Thermo-chemical modelling of the formation of a composite material

Abstract

We consider a composite material composed of carbon or glass fibres included in a resin which becomes solid when it is heated up (the reaction of reticulation).

A mathematical model of the cure process is given by a kinetic equation describing the evolution of the reaction of reticulation coupled with the heat equation. The geometry of the composite material is periodic, with a small period ϵ >0, thus we get a coupled system of nonlinear partial differential equations.

First we prove the existence and uniqueness of a solution by using a fixed point theorem and we obtain a priori estimates. Then we derive the homogenized problem which describes the macroscopic behaviour of the material. We prove the convergence of the solution of the problem to the solution of the homogenized problem when ϵ tends to zero as well as the estimates for the difference of the exact and the approximate solutions.

Keywords:

• Homogenization
• Composite material
• Estimates
• Mathematics Subject Classification (1991): 35K55
• 35B27
• 74A40
• 80A30

Acknowledgement

This work was supported by the Region Rhône-Alpes grants, project non. 02 020611 01 and 02 02061301.