Towards a Mesoscopic Biophysical FSI

Transcription

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
Mesoscopic
i Bi
Biophysics
h i P
Problems
bl
iin th
the P
Production
d ti
Process of Novel Spider Silk Materials Towards a Mesoscopic Biophysical FSI-Method
Ursula M. Mayer, A. Gerstenberger, W.A. Wall
Institute for Computational
p
Mechanics,, TU München,, Germany
y
Motivation
Towards a mesoscopic XFEM fluid-structure interaction-method
applicable to a variety of biophysical problems:

Production process of novel spider silk
materials (e.g. drug delivery systems,
implant coating, silk fibers)

Red blood cell suspensions, blood cell
in a contracting
g vessel

Efficient swimming techniques of
((deformable)) microswimmers and
www.lifeforcehospitals.com
microrobots

...
Towards a Mesoscopic Biophysical XFEM Fluid-Structure Interaction Method
Ursula M. Mayer, W. A. Wall – Institute for Computational Mechanics, TU München, Germany
http://robotics.technion.ac.il/Projects/
microrobot.jpg
http://www.monash.edu.au/news/newsline/story/1038
Requirements of a (Mesoscopic) FSI-Method
Structure :
Arbitrary movement, large deformation, large strain, arbitrary material model
Multiple bulky and thin-walled
thin walled structures (with consideration of the volume)
Fluid :
Incompressible,
I
ibl viscous
i
flflow (i
(in many engineering
i
i problems)
bl
)
Wide range of applicable Reynolds number Æ laminar & turbulent flows
IInterface
t f
:
Physics of the interface
Conservation / dissipation properties
Proper approximation of the fluid boundary layer
No loss of accuracy due to coupling algorithm
Additional mesoscopic physical effects:
Macromolecular interaction and contact
Brownian motion
http://robotics.technion.ac.il/Projects/
microrobot.jpg
http://www.monash.edu.au/news/newsline/story/1038
Overview

3D higher-order
g
XFEM/LM-based fluid-structure interaction method
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
Fluid Continuum
Solid Continuum
Fluid-Structure Interface
Domain
Boundary
Fluid Momentum Balance
Fluid Continuity Equation
Solid Momentum Balance
Fluid-Solid-Interface (e.g. no slip)
+ constitutive equations (Newtonian / Non-Newtonian; nonlinear viscoelastic)
→ purely FE-based (stabilized & mixed/hybrid)
→ in-house
i h
research
h code
d (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 domain
Enforce velocity/force conditions at the interface
XFEM - FSI
EXtended Finite Element Method
Extended Finite Element Method:
Applied
pp ed to
o model
ode the
ed
discontinuities
sco
u es
Enrichment of Finite Element space
Enrichment with Heaviside function :
XFEM - FSI
Interface handling :
Localization of curved interfaces
in a possibly curved fixed-grid mesh
Subtetrahedralization of the
intersected fluid element
for exact numerical integration
Octtree-based determination of
th fluid
the
fl id d
domain
i
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
higher
order XFEM
XFEM-computations
computations in fluid
fluid-structure
structure interaction; IJNME; 2009
Interface Handling
XFEM - FSI
Interface Handling and Enrichment
Pressure Solution
Standard DOF
Left Surface DOF
Right Surface DOF
XFEM - FSI
Embedded Dirichlet Conditions
3-field mixed/hybrid fluid formulation :
Velocity,
Velocity pressure
pressure, stress :
Corresponding test functions:
Semi-discrete weak form with interface conditions:
Element stiffness matrix:
A. Gerstenberger, W.A. Wall; An embedded Dirichlet
formulation for 3D continua; IJNME, 2009; submitted
Non-intersected elements:
¾ decoupled
p
element stresses
Intersected Elements:
¾ condensation of element
stresses
XFEM-FSI
Hybrid ALE-XFEM/LM approaches
Moving mesh approach
ALE
Fixed grid approaches
Hybrid ALE-XFEM/LM
XFEM/LM
W A Wall,
W.A.
Wall P
P. Gamnitzer
Gamnitzer, A
A. Gerstenberger
Gerstenberger, Fluid
Fluid-Structure
Structure interaction approaches on fixed grids based on two different domain decomposition ideas,
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 an
i t
intermediate
di t ((moving)
i )
ALE mesh that
fits the structural surface
XFEM Fluid-Fluid Coupling
XFEM - FSI
Elastic ring in shear flow : towards red blood cell simulation
Cylinder in flow with Re = 49:
Examples
XFEM - FSI
Intermediate Summary
3D higher-order XFEM/LM-based FSI-approach :
No limitation on complexity of structure (shape
(shape, material
material, deformation
deformation,…))
Sharply defined interface with embedded Dirichlet conditions
Local condensation of Lagrange multipliers
Iterative,
Iterative parallel solution with AMG preconditioner for fluid and structure
Influence of “fictitious” fluid domain eliminated
No incompressibility constraint on structure
No artificial viscosity
Fluid solved on fixed Eulerian grid
No mesh distortion + update algorithm
Any fluid element type possible (hex
(hex, tet
tet, wedge
wedge,…))
Simple extension to hybrid (fixed/ALE) meshes
Based on established FSI coupling schemes
Implementation in parallel
Macromolecular Interaction Potentials
Finite element formulation for macromolecular interaction potentials :
Treatment
T t
t off multi-body
lti b d macromolecular
l
l iinteraction
t
ti ((„mesoscopic“
i “ contact)
t t)
3D dynamic finite element formulation (integrated in XFEM FSI-method)
Arbitrary 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
Total energy :
Potential energy term due to a surface interaction potential :
Potential energy term due to a volume interaction potential :
Variational formulation
Volume 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)
Maugis Dugdale)
Half sphere is pushed towards a block:
Long-range attraction and short-range
repulsion modelled by a Lennard-Jones
potential :
Resulting
R
lti fforce :
Example
Finite Element Mortar Contact Formulation

3D finite element Mortar contact formulation
for finite deformations

No limitations for geometrical and material nonlinearities

Gap function :

KKT conditions and frictionless sliding :

Lagrange multipliers (dual trace space) :

Weak non-penetration condition :

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 method
A Popp,
A.
P
M.W.
M W Gee,
G
W.A.Wall;
W A W ll A finite
fi it deformation
d f
ti mortar
t
contact 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
Ongoing
i work
k:

Integration of Brownian motion

Application 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
Surface
S f
mesh
h off structure redundant
d d
on allll processors
Parallel octtree-based search for the determination of the fluid domain,
i t
interaction
ti surface
f
elements
l
t and
d contacting
t ti surface
f
elements
l
t