Damage mechanics of cement concrete modeled as a four-phase composite

In this contribution, a four-phase micromechanical model is proposed in order to simulate the non-linear instantaneous pre-peak response of cement concrete subjected to monotonically increasing loads. The non-linear behavior is attributed to the creation of cracks in the cement paste of the concrete; the effect of the cracks is taken into account by introducing equivalent voids in the cement paste. The concrete material is modeled as a four-phase composite with three different types of heterogeneities: gravel, sand and voids, embedded in a cement pure paste matrix. The composite homogenization is realized with the Mori-Tanaka method and the overall non-linear response of the concrete is determined by a secant approach. The proposed micromechanical model is able to capture peculiar aspects of the concrete stress-strain curve of uniaxial compression: in most concrete materials, a higher compressive strength is associated with a higher initial tangent Young's modulus. Further analogies between the theoretical curves of the proposed method and the experimental curves are shown.