Homogenization of a model of cure process for composites Original Research Article

We consider a composite material composed of carbon or glass fibres included in a resin which becomes solid when it is heated (reaction of reticulation). The mathematical modelisation 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 (Pε). First, we prove the existence and uniqueness of a solution for problem (Pε) by using a fixed point argument and we obtain a priori estimates. Then, we derive the homogenized problem (Ph) which describes the macroscopic behaviour of the material. We establish that problem (Ph) admits an unique solution and we prove the convergence of the solution of problem (Pε) to the solution of (Ph), as ε tends to zero, by using the energy method.