Micro/macro analysis of a composite Casa Day 22/11/06.
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Transcript of Micro/macro analysis of a composite Casa Day 22/11/06.
Micro/macro analysis of a compositeCasa Day 22/11/06
Aloha Airlines Flight 243
Motivation
Honolulu International Airport, Hawaii
At 24000 feet… loud clap
No visual exterior inspection (nor required)
Flight attendant swept out of the cabin
1 dead, 65 injured
$5 million damage
Peel Test
45º
Force Displacement (constant speed)
Nickel layer
Substrate
Peel-Test Support
Composites
Matrix
Inclusions
Elasticity problem for a composite material
Matrix
InclusionsMatrix Inclusions
Material Interface
Modelling
Matrix
InclusionsMatrix Inclusions
Material Interface
Homogenisation
Homogenisation
fu Α fu Α
0
uu
Homogenisation
Homogenised equations
Boundary Conditions
Macro results
Micro/Macro
Domain decomposition
Dirichlet – Neumann scheme
Finite element approximation
Finite element approximation
Schur complement system
• symmetric
• positive definite
• ill conditioned
Algorithm
Dirichlet problem
Neumann Problem
Relaxation step
Algorithm
is a preconditioner for
Theorem:
This process converges if
where is the maximum eigenvalue of .
Heterogeneous domain decomposition
Heterogeneous domain decomposition
Interface conditions
Overview
homoge-
nisation
D-N
Interface conditions?
Example
Reference solution
Macro domain
Meso domain
Example
Macro domain
Meso domain
Absolute error for
the horizontal displacementu1-uref 0.6012
u2-uref 0.6701
u3-uref 0.1392
u4-uref 0.0305
u5-uref 0.0176
Future Work
- Interface conditions discussion
- Crack propagation