ArticleComputer methods in applied mechanics and engineering2018
A unified continuum and variational multiscale formulation for fluids, solids, and fluid-structure interaction.
Article in Computer methods in applied mechanics and engineering, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 18 papers.
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Who cites it
18 citing papers in PubMed.
- HeartSimSage: Attention-Enhanced Graph Neural Networks for Accelerating Cardiac Mechanics Modeling.Journal of computational physics · 2026Article
- Efficient Multi-Fidelity Fluid-Structure Interaction Modeling for Pulsatile Blood Flow in Deformable Biological Tissues.Annals of biomedical engineering · 2026Article
- Computational modeling of immersed non-spherical bodies in viscous flows to study embolus-hemodynamics interactions in large-vessel occlusion stroke.Engineering with computers · 2026Article
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- DIRECT MEDICAL IMAGE TO SIMULATION USING AUTO-SEGMENTATION AND POINT CLOUD-BASED CFD.Advances in computational science and engineering · 2025Article
- Fluid-structure interaction analysis for abdominal aortic aneurysms: the role of multi-layered tissue architecture and intraluminal thrombus.Frontiers in bioengineering and biotechnology · 2025Article
- A mechanically consistent unified formulation for fluid-porous-structure-contact interaction.Computer methods in applied mechanics and engineering · 2024Article
- A Modular Framework for Implicit 3D-0D Coupling in Cardiac Mechanics.Computer methods in applied mechanics and engineering · 2024Article
- Beyond CFD: Emerging methodologies for predictive simulation in cardiovascular health and disease.Biophysics reviews · 2023Review
- Validation of the Reduced Unified Continuum Formulation Against In Vitro 4D-Flow MRI.Annals of biomedical engineering · 2023Article
- How viscous is the beating heart?: Insights from a computational study.Computational mechanics · 2022Article
- A distributed lumped parameter model of blood flow with fluid-structure interaction.Biomechanics and modeling in mechanobiology · 2021Article
- Modeling intracranial aneurysm stability and growth: an integrative mechanobiological framework for clinical cases.Biomechanics and modeling in mechanobiology · 2020Article
- The nested block preconditioning technique for the incompressible Navier-Stokes equations with emphasis on hemodynamic simulations.Computer methods in applied mechanics and engineering · 2020Article
- Fluid-structure interaction modeling of blood flow in the pulmonary arteries using the unified continuum and variational multiscale formulation.Mechanics research communications · 2020Article
- An energy-stable mixed formulation for isogeometric analysis of incompressible hyper-elastodynamics.International journal for numerical methods in engineering · 2019Article
- 4D Flow MRI Estimation of Boundary Conditions for Patient Specific Cardiovascular Simulation.Annals of biomedical engineering · 2019Article
- A robust and efficient iterative method for hyper-elastodynamics with nested block preconditioning.Journal of computational physics · 2019Article
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2 authors.
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Abstract
We develop a unified continuum modeling framework using the Gibbs free energy as the thermodynamic potential. This framework naturally leads to a pressure primitive variable formulation for the continuum body, which is well-behaved in both compressible and incompressible regimes. Our derivation also provides a rational justification of the isochoric-volumetric additive split of free energies in nonlinear elasticity. The variational multiscale analysis is performed for the continuum model to construct a foundation for numerical discretization. We first consider the continuum body instantiated as a hyperelastic material and develop a variational multiscale formulation for the hyper-elastodynamic problem. The generalized-
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