A micro-structural model for dissipation phenomena in the concrete

Summary: In the present paper, a constitutive model for the description of the dissipation in the concrete is provided. The theoretical description is based on a micromorphic model in which the microstructure is constituted by a kinematical scalar descriptor ϕ whose time derivative is linked to a dissipative potential. The scalar ϕ can be interpreted as the relative displacement between two opposite faces of the microcracks, and our physical interpretation of dissipation is indeed linked to the friction force (in a mixed Coulomb-type and viscous-type behavior) between them. To evaluate the effects of bending on the dissipation, the 3D model is then reduced by means of standard Saint-Venant's procedure in case of combined compression and bending over a cylindrical domain. A qualitative analysis of the reduced ODEs model is then provided. Numerical results showing comparison between different types of dissipative force and between pure compression and combined compression and bending are included in a dedicated section. Finally, the proposed model and our physical interpretation of the dissipation are supported by some experimental data concerning standard concrete and a concrete enriched by adding to the mixture a filler constituted by micro-particles capable of improving the dissipative behavior of the material. Measured data show very good fit with our theoretical previsions and provide a sufficiently sound basis for further deepening of the theoretical description of the considered phenomena.