A micromechanical approach to the strength criterion of composite materials

At the microscopic scale, concrete can be considered as a frictional matrix (cement paste) surrounding rigid inclusions (aggregate or sand inclusions). A theoretical approach to the strength criterion of such a composite material has been recently proposed in (Lemarchand et al. 2002). This approach exploits a nonlinear homogenization scheme based on the definition of an equivalent nonlinear behavior for the matrix. Whereas it provides good results as regards the strength criterion, it is not completely satisfactory as regards the local flow rule of the Drucker-Prager frictional type matrix. Our contribution aims at improving this approach in order to ensure the consistency of the local strains with the flow rule of a Drucker-Prager material and, in particular, the dilatancy which characterizes such a flow rule. For this purpose, a nonlinear equivalent viscoelastic behavior is introduced and a nonlinear homogenization scheme is implemented so as to determine the macroscopic strength criterion. Assuming perfect adherence between matrix and inclusions, the method yields a macroscopic strength criterion of Drucker-Prager type with increased friction angle and cohesion.