Abstract
We consider a mathematical model of a high contrast two phase composite material with inclusions (fibres) close to touching in two space dimensions. The inclusions form a periodic array and have an optimal shape which is a curvilinear square with rounded-off angles ('nearly square' shape) described by a flattening parameter m. We derive an asymptotic formula for the effective conductivity Âδ of the composite when the interparticle distance δ goes to zero. This formula captures the dependence of Âδ on the parameter m. We provide a rigorous justification for this asymptotic formula by a variational duality approach.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 83-106 |
| Number of pages | 24 |
| Journal | Quarterly Journal of Mechanics and Applied Mathematics |
| Volume | 58 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 2005 |
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics