1. Micro/macro analysis of a composite Casa Day 22/11/06

2. 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

3. Peel Test 45º ForceDisplacement (constant speed) Nickel layer Substrate Peel-Test Support

4. Composites Matrix Inclusions

5. Elasticity problem for a composite material Matrix Inclusions Matrix Inclusions Material Interface

6. Modelling Matrix Inclusions MatrixInclusions Material Interface

7. Homogenisation

10. Homogenised equations Boundary Conditions

11. Macro results

12. Micro/Macro

13. Domain decomposition

14. Dirichlet – Neumann scheme

15. Finite element approximation

16. Schur complement system symmetric positive definite ill conditioned

17. Algorithm Dirichlet problem Neumann Problem Relaxation step

18. Algorithm is a preconditioner for Theorem: This process converges if where is the maximum eigenvalue of.

19. Heterogeneous domain decomposition

20. Interface conditions

21. Overview homoge- nisation D-N Interface conditions?

22. Example Reference solution Macro domain Meso domain

23. Example Macro domain Meso domain Absolute error for the horizontal displacement u1-uref0.6012 u2-uref0.6701 u3-uref0.1392 u4-uref 0.0305 u5-uref0.0176

24. Future Work - Interface conditions discussion - Crack propagation