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Multi-scale concrete model with rate-dependent internal friction

In this paper, a micromorphic, non-linear 3D model aiming to describe internal friction phenomena in concrete is considered. A reduced two-degrees-of-freedom model is employed for the sake of easy handling to explain dissipative loops which have been observed in some concrete specimens tested under cyclic uniaxial compression loading with different frequencies and having various amplitudes but never inducing large strains. As (linear or non-linear) viscoelastic models do not seem suitable to describe neither qualitatively nor quantitatively the measured dissipation loops, we propose to introduce a multi-scale micromechanism of Coulomb-type internal dissipation associated to the relative motion of the faces of the microcracks present in the material and to the asperities inside the microcracks. We finally present numerical simulations showing that the proposed model is suitable to describe some of the available experimental evidence.