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

Abstract

SUMMARYThis 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.

A numerical and experimental study on the tensile behavior of plasma shocked granite under dynamic loading

“…The contacts between the BD sample and the incident and transmitter bars are modeled in a standard manner by imposing contact constraints between the bar end nodes and the edge nodes of the discretized BD sample. The contact constraints are imposed with the forward increment Lagrange multiplier method, and the explicit modified Euler time integrator is employed in solving the response of the system in time [27]. The local element level solution, i.e., integration of Equations (1) and (3), is presented in [28].…”

“…A substantial amount of effort has already been put into this matter. For example, Saksala [27] simulated the percussive drilling with a triplebutton indenter using a finite elements based approach, where the rock fracture was modeled with a continuum viscoelastic-damage model. Saksala et al [29] continued their work and created a 3D model where the cracks are embedded as strong displacement discontinuities.…”

“…[27,29] to the numerical simulation of the Brazilian disc test on plasma shocked granite. This method is based on a combination of isotropic rate-dependent damage model and an embedded discontinuity model.…”

Numerical modelling of dynamic spalling test on rock with an emphasis on the influence of pre-existing cracks

“…In the classical method to incorporate rate-dependency into a continuum constitutive model, a constant viscosity term is added to static strength (see [15] for example). If the pre-peak and post-peak response is governed by a single yield function, this approach leads to unrealistically wide and messy failure bands [16].…”

“…These constraints are of form u bar,z −u n,z = b n where u bar,z and u n,z are the axial degrees of freedom of the bar node and a rock contact node n, respectively, and b n is the distance between the bar end and rock boundary node. The contact constraints are imposed with the forward increment Lagrange multiplier method (see [15] for details).…”