An enhanced beam model incorporating a hysteresis-based solid friction damping mechanism for cementitious materials

In this work, we investigate a dynamic internal dissipation mechanism in the context of cement-based materials by introducing a 1D-enhanced micromorphic beam model with a dynamic internal friction term. Here, we consider an inherent feature in concrete-like materials arising from the multi-scale structure, namely, microcracks. Thus, we assume that the internal dissipation of the energy depends on the overall relative sliding displacement of the opposite faces in the microcracks under the effects of an applied cyclic load whenever no significant phenomena related to damage occur at the macroscopic level. The dynamic friction term is based on a well-known model for dry friction in solids due to P. R. Dahl, where the friction force depends only on the sliding displacement and evolves in time, reproducing an elastoplastic behavior. The model proposed in this paper takes into account a mechanical energy interchange between both bending and shear distortion in the beam with the sliding occurring at the microcracks, a storage of mechanical energy because of the asperities inside the faces of the microcracks, and the dissipation of the energy that follows from the interaction between the bending and the microcracks. Numerical simulations of the kinematic descriptors and the dissipative cycles are also provided by using the Finite Element Method and the commercial software COMSOL Multiphysics^®.