Failure analysis of reinforced concrete frames by beam finite element that combines damage, plasticity and embedded discontinuity

We present a multi-layer beam finite element formulation for failure analysis of planar reinforced concrete beams and frames, which is based on the Timoshenko beam model. Material behavior of the concrete and the steel layer is described by an elasto-damage and an elasto-plastic material model, respectively. In order to be able to describe the fracture energy, a layer-wise application of the embedded discontinuity concept is adopted. In particular, a jump in the layer-axial-displacement is embedded into the standard beam kinematics when the layer stress state fulfills the material failure criterion and the layer functions in the softening phase. This allows applying a softening-damage and a softening-plasticity traction-separation cohesive law in concrete and steel layers, respectively. The computer code implementation is described in detail. A set of numerical examples is presented in order to illustrate an ability of the formulation to model and compute failure response of reinforced concrete beams and frames under monotonic static loading. Finally, the formulation is critically assessed.