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Inexact accurate partitioned algorithms for fluid-structure interaction problems with finite elasticity in haemodynamics

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JOURNAL OF COMPUTATIONAL PHYSICS 2014年 273卷 598-617页

作者： Nobile, Fabio Pozzoli, Matteo Vergara, Christian Ecole Polytech Fed Lausanne CSQI MATHICSE CH-1015 Lausanne Switzerland AgustaWestland Cascina Costa VA Italy Univ Bergamo Dipartimento Ingn Bergamo Italy

In this paper we consider the numerical solution of the three-dimensional fluid-structure interaction problem in haemodynamics, in the case of real geometries, physiological data and finite elasticity vessel deformations. We study some new inexact schemes, obtained from semi-implicit approximations, which treat exactly the physical interface conditions while performing just one or few iterations for the management of the interface position and of the fluid and structure non-linearities. We show that such schemes allow to improve the efficiency while preserving the accuracy of the related exact (implicit) scheme. To do this we consider both a simple analytical test case and two real cases of clinical interest in haemodynamics. We also provide an error analysis for a simple differential model problem when a BDF method is considered for the time discretization and only few Newton iterations are performed at each temporal instant. (C) 2014 Elsevier Inc. All rights reserved.

关键词： fluid-structure interaction Finite elasticity Robin transmission conditions BDF schemes Newton method Haemodynamics

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fluid flow in the osteocyte mechanical environment: a fluid-structure interaction approach

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BIOMECHANICS AND MODELING IN MECHANOBIOLOGY 2014年第1期13卷 85-97页

作者： Verbruggen, Stefaan W. Vaughan, Ted J. McNamara, Laoise M. Natl Univ Ireland Coll Engn & Informat Biomech Res Ctr BMEC Galway Ireland Natl Univ Ireland Dept Mech & Biomed Engn Galway Ireland

Osteocytes are believed to be the primary sensor of mechanical stimuli in bone, which orchestrate osteoblasts and osteoclasts to adapt bone structure and composition to meet physiological loading demands. Experimental studies to quantify the mechanical environment surrounding bone cells are challenging, and as such, computational and theoretical approaches have modelled either the solid or fluid environment of osteocytes to predict how these cells are stimulated in vivo. Osteocytes are an elastic cellular structure that deforms in response to the external fluid flow imposed by mechanical loading. This represents a most challenging multi-physics problem in which fluid and solid domains interact, and as such, no previous study has accounted for this complex behaviour. The objective of this study is to employ fluid-structure interaction (FSI) modelling to investigate the complex mechanical environment of osteocytes in vivo. Fluorescent staining of osteocytes was performed in order to visualise their native environment and develop geometrically accurate models of the osteocyte in vivo. By simulating loading levels representative of vigorous physiological activity ( compression and 300 Pa pressure gradient), we predict average interstitial fluid velocities and average maximum shear stresses surrounding osteocytes in vivo. Interestingly, these values occur in the canaliculi around the osteocyte cell processes and are within the range of stimuli known to stimulate osteogenic responses by osteoblastic cells in vitro. Significantly our results suggest that the greatest mechanical stimulation of the osteocyte occurs in the cell processes, which, cell culture studies have indicated, is the most mechanosensitive area of the cell. These are the first computational FSI models to simulate the complex multi-physics mechanical environment of osteocyte in vivo and provide a deeper understanding of bone mechanobiology.

关键词： Bone Osteocyte Mechanobiology Lacuna fluid-structure interaction Shear stress

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Coupling of SPH-ALE method and finite element method for transient fluid-structure interaction

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COMPUTERS & fluidS 2014年 103卷 6-17页

作者： Li, Zhe Leduc, Julien Combescure, Alain Leboeuf, Francis Ecole Cent Lyon Lab Mecan Fluides & Acoust F-69134 Ecully France INSA Lyon Lab Mecan Contacts & Struct F-69621 Villeurbanne France ANDRITZ Hydro F-69100 Villeurbanne France

This article presents an interface-energy-conserving coupling strategy for transient fluid-structure interaction. The solid sub-domain is discretized by finite element method with Newmark time integrator, whereas for the fluid sub-domain we use the mesh-less method SPH-ALE with 2nd order Runge-Kutta scheme. This paper proposes a method to impose a mean interface normal velocity continuity in such a way that the algorithmic interface energy is zero during the whole period of numerical simulation. This coupling method thus ensures that the coupled problem shall be stable in time. Secondly it will converge in time with the rate of convergence of the worst time integrator chosen for each problem. The proposed method is first applied to a mono-dimensional problem by which we investigate the phenomena of propagation of shock waves across the fluid-structure interface. A good agreement is observed between the numerical result and the analytical solution in the 1D shock wave propagation test cases. Finally, a multidimensional example is presented and compared to another coupling approach. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： fluid-structure interaction SPH-ALE method Interface energy Different time integrators

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An unfitted Nitsche method for incompressible fluid-structure interaction using overlapping meshes

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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 2014年第Sep.1期279卷 497-514页

作者： Burman, Erik Fernandez, Miguel A. UCL Dept Math London WC1E 6BT England Inst Natl Rech Informat & Automat REO Project Team F-78153 Le Chesnay France Univ Paris 06 REO Project Team UMR LJLL 7958 F-75005 Paris France

We consider the extension of the Nitsche method to the case of fluid structure interaction problems on unfitted meshes. We give a stability analysis for the space semi-discretized problem and show how this estimate may be used to derive optimal error estimates for smooth solutions, irrespectively of the mesh/interface intersection. We also discuss different strategies for the time discretization, using either fully implicit or explicit coupling (loosely coupled) schemes. Some numerical examples illustrate the theoretical discussion. (C) 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/3.0/).

关键词： fluid-structure interaction Incompressible fluid Unfitted meshes Fictitious domain method Nitsche method Coupling schemes

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A finite strain nonlinear human mitral valve model with fluid-structure interaction

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2014年第12期30卷 1597-1613页

作者： Gao, Hao Ma, Xingshuang Qi, Nan Berry, Colin Griffith, Boyce E. Luo, Xiaoyu Univ Glasgow Sch Math & Stat Glasgow Lanark Scotland Chongqing Univ Bioengn Coll Chongqing 630044 Peoples R China Univ Glasgow Inst Cardiovasc & Med Sci Glasgow Lanark Scotland Univ N Carolina Dept Math Chapel Hill NC USA

A computational human mitral valve (MV) model under physiological pressure loading is developed using a hybrid finite element immersed boundary method, which incorporates experimentally-based constitutive laws in a three-dimensional fluid-structure interaction framework. A transversely isotropic material constitutive model is used to characterize the mechanical behaviour of the MV tissue based on recent mechanical tests of healthy human mitral leaflets. Our results show good agreement, in terms of the flow rate and the closing and opening configurations, with measurements from in vivo magnetic resonance images. The stresses in the anterior leaflet are found to be higher than those in the posterior leaflet and are concentrated around the annulus trigons and the belly of the leaflet. The results also show that the chordae play an important role in providing a secondary orifice for the flow when the valve opens. Although there are some discrepancies to be overcome in future work, our simulations show that the developed computational model is promising in mimicking the in vivo MV dynamics and providing important information that are not obtainable by in vivo measurements. (c) 2014 The Authors. International Journal for Numerical Methods in Biomedical Engineering published by John Wiley & Sons Ltd.

关键词： human mitral valve clinical imaging magnetic resonance imaging fluid-structure interaction finite element immersed boundary method nonlinear finite strain fibre-reinforced constitutive law

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The influence of wind shear on vibration of geometrically nonlinear wind turbine blade under fluid-structure interaction

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OCEAN ENGINEERING 2014年 84卷 14-19页

作者： Zhang, Jianping Guo, Liang Wu, Helen Zhou, Aixi Hu, Danmei Ren, Jianxing Shanghai Univ Elect Power Coll Energy & Mech Engn Shanghai 200090 Peoples R China Univ Western Sydney Sch Comp Engn & Math Sydney NSW 2751 Australia Univ N Carolina Dept Engn Technol & Construct Management Charlotte NC 28223 USA

For the large-scale offshore wind turbine blades, the governing equations in fluid domain and the motion equations in structural domain with geometric nonlinearity were developed based on ALE description, and the corresponding discrete equations were obtained. Blade entity model was built up using Pro/E, and the blade vibration characteristics under fluid-structure interaction (FSI) were simulated using ANSYS. Numerical results show that wind shear effect greatly increases the peak values of response curves for displacement and stress, makes the effect of bi-directional fluid-structure interaction (BFSI) more obvious, and also accelerates the attenuation of vibration curves. The displacement of blade airfoil increases nonlinearly along the span direction, and reaches the maximum at the blade tip. The maximum Mises stress appears in the middle of the blade, and reduces gradually towards each end of the blade. Furthermore, the contribution of wind shear effect (WSE) to displacement and Mises stress is much greater than that of FSI. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Wind turbine blade Wind shear effect fluid-structure interaction Geometric nonlinearity Vibration characteristics

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Finite element analysis for a pressure-stress formulation of a fluid-structure interaction spectral problem

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2014年第12期68卷 1733-1750页

作者： Meddahi, Salim Mora, David Rodriguez, Rodolfo Univ Oviedo Fac Ciencias Dept Matemat Oviedo Spain Univ Bio Bio Dept Matemat Concepcion Chile Univ Concepcion CP2MA Concepcion Chile Univ Concepcion Dept Ingn Matemat CI2MA Concepcion Chile

The aim of this paper is to analyze an elastoacoustic vibration problem employing a dual-mixed formulation in the solid domain. The Cauchy stress tensor and the rotation are the primary variables in the elastic structure while the standard pressure formulation is considered in the acoustic fluid. The resulting mixed eigenvalue problem is approximated by a conforming Galerkin scheme based on the lowest order Lagrange and Arnold-Falk-Winther finite element subspaces in the fluid and solid domains, respectively. We show that the scheme provides a correct approximation of the spectrum and prove quasi-optimal error estimates. Finally, we report some numerical experiments. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： fluid-structure interaction Elastoacoustic vibrations Sloshing Mixed elasticity equations Eigenvalue problem Finite elements

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A stable second-order scheme for fluid-structure interaction with strong added-mass effects

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JOURNAL OF COMPUTATIONAL PHYSICS 2014年 270卷 687-710页

作者： Liu, Jie Jaiman, Rajeev K. Gurugubelli, Pardha S. Natl Univ Singapore Dept Math Singapore 117548 Singapore Natl Univ Singapore Dept Mech Engn Singapore 117548 Singapore

In this paper, we present a stable second-order time accurate scheme for solving fluid-structure interaction problems. The scheme uses so-called Combined Field with Explicit Interface (CFEI) advancing formulation based on the Arbitrary Lagrangian-Eulerian approach with finite element procedure. Although loosely-coupled partitioned schemes are often popular choices for simulating FSI problems, these schemes may suffer from inherent instability at low structure to fluid density ratios. We show that our second-order scheme is stable for any mass density ratio and hence is able to handle strong added-mass effects. Energy-based stability proof relies heavily on the connections among extrapolation formula, trapezoidal scheme for second-order equation, and backward difference method for first-order equation. Numerical accuracy and stability of the scheme is assessed with the aid of two-dimensional fluid-structure interaction problems of increasing complexity. We confirm second-order temporal accuracy by numerical experiments on an elastic semi-circular cylinder problem. We verify the accuracy of coupled solutions with respect to the benchmark solutions of a cylinder-elastic bar and the Navier-Stokes flow system. To study the stability of the proposed scheme for strong added-mass effects, we present new results using the combined field formulation for flexible flapping motion of a thin-membrane structure with low mass ratio and strong added-mass effects in a uniform axial flow. Using a systematic series of fluid-structure simulations, a detailed analysis of the coupled response as a function of mass ratio for the case of very low bending rigidity has been presented. (C) 2014 Elsevier Inc. All rights reserved.

关键词： fluid-structure interaction Low mass density ratio Combined field with explicit interface Second order Stability proof Flapping dynamics Strong added-mass

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Human coronary plaque wall thickness correlated positively with flow shear stress and negatively with plaque wall stress: an IVUS-based fluid-structure interaction multi-patient study

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BIOMEDICAL ENGINEERING ONLINE 2014年第1期13卷 1-14页

作者： Fan, Rui Tang, Dalin Yang, Chun Zheng, Jie Bach, Richard Wang, Liang Muccigrosso, David Billiar, Kristen Zhu, Jian Ma, Genshan Maehara, Akiko Mintz, Gary S. Beijing Univ Posts & Telecommun Sch Informat & Commun Engn Beijing 100088 Peoples R China Southeast Univ Sch Biol Sci & Med Engn Nanjing 210009 Jiangsu Peoples R China Worcester Polytech Inst Dept Math Sci Worcester MA 01609 USA China United Network Commun Co Ltd Network Technol Res Inst Beijing Peoples R China Washington Univ Mallinckrodt Inst Radiol St Louis MO USA Washington Univ Sch Med Div Cardiovasc St Louis MO 63110 USA Worcester Polytech Inst Dept Biomed Engn Worcester MA 01609 USA Southeast Univ Zhongda Hosp Dept Cardiol Nanjing 210009 Jiangsu Peoples R China Columbia Univ Cardiovasc Res Fdn New York NY USA

Background: Atherosclerotic plaque progression and rupture are believed to be associated with mechanical stress conditions. In this paper, patient-specific in vivo intravascular ultrasound (IVUS) coronary plaque image data were used to construct computational models with fluid-structure interaction (FSI) and cyclic bending to investigate correlations between plaque wall thickness and both flow shear stress and plaque wall stress conditions. Methods: IVUS data were acquired from 10 patients after voluntary informed consent. The X-ray angiogram was obtained prior to the pullback of the IVUS catheter to determine the location of the coronary artery stenosis, vessel curvature and cardiac motion. Cyclic bending was specified in the model representing the effect by heart contraction. 3D anisotropic FSI models were constructed and solved to obtain flow shear stress (FSS) and plaque wall stress (PWS) values. FSS and PWS values were obtained for statistical analysis. Correlations with p < 0.05 were deemed significant. Results: Nine out of the 10 patients showed positive correlation between wall thickness and flow shear stress. The mean Pearson correlation r-value was 0.278 +/- 0.181. Similarly, 9 out of the 10 patients showed negative correlation between wall thickness and plaque wall stress. The mean Pearson correlation r-value was -0.530 +/- 0.210. Conclusion: Our results showed that plaque vessel wall thickness correlated positively with FSS and negatively with PWS. The patient-specific IVUS-based modeling approach has the potential to be used to investigate and identify possible mechanisms governing plaque progression and rupture and assist in diagnosis and intervention procedures. This represents a new direction of research. Further investigations using more patient follow-up data are warranted.

关键词： Coronary fluid-structure interaction Plaque rupture Plaque progression IVUS

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Experimental and numerical studies of fluid-structure interaction phenomena inside the head when subjected to a dynamical loading

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COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING 2014年第Sup1期17卷 46-47页

作者： Fontenier, B. Hault-Dubrulle, A. Rahmoun, J. Naceur, H. Drazetic, P. Fontaine, C. Univ Lille Nord France CNRS UMR 8201 Univ Valenciennes UVHC Lab Automat Mech & Human & Ind Comp LAMIH Lille France Univ Hosp Lille Anat Lab Fac Med Lille France

"Experimental and numerical studies of fluid–structure interaction phenomena inside the head when subjected to a dynamical loading."Computer Methods in Biomechanics and Biomedical Engineering, 17(sup1), pp.... 详细信息

关键词： biomechanics brain injuries fluid-structure interaction

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