Rate sensitive plasticity-based damage model for concrete under dynamic loading

In this manuscript, a rate-sensitive plasticity-based damage model for concrete subjected to dynamic loads is presented. The developed rate-sensitive damage model incorporates the key experimental evidence related to strain rate and damage rate. With increasing strain rates, the model is able to predict a decrease in the rate of damage evolution due to artificial stiffening effects together with a final higher level of damage. The major contribution of the work is to include the effect of damage rate, strain rate and also to consider all the physical mechanisms of damage. This is achieved by using a power law model to relate the rate of damage to the equivalent plastic strain rate. The damage parameter considers hydrostatic, tension and compression damage. Such a damage definition helps in the prediction of pulverized damage due to a loss in cohesive strength at increased hydrostatic stress, shear-induced compressive damage and tensile microcracking. Strong volumetric deformation of the material that includes hydrostatic and compaction damage is also considered in the model. Because hydrostatic damage accounts for the reduction in stiffness and compaction damage accounts for the increase in stiffness under pure compressive loading. A strain rate-dependent failure surface is considered and with increasing strain rate there is an increase in the size of the failure surface which is capped at an upper limiting value. The incremental effective stress-strain relationship is defined in terms of rate of damage, accumulated damage and viscosity parameters reflecting the inherent inertial, thermal and viscous mechanisms respectively. The stress-strain relationship in the model also accounts for stress reversals that occur due to interference of an incident and reflected wave, by including a Heaviside function. The developed model is implemented in LS-DYNA using vectorized UMAT. Verification, validation and parameterization of the developed model have been made through several numerical analyses.