ArticleComputer methods in applied mechanics and engineering2020
Stabilization approaches for the hyperelastic immersed boundary method for problems of large-deformation incompressible elasticity.
Article in Computer methods in applied mechanics and engineering, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 16 papers.
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16 citing papers in PubMed.
- A Whole-Heart Fluid-Structure Interaction Model for Transcatheter Mitral Valve Repair in Primary Mitral Regurgitation.Annals of biomedical engineering · 2026Article
- LOCAL DIVERGENCE-FREE IMMERSED FINITE ELEMENT-DIFFERENCE METHOD USING COMPOSITE B-SPLINES.Advances in computational science and engineering · 2025Article
- Simulating cardiac fluid dynamics in the human heart.PNAS nexus · 2024Article
- An immersed peridynamics model of fluid-structure interaction accounting for material damage and failure.Journal of computational physics · 2023Article
- A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction.Journal of computational physics · 2023Article
- A model of fluid-structure and biochemical interactions for applications to subclinical leaflet thrombosis.International journal for numerical methods in biomedical engineering · 2023Article
- A Nodal Immersed Finite Element-Finite Difference Method.Journal of computational physics · 2023Article
- Beyond CFD: Emerging methodologies for predictive simulation in cardiovascular health and disease.Biophysics reviews · 2023Review
- A stabilized linear finite element method for anisotropic poroelastodynamics with application to cardiac perfusion.Computer methods in applied mechanics and engineering · 2023Article
- On the Lagrangian-Eulerian Coupling in the Immersed Finite Element/Difference Method.Journal of computational physics · 2022Article
- A fully resolved multiphysics model of gastric peristalsis and bolus emptying in the upper gastrointestinal tract.Computers in biology and medicine · 2022Article
- Article
- A poroelastic immersed finite element framework for modelling cardiac perfusion and fluid-structure interaction.International journal for numerical methods in biomedical engineering · 2021Article
- Fluid-Structure Interaction Models of Bioprosthetic Heart Valve Dynamics in an Experimental Pulse Duplicator.Annals of biomedical engineering · 2020Article
- Immersed Methods for Fluid-Structure Interaction.Annual review of fluid mechanics · 2020Article
- Analysis of a coupled fluid-structure interaction model of the left atrium and mitral valve.International journal for numerical methods in biomedical engineering · 2019Article
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5 authors.
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Abstract
The immersed boundary method is a mathematical framework for modeling fluid-structure interaction. This formulation describes the momentum, viscosity, and incompressibility of the fluid-structure system in Eulerian form, and it uses Lagrangian coordinates to describe the structural deformations, stresses, and resultant forces. Integral transforms with Dirac delta function kernels connect the Eulerian and Lagrangian frames. The fluid and the structure are both typically treated as incompressible materials. Upon discretization, however, the incompressibility of the structure is only maintained approximately. To obtain an immersed method for incompressible hyperelastic structures that is robust under large structural deformations, we introduce a volumetric energy in the solid region that stabilizes the formulation and improves the accuracy of the numerical scheme. This formulation augments the discrete Lagrange multiplier for the incompressibility constraint, thereby improving the original method's accuracy. This volumetric energy is incorporated by decomposing the strain energy into isochoric and dilatational components, as in standard solid mechanics formulations of nearly incompressible elasticity. We study the performance of the stabilized method using several quasi-static solid mechanics benchmarks, a dynamic fluid-structure interaction benchmark, and a detailed three-dimensional model of esophageal transport. The accuracy achieved by the stabilized immersed formulation is comparable to that of a stabilized finite element method for incompressible elasticity using similar numbers of structural degrees of freedom.
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