Tensile stiffness and strength of fiber-reinforced concrete

The nonlinear behavior of concrete reinforced by short fibers subjected to tensile load is investigated. This material is modeled as a composite with brittle matrix and elastic fibers. The constitutive law of the matrix is assumed elastoplastic with no tensile strength and finite compression yield. A rigid plastic bonding is considered between matrix and fibers. Then, the overall behavior of the material is studied using the homogenization procedure and the dual extreme principles in terms of displacements and stresses. By applying these principles, upper and lower bounds on the overall stiffness of the material and on the limit tensile strength are obtained. Finally, a two-dimensional model and a three-dimensional model of concrete matrix reinforced with fibers aligned in the tensile direction are analyzed. For both of them, simple expressions for the bounds on the overall stiffness and strength of the material are derived by a direct investigation of the micro displacement and stress fields.