Modeling of concrete spallation with damaged viscoelasticity and retarded damage

Abstract

• High strain-rate stresses by far exceed quasi-static strength as a material property. • High strain-rate stresses are maintained only for short periods followed by failure. • Energy dissipation is much higher under high strain-rates compared to quasi-statics. • A model with damaged viscoelasticity and retarded damage is suitable for these effects. A proposal for a triaxial constitutive law is developed to model strain-rate sensitivity of quasi-brittle materials like concrete. It is based on a standard isotropic quasi-static damage law which is extended with damaged viscoelasticity and retarded damage to consider the physical mechanisms of strain-rate sensitivity. Dynamic uniaxial compressive and tensile stress–strain relations are derived as a special case. The material parameters for strain-rate sensitivity are calibrated to reproduce experimental increase factors for uniaxial compressive and tensile strength. A fully triaxial setup is used for modeling of stress wave propagation in cylindrical concrete specimens with spallation of fragments as part of modified Split–Hopkinson–Bar configurations. The validation of the material model is performed with the comparison of computed and experimental pull-back velocities of the specimen’s free end. It is shown that the validation is only possible considering both damaged viscoelasticity and retarded damage in the material model. The numerical computations yield stresses far beyond quasi-static strength, but high stresses are maintained only for short periods before material destruction. Furthermore, the computations show that the amount of dissipated energy due to dynamic spallation is much higher compared to quasi-static crack energy.