Micromacro analysis of a composite Casa Day 221106

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

Motivation Aloha Airlines Flight 243 Honolulu International Airport, Hawaii No visual exterior inspection (nor required) At 24000 feet… loud clap Flight attendant swept out of the cabin 1 dead, 65 injured $5 million damage

Peel Test Force Displacement (constant speed) Nickel layer 45º Substrate Peel-Test Support

Composites Inclusions Matrix

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

Modelling Inclusions Matrix Material Interface Matrix Inclusions

Homogenisation

Homogenisation

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 homogenisation D-N Interface conditions?

Example Macro domain Reference solution Meso domain

Example Absolute error for the horizontal displacement u 1 -uref 0. 6012 u 2 -uref 0. 6701 u 3 -uref 0. 1392 u 4 -uref 0. 0305 u 5 -uref 0. 0176 Macro domain Meso domain

Future Work - Interface conditions discussion - Crack propagation