A simplified lumped damage model for reinforced concrete beams under impact loads

This paper presents a simple lumped damage model to analyse reinforced concrete beams under impact loads. The proposed model is based on the thermodynamics of irreversible processes. In this framework, key concepts of fracture and damage mechanics are applied on plastic hinges. Since the inelastic phenomena are modelled by two internal variables, named damage and plastic rotation, the plastic hinges are now called inelastic hinges. Therefore, the proposed finite element is an assemblage of an elastic beam with two inelastic hinges at its edges. Experimental results are used to propose the evolution laws of the internal variables. The proposed model is applied to other experiments and the obtained results show its accuracy. Finally, if an extensive experimental campaign could be carried out, a practical engineering criterion can be elaborated in terms of the damage variable (concrete cracking), which may be useful as a decision-making criteria for retrofit worthiness.