A semi-analytic modeling of self-healing concrete beam in the framework of continuum damage-healing mechanic

Self-healing materials are a class of smart materials that have a structurally capability to recover damage caused by environmental stimuli over time. In this paper, a semi-analytic modeling is presented for predicting the mechanical behavior of a self-healing concrete beam. Along this purpose, a continuum damage-healing constitutive model is used to investigate the effect of damage and healing in stress field of concrete pressure vessels. This model use stress spectral decomposition method to model the different behavior of concrete in tensile and compressive loadings. Also, Clausius-Duhem inequality and the thermodynamics of irreversible processes are considered and conjugate forces of damage and healing are derived for a concrete beam. Gibbs potential energy is divided into three parts; elastic energy, damage energy and healing energy. In this regard, the model introduce damage and healing surfaces to detect damage and healing behaviors from elastic one. Then, two linear isotropic hardening functions are used in these surfaces for evolving of damage and healing variables. The verification of the solution is shown by solving an example for a simply supported beam having uniformly distributed the load. Finally, a result of a self-healing concrete beam is compared to elastic one to demonstrate the capability of the proposed analytical method in simulating concrete beam behavior. The results show that for the specific geometry, the self-healing concrete beam has 21% more weight tolerate, and the deflection of the entire beam up to failure load is about 27% larger than elastic solution under ultimate elastic load.