Damage–viscoplastic consistency model with a parabolic cap for rocks with brittle and ductile behavior under low‐velocity impact loading

Abstract

AbstractThis paper presents a damage–viscoplastic cap model for rocks with brittle and ductile behavior under low‐velocity impact loading, which occurs, e.g. in percussive drilling. The model is based on a combination of the recent viscoplastic consistency model by Wang and the isotropic damage concept. This approach does not suffer from ill posedness—caused by strain softening—of the underlying boundary/initial‐value problem since viscoplasticity provides a regularization under dynamic loading by introducing an internal length scale. The model uses the Drucker–Prager (DP) yield function with the modified Rankine criterion as a tension cut‐off and a parabolic cap surface as a compression cut‐off. The parabolic cap is smoothly fitted to the DP cone. The strain softening law in compression is calibrated with the degradation index concept of Fang and Harrison. Thereby, the model is able to capture the brittle‐to‐ductile transition and hardening behavior of geomaterials under highly confined compression, which is the prevailing stress state under a bit‐button in percussive drilling. Rock strength heterogeneity is characterized statistically at the structural level using the Weibull distribution. An explicit time integrator is chosen for solving the FE‐discretized equations of motion. The contact constraints due to the impact of an indenter are imposed with the forward increment Lagrange multiplier method that is compatible with explicit time integrators. The model is tested at the material point level with various uniaxial and triaxial tests. At the structural level confined compression, uniaxial tension tests and a rock sample under low‐velocity impact are simulated. Copyright © 2009 John Wiley & Sons, Ltd.