Viscoplastic Damage-Softening Constitutive Model for Concrete Subjected to Uniaxial Dynamic Compression

A new viscoplastic damage-softening constitutive model is presented. It is developed by integrating a Bodner-Partom viscoplastic model with a new damage evolution equation. A set of ordinary differential equations (ODEs) is formulated, and a Runge-Kutta integral method is used to get stress-strain curves given by the model. Also, stress-strain curves of a wide range of strain-rates for concrete were obtained by split Hopkinson pressure bar (SHPB) tests. By fitting the integral stress-strain curves to the experimental ones with the least square optimization method, we determined the material parameters in our model. Some properties of the new model, such as strain-rate sensitivity, damage evolution characteristics, strain-rate jump effects and unloading feature, are explored. These results show that our new model can describe dynamic behaviors of concrete very well, and our integrating-fitting-optimizing method to get material parameters is valid.