A micromechanical approach to the strength criterion of Drucker‐Prager materials reinforced by rigid inclusions

Abstract At the microscopic scale, concrete can be considered as a frictional matrix (cement paste) surrounding rigid inclusions (aggregate or sand inclusions). The present paper proposes a theoretical approach to the strength criterion of such a composite material. It is shown that the macroscopic stress states on the yield surface can be obtained from the solution to non‐linear viscous problems defined on a representative volume element. The practical determination of the yield surface implements a non‐linear homogenization scheme based on the modified secant method. The role of the interface between the matrix and the inclusions is also investigated. Two extreme modellings are considered: perfect bonding and non‐frictional interfaces. In both cases, the method yields a macroscopic strength criterion of the Drucker–Prager type. The macroscopic friction angle is a function of that of the matrix and of the volume fraction of the inclusions. In the case of perfect bonding, the inclusions have a reinforcing effect. In contrast, this may not be true for a non‐frictional interface. Copyright © 2004 John Wiley & Sons, Ltd.