A dissipation model for concrete based on an enhanced Timoshenko beam

A novel Timoshenko beam model enriched to account for dissipation in cement-based materials was presented in this paper. The model introduced a new variable representing the relative sliding inside microcracks within the material. In the paper, the microcrack density was not supposed to increase, assuming a small deformation regime that implied no damage growth. The model utilized an expanded version of the principle of virtual work whose contributions came from external forces, internal elastic forces, and dissipation due to the microcrack's microstructure. The elastic energy included terms related to microcrack sliding and micro-macro interactions, accounting for nonlinearity in the material behavior. Numerical simulations, conducted using the finite element method, evaluated the mechanical properties of cement-based materials under three-point flexural tests and compression tests. These tests enabled the assessment of the material dissipative behavior under cyclic loading. Results showed dissipated energy cycles and mechanical responses influenced by the microcrack mechanics. Additionally, a parametric study, varying the friction force amplitude, revealed its impact on dissipated energy. The study highlighted a non-monotonic relationship between friction force amplitude and dissipated energy, with an optimal value maximizing dissipation. Overall, the model provided insights into the mechanics of cement-based materials, particularly regarding dissipation, which was essential for understanding their behavior in structural applications.