2,872 research outputs found
An unstructured immersed finite element method for nonlinear solid mechanics.
We present an immersed finite element technique for boundary-value and interface problems from nonlinear solid mechanics. Its key features are the implicit representation of domain boundaries and interfaces, the use of Nitsche's method for the incorporation of boundary conditions, accurate numerical integration based on marching tetrahedrons and cut-element stabilisation by means of extrapolation. For discretisation structured and unstructured background meshes with Lagrange basis functions are considered. We show numerically and analytically that the introduced cut-element stabilisation technique provides an effective bound on the size of the Nitsche parameters and, in turn, leads to well-conditioned system matrices. In addition, we introduce a novel approach for representing and analysing geometries with sharp features (edges and corners) using an implicit geometry representation. This allows the computation of typical engineering parts composed of solid primitives without the need of boundary-fitted meshes.This work was partially supported by the EPSRC (second author, Grant #EP/G008531/1), by the European Research
Council (third author, Grant #ERC-2012-StG 306751), and by the Spanish Ministry of Economy and Competitiveness (third
author, Grant #DPI2015-64221-C2-1-R).This is the final version of the article. It first appeared from Springer at http://dx.doi.org/10.1186/s40323-016-0077-5
A Nitsche-based cut finite element method for a fluid--structure interaction problem
We present a new composite mesh finite element method for fluid--structure
interaction problems. The method is based on surrounding the structure by a
boundary-fitted fluid mesh which is embedded into a fixed background fluid
mesh. The embedding allows for an arbitrary overlap of the fluid meshes. The
coupling between the embedded and background fluid meshes is enforced using a
stabilized Nitsche formulation which allows us to establish stability and
optimal order \emph{a priori} error estimates,
see~\cite{MassingLarsonLoggEtAl2013}. We consider here a steady state
fluid--structure interaction problem where a hyperelastic structure interacts
with a viscous fluid modeled by the Stokes equations. We evaluate an iterative
solution procedure based on splitting and present three-dimensional numerical
examples.Comment: Revised version, 18 pages, 7 figures. Accepted for publication in
CAMCo
Quasi-static imaged-based immersed boundary-finite element model of human left ventricle in diastole
SUMMARY:
Finite stress and strain analyses of the heart provide insight into the biomechanics of myocardial function and dysfunction. Herein, we describe progress toward dynamic patient-specific models of the left ventricle using an immersed boundary (IB) method with a finite element (FE) structural mechanics model. We use a structure-based hyperelastic strain-energy function to describe the passive mechanics of the ventricular myocardium, a realistic anatomical geometry reconstructed from clinical magnetic resonance images of a healthy human heart, and a rule-based fiber architecture. Numerical predictions of this IB/FE model are compared with results obtained by a commercial FE solver. We demonstrate that the IB/FE model yields results that are in good agreement with those of the conventional FE model under diastolic loading conditions, and the predictions of the LV model using either numerical method are shown to be consistent with previous computational and experimental data. These results are among the first to analyze the stress and strain predictions of IB models of ventricular mechanics, and they serve both to verify the IB/FE simulation framework and to validate the IB/FE model. Moreover, this work represents an important step toward using such models for fully dynamic fluid–structure interaction simulations of the heart
Arbitrary Lagrangian-Eulerian form of flowfield dependent variation (ALE-FDV) method for moving boundary problems
Flowfield Dependent Variation (FDV) method is a mixed explicit-implicit numerical
scheme that was originally developed to solve complex flow problems through the use
of so-called implicitness parameters. These parameters determine the implicitness of
FDV method by evaluating local gradients of physical flow parameters, hence vary
across the computational domain. The method has been used successfully in solving
wide range of flow problems. However it has only been applied to problems where the
objects or obstacles are static relative to the flow. Since FDV method has been proved
to be able to solve many complex flow problems, there is a need to extend FDV
method into the application of moving boundary problems where an object
experiences motion and deformation in the flow. With the main objective to develop a
robust numerical scheme that is applicable for wide range of flow problems involving
moving boundaries, in this study, FDV method was combined with a body
interpolation technique called Arbitrary Lagrangian-Eulerian (ALE) method. The
ALE method is a technique that combines Lagrangian and Eulerian descriptions of a
continuum in one numerical scheme, which then enables a computational mesh to
follow the moving structures in an arbitrary movement while the fluid is still seen in a
Eulerian manner. The new scheme, which is named as ALE-FDV method, is
formulated using finite volume method in order to give flexibility in dealing with
complicated geometries and freedom of choice of either structured or unstructured
mesh. The method is found to be conditionally stable because its stability is dependent
on the FDV parameters. The formulation yields a sparse matrix that can be solved by
using any iterative algorithm. Several benchmark stationary and moving body
problems in one, two and three-dimensional inviscid and viscous flows have been
selected to validate the method. Good agreement with available experimental and
numerical results from the published literature has been obtained. This shows that the
ALE-FDV has great potential for solving a wide range of complex flow problems
involving moving bodies
Pore-scale modeling of fluid-particles interaction and emerging poromechanical effects
A micro-hydromechanical model for granular materials is presented. It
combines the discrete element method (DEM) for the modeling of the solid phase
and a pore-scale finite volume (PFV) formulation for the flow of an
incompressible pore fluid. The coupling equations are derived and contrasted
against the equations of conventional poroelasticity. An analogy is found
between the DEM-PFV coupling and Biot's theory in the limit case of
incompressible phases. The simulation of an oedometer test validates the
coupling scheme and demonstrates the ability of the model to capture strong
poromechanical effects. A detailed analysis of microscale strain and stress
confirms the analogy with poroelasticity. An immersed deposition problem is
finally simulated and shows the potential of the method to handle phase
transitions.Comment: accepted in Int. Journal for Numerical and Analytical Methods in
Geomechanic
Hybrid finite difference/finite element immersed boundary method
The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian
description of the structural deformations, stresses, and forces along with an Eulerian description of the
momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary
methods described immersed elastic structures using systems of flexible fibers, and even now, most
immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This
work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian
variables that facilitates independent spatial discretizations for the structure and background grid. This
approach employs a finite element discretization of the structure while retaining a finite difference scheme
for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively
contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases
in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors
that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes.
The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse
structural meshes with the immersed boundary method. This work also contrasts two different weak forms
of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations
facilitated by our coupling approach
Modelling mitral valvular dynamics–current trend and future directions
Dysfunction of mitral valve causes morbidity and premature mortality and remains a leading medical problem worldwide. Computational modelling aims to understand the biomechanics of human mitral valve and could lead to the development of new treatment, prevention and diagnosis of mitral valve diseases. Compared with the aortic valve, the mitral valve has been much less studied owing to its highly complex structure and strong interaction with the blood flow and the ventricles. However, the interest in mitral valve modelling is growing, and the sophistication level is increasing with the advanced development of computational technology and imaging tools. This review summarises the state-of-the-art modelling of the mitral valve, including static and dynamics models, models with fluid-structure interaction, and models with the left ventricle interaction. Challenges and future directions are also discussed
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