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This paper deals with the homogenization of a composite material built with an elastic matrix periodically reinforced by elastic notched fibres. We assume that the Lame constants in the fibres are highly contrasted with respect to those of the matrix. We derive a class of energy functionals involving additional degrees of freedom implying nonlocal description of localized geometrical discontinuities due to the fibre-notches, nonlocal effects associated with thin boundary layer phenomena, and nonlocal terms including macroscopic fields of extension or flexion.

A model of forest fire propagation, including drying, pyrolysis, heat convection, heat conduction, and radiative transfer, is presented. This model has been obtained by asymptotic expansion and has the generic form of a system of reaction-diffusion equations. One of the aims of the present work is to link this type of reaction diffusion models to models that rely on the concept of rate of spread. The rate of spread is defined as the solution to a nonlinear eigenvalue problem. The solution to this eigenvalue problem is obtained as a perturbation expansion in the thermal conductivity of the solid phase. The calculated rates of spread for two flame models compare favorably to experimental values.