Modeling high rate stress upturn for brittle materials.

High rate stress upturn for ductile materials at rates between 103-104/s has been known since the 1980s, and previously we've shown how to model this behavior based on our overstress approach to dynamic viscoplasticity. It turns out that brittle materials also undergo high rate stress upturn, but at a lower rate of 1-10/s. most available data on high rate stress upturn of brittle materials is for concrete (from obvious reasons), and they are usually represented by DIF as function of strain rate, where DIF=Dynamic Increase Factor. Here we model high rate stress upturn for brittle materials using our overstress brittle response (OBR) model. Our OBR model includes: 1) damage onset curve for both compression and tension; 2) damage accumulation rate as function of damage onset overstress; 3) damage onset reduction as function of damage level down to the fully damaged state; 4) plastic flow of the fully damaged material as for a granular material; and 5) finite limit for damage accumulation rate. This last item stems from the finite rate of fracturing, and from the finite speed of crack growth, and it turns out that this is the feature that leads to the high rate stress upturn response. To demonstrate how the model works we compute several examples in cylindrical symmetry with different ratios of radial to axial velocities. [ABSTRACT FROM AUTHOR]