersed in a structured background mesh -suffers from conditioning problems when cells with small volume fractions occur. In this contribution, we establish a rigorous scaling relation between the condition number of (I)FCM system matrices and the smallest cell volume fraction. Ill-conditioning stems either from basis functions being small on cells with small volume fractions, or from basis functions being nearly linearly dependent on such cells. Based on these two sources of ill-conditioning, an algebraic preconditioning technique is developed, which is referred to as Symmetric Incomplete Permuted Inverse Cholesky (SIPIC). A detailed numerical investigation of the effectivity of the SIPIC preconditioner in improving (I)FCM condition numbers and in improving the convergence speed and accuracy of iterative solvers is presented for the Poisson problem and for two-and three-dimensional problems in linear elasticity, in which Nitche's method is applied in either the normal or tangential direction. The accuracy of the preconditioned iterative solver enables mesh convergence studies of the finite cell method.

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Section: Introductionmentioning

confidence: 99%

Condition number analysis and preconditioning of the finite cell method

Prenter

Verhoosel

Zwieten

et al. 2017

Computer Methods in Applied Mechanics and Engineering

139

179

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“…Extension to general hyperelastic material can be found in [4]. The formulation has been successfully used in computation of a good number of challenging problems, including wind-turbine fluid-structure interaction (FSI) [3,[5][6][7][8][9], bioinspired flapping-wing aerodynamics [10], bioprosthetic heart valves [11][12][13][14][15], fatigue and damage [16][17][18][19][20][21], and design [22,23].…”

Section: Introductionmentioning

confidence: 99%

“…Fung's model has different versions. In the version used in [12], the first invariant of the Cauchy-Green deformation tensor appears in a squared form. In the version we use in this article, it appears without being squared, and this version has been used in a number of arterial FSI computations [24][25][26][27][28][29][30][31] with the continuum model.…”

Section: Introductionmentioning

confidence: 99%

Isogeometric hyperelastic shell analysis with out-of-plane deformation mapping

2018

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We derive a hyperelastic shell formulation based on the Kirchhoff-Love shell theory and isogeometric discretization, where we take into account the out-of-plane deformation mapping. Accounting for that mapping affects the curvature term. It also affects the accuracy in calculating the deformed-configuration out-of-plane position, and consequently the nonlinear response of the material. In fluid-structure interaction analysis, when the fluid is inside a shell structure, the shell midsurface is what it would know. We also propose, as an alternative, shifting the "midsurface" location in the shell analysis to the inner surface, which is the surface that the fluid should really see. Furthermore, in performing the integrations over the undeformed configuration, we take into account the curvature effects, and consequently integration volume does not change as we shift the "midsurface" location. We present test computations with pressurized cylindrical and spherical shells, with Neo-Hookean and Fung's models, for the compressible-and incompressible-material cases, and for two different locations of the "midsurface." We also present test computation with a pressurized Y-shaped tube, intended to be a simplified artery model and serving as an example of cases with somewhat more complex geometry.Keywords Kirchhoff-Love shell theory · Isogeometric discretization · Hyperelastic material · Out-of-plane deformation mapping · Neo-Hookean material model · Fung's material model · Artery

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“…It should be noted that the immersogeometric concept is independent of a specific basis and can be used with any basis function technology and element type. For example, Hsu et al (2014Hsu et al ( , 2015a successfully immersed NURBS and T-spline geometries into trivariate NURBS background mesh and Xu et al (2016) immersed a triangulated surface into tetrahedral background elements.…”

Section: Flow Around a Spherementioning

confidence: 99%

“…The method analyzed a surface representation of the structure by immersing it into a non-boundary-fitted discretization of the background fluid domain and focused on accurately capturing the immersed geometry (and hence the name immersogeometric) within non-boundary-fitted analysis meshes. The method was successfully applied to the FSI simulation of bioprosthetic heart valves (Kamensky et al, 2015;Hsu et al, 2014Hsu et al, , 2015a. The immersogeometric method was further investigated by Xu et al (2016) in the context of a tetrahedral finite cell approach for the simulation of incompressible flow, both laminar and turbulent, around geometrically complex objects.…”

Section: Introductionmentioning

confidence: 99%

Direct immersogeometric fluid flow analysis using B-rep CAD models

Hsu

Wang

et al. 2016

Computer Aided Geometric Design

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We present a new method for immersogeometric fluid flow analysis that directly uses the CAD boundary representation (B-rep) of a complex object and immerses it into a locally refined, non-boundary-fitted discretization of the fluid domain. The motivating applications include analyzing the flow over complex geometries, such as moving vehicles, where the detailed geometric features usually require time-consuming, labor-intensive geometry cleanup or mesh manipulation for generating the surrounding boundary-fitted fluid mesh. The proposed method avoids the challenges associated with such procedures. A new method to perform point membership classification of the background mesh quadrature points is also proposed. To faithfully capture the geometry in intersected elements, we implement an adaptive quadrature rule based on the recursive splitting of elements. Dirichlet boundary conditions in intersected elements are enforced weakly in the sense of Nitsche's method. To assess the accuracy of the proposed method, we perform computations of the benchmark problem of flow over a sphere represented using B-rep. Quantities of interest such as drag coefficient are in good agreement with reference values reported in the literature. The results show that the density and distribution of the surface quadrature points are crucial for the weak enforcement of Dirichlet boundary conditions and for obtaining accurate flow solutions. Also, with sufficient levels of surface quadrature element refinement, the quadrature error near the trim curves becomes insignificant. Finally, we demonstrate the effectiveness of our immersogeometric method for high-fidelity industrial scale simulations by performing an aerodynamic analysis of an agricultural tractor directly represented using B-rep. AbstractWe present a new method for immersogeometric fluid flow analysis that directly uses the CAD boundary representation (B-rep) of a complex object and immerses it into a locally refined, non-boundary-fitted discretization of the fluid domain. The motivating applications include analyzing the flow over complex geometries, such as moving vehicles, where the detailed geometric features usually require time-consuming, labor-intensive geometry cleanup or mesh manipulation for generating the surrounding boundary-fitted fluid mesh. The proposed method avoids the challenges associated with such procedures. A new method to perform point membership classification of the background mesh quadrature points is also proposed. To faithfully capture the geometry in intersected elements, we implement an adaptive quadrature rule based on the recursive splitting of elements. Dirichlet boundary conditions in intersected elements are enforced weakly in the sense of Nitsche's method. To assess the accuracy of the proposed method, we perform computations of the benchmark problem of flow over a sphere represented using B-rep. Quantities of interest such as drag coefficient are in good agreement with reference values reported in the literature. The results show that the ...

show abstract

Dynamic and fluid–structure interaction simulations of bioprosthetic heart valves using parametric design with T-splines and Fung-type material models

Cited by 226 publications

References 104 publications

Condition number analysis and preconditioning of the finite cell method

Condition number analysis and preconditioning of the finite cell method

Isogeometric hyperelastic shell analysis with out-of-plane deformation mapping

Direct immersogeometric fluid flow analysis using B-rep CAD models

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