A 3D higher-order FSI-Approach Applied to M iBi h i Pbl ...dutw1479.wbmt.tudelft.nl/~wim/academy/presentations/b4/pres_mayer.pdf · ALE Hybrid ALE-XFEM/LM XFEM/LM W A Wall P Gamnitzer

Academy Colloquium on Immersed Boundary Methods:Current Status and Future Research Directions,

Amsterdam, Netherlands, 15.6.09 -17.6.09

A 3D higher-order FSI-Approach Applied to

M i Bi h i P bl i th P d tiMesoscopic Biophysics Problems in the Production

Process of Novel Spider Silk Materials -

Towards a Mesoscopic Biophysical FSI-Method

Ursula M. Mayer, A. Gerstenberger, W.A. Wall

Institute for Computational Mechanics, TU München, Germanyp , , y

Motivation

Towards a mesoscopic XFEM fluid-structure interaction-method

applicable to a variety of biophysical problems:

Production process of novel spider silkProduction process of novel spider silk

materials (e.g. drug delivery systems,

implant coating, silk fibers)implant coating, silk fibers)

Red blood cell suspensions, blood cell

in a contracting vessel g

Efficient swimming techniques of

(deformable) microswimmers and www.lifeforcehospitals.com ( )

microrobots

... http://robotics.technion.ac.il/Projects/microrobot.jpg

Towards a Mesoscopic Biophysical XFEM Fluid-Structure Interaction Method Ursula M. Mayer, W. A. Wall – Institute for Computational Mechanics, TU München, Germany

http://www.monash.edu.au/news/newsline/story/1038microrobot.jpg

Requirements of a (Mesoscopic) FSI-Method

Structure :Arbitrary movement, large deformation, large strain, arbitrary material modelMultiple bulky and thin walled structures (with consideration of the volume)Multiple bulky and thin-walled structures (with consideration of the volume)

Fluid :I ibl i fl (i i i bl )Incompressible, viscous flow (in many engineering problems)Wide range of applicable Reynolds number laminar & turbulent flows

I t fInterface :Physics of the interfaceConservation / dissipation propertiesProper approximation of the fluid boundary layerNo loss of accuracy due to coupling algorithm

Additional mesoscopic physical effects:Macromolecular interaction and contactBrownian motion http://robotics.technion.ac.il/Projects/

microrobot.jpg


http://www.monash.edu.au/news/newsline/story/1038microrobot.jpg

Overview

3D higher-order XFEM/LM-based fluid-structure interaction methodg

for arbitrarily moving and deforming structures

Interface localization and enrichment

Embedded Dirichlet conditions

Hybrid ALE – XFEM/LM approach

FE formulation of macromolecular interaction

FE contact formulation

(Brownian Motion)

Example applications

Conclusions and outlook


Fluid-Structure Interaction Problem Formulation

Solid Continuum

Fluid Continuum

Solid Continuum

Fluid-Structure Interface

Fluid Momentum Balance

BoundaryDomain

Fluid Momentum Balance

Solid Momentum Balance

Fluid Continuity Equation

Fluid-Solid-Interface (e.g. no slip)

+ constitutive equations (Newtonian / Non-Newtonian; nonlinear viscoelastic)+ constitutive equations (Newtonian / Non-Newtonian; nonlinear viscoelastic)

→ purely FE-based (stabilized & mixed/hybrid)i h h d (BACI)


→ in-house research code (BACI)

Fluid-Structure Interaction from XFEM Perspective

Explicit fluid surface description : Embedded discontinuity :

Express the discontinuity in FE formulation (XFEM)Interface localization and removal of fictitious fluid domainEnforce velocity/force conditions at the interface


XFEM - FSI EXtended Finite Element Method

Extended Finite Element Method:

Applied to model the discontinuitiespp ed o ode e d sco u esEnrichment of Finite Element space

Enrichment with Heaviside function :


XFEM - FSI Interface Handling

Interface handling :

Localization of curved interfaces

in a possibly curved fixed-grid mesh

Subtetrahedralization of the

intersected fluid element

ffor exact numerical integration

Octtree-based determination of

th fl id d ithe fluid domain

Thin and thick structures

All element types: HEX8, HEX27, TET4, TET10, …

U.M. Mayer, A. Gerstenberger, W.A.Wall; Interface handling for three-dimensional higher-order XFEM-computations in fluid-structure interaction; IJNME; 2009


higher order XFEM computations in fluid structure interaction; IJNME; 2009

XFEM - FSI Interface Handling and Enrichment

Standard DOFLeft Surface DOF

Right Surface DOF

Pressure Solution


Right Surface DOF

XFEM - FSI Embedded Dirichlet Conditions

3-field mixed/hybrid fluid formulation :

Velocity pressure stress :Velocity, pressure, stress :

Corresponding test functions:

Semi-discrete weak form with interface conditions: A. Gerstenberger, W.A. Wall; An embedded Dirichlet formulation for 3D continua; IJNME, 2009; submitted

Element stiffness matrix:Non-intersected elements:

decoupled element stressesp

Intersected Elements:condensation of element stresses


stresses

XFEM-FSI Hybrid ALE-XFEM/LM approaches

Moving mesh approach Fixed grid approaches

XFEM/LMHybrid ALE-XFEM/LMALE

W A Wall P Gamnitzer A Gerstenberger Fluid Structure interaction approaches on fixed grids based on two different domain decomposition ideasW.A. Wall, P. Gamnitzer, A. Gerstenberger, Fluid-Structure interaction approaches on fixed grids based on two different domain decomposition ideas, International Journal of Computational Fluid Dynamics, in press, 2008

A. Gerstenberger, W.A. Wall, Efficient treatment of moving interfaces on fixed grids for surface coupled problems, International Journal for Numerical Methods in Fluids, in press, 2008


XFEM-FSI Hybrid ALE-XFEM/LM approach

Starting point:3-field setup for FSI

Basic Idea: Add ani t di t ( i ) intermediate (moving) ALE mesh that fits the structural surface

XFEM Fluid-Fluid Coupling


XFEM - FSI Examples

Elastic ring in shear flow : towards red blood cell simulation

Cylinder in flow with Re = 49:


XFEM - FSI Intermediate Summary

3D higher-order XFEM/LM-based FSI-approach :

No limitation on complexity of structure (shape material deformation )No limitation on complexity of structure (shape, material, deformation,…)

Sharply defined interface with embedded Dirichlet conditionsLocal condensation of Lagrange multipliersIterative parallel solution with AMG preconditioner for fluid and structureIterative, parallel solution with AMG preconditioner for fluid and structure

Influence of “fictitious” fluid domain eliminatedNo incompressibility constraint on structureNo artificial viscosityNo artificial viscosity

Fluid solved on fixed Eulerian gridNo mesh distortion + update algorithmAny fluid element type possible (hex tet wedge )Any fluid element type possible (hex, tet, wedge,…)

Simple extension to hybrid (fixed/ALE) meshes

Based on established FSI coupling schemesBased on established FSI coupling schemes

Implementation in parallel


Macromolecular Interaction Potentials

Finite element formulation for macromolecular interaction potentials :

T t t f lti b d l l i t ti ( i “ t t)Treatment of multi-body macromolecular interaction („mesoscopic“ contact)

3D dynamic finite element formulation (integrated in XFEM FSI-method)

Arbitrary shape of mesoscopic structures under finite deformationsArbitrary shape of mesoscopic structures under finite deformations

Applicable for any additive macromolecular interaction potentials


Sauer R., Li S.; A contact mechanics model for quasi-continua; IJNME; 2007

Macromolecular Interaction Potentials

Total energy :

Potential energy term due to a surface interaction potential :

Potential energy term due to a volume interaction potential :Potential energy term due to a volume interaction potential :

Variational formulation

Volume and surface potential formulation allows to study both effects separatelyVolume and surface potential formulation allows to study both effects separately

Avoids LBB-conditions and fulfills the contact patch test

Excellent agreement with analytical contact methods (JKR, Maugis-Dugdale)


Excellent agreement with analytical contact methods (JKR, Maugis Dugdale)

Macromolecular Interaction Potentials Example

Half sphere is pushed towards a block:

Long-range attraction and short-range

repulsion modelled by a Lennard-Jones

potential :

R lti fResulting force :


Finite Element Mortar Contact Formulation

3D finite element Mortar contact formulation

for finite deformationsfor finite deformations

No limitations for geometrical and material nonlinearities

Gap function :Gap function :

KKT conditions and frictionless sliding :

Lagrange multipliers (dual trace space) :Lagrange multipliers (dual trace space) :

Weak non-penetration condition :

Contact virtual work :Contact virtual work :

Dual shape functions for Lagrange Multipliers => static condensation

Solution algorithm based on a primal-dual active set strategy for

contact non-linearity, equivalent to a semi-smooth Newton methodA P M W G W A W ll A fi it d f ti t


A. Popp, M.W. Gee, W.A.Wall; A finite deformation mortarcontact formulation using a primal-dual active set strategy; IJNME; 2009

Contact and Interaction Example

Half sphere is pushed towards a block:

Long-range attraction is described by a Lennard-Jones potential

Macroscopic contact is performed instead of short-range repulsion

or excluded volume potentials


Numerical Examples Contact Elastic Brick with Wall

Subwater contact of an elastic brick with a rigid wall :


Numerical Examples Suspension of Microspheres

Suspension of spider silk nano/microspheres in shear flow including

macromolecular attraction and repulsion:

Stability of suspension necessary for the production of

drug delivery systems, coating of thin films


Conclusions and Outlook

Current status :

XFEM-based fluid-structure interaction approach

for arbitrarily moving and deforming structures

no restrictions to structural formulation

highly accurate resolution of flow patterns around a sharp interface

Additive macromolecular interaction potential formulation

Subwater contact formulation

O i kOngoing work :

Integration of Brownian motion

Application to various biophysics problems and experimental validationApplication to various biophysics problems and experimental validation

(silk microsphere suspensions, blood cell in contracting vessel, microswimmers)


Thank You Very Much For Your Attention !


Parallelization for Distributed Memory

Parallelization approach :Fluid and structure mesh uniformly distributed

S f h f d d llSurface mesh of structure redundant on all processors

Parallel octtree-based search for the determination of the fluid domain,

i t ti f l t d t ti f l tinteraction surface elements and contacting surface elements


Documents

A 3D higher-order FSI-Approach Applied to M iBi h i Pbl ...dutw1479.wbmt.tudelft.nl/~wim/academy/presentations/b4/pres_mayer.pdf · ALE Hybrid ALE-XFEM/LM XFEM/LM W A Wall P Gamnitzer