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A novel multi-fiber beam finite element formulation based on the Timoshenko model is proposed in this paper to simulate failure of reinforced concrete structural elements subjected to static monotonic loadings. The beam section can have an arbitrary shape and each fiber has a local constitutive law representing a specific material. The embedded discontinuity concept is adopted to enrich the displacement field of the fibers in order to describe the opening of cracks and the development of plastic hinges. The material behavior at the discontinuity is characterized by a cohesive law linking the axial stress and the displacement jump by a linear relation, which allows capturing the released fracture energy. The variational formulation is presented in the context of the incompatible modes method. Moreover, the additional modes are statically condensed at the element level. The corresponding computational procedure is detailed in the paper. Several numerical applications and general remarks are finally provided to illustrate the performance of the proposed element.

A novel multi-fiber Timoshenko beam finite element formulation with embedded discontinuities to describe reinforced concrete failure under static loadings