A dilatant visco-elasto-viscoplasticity model with globally continuous tensile cap: stable two-field mixed formulation

Abstract. Rocks break if shear stresses exceed their strength. It is therefore important for typical geoscientific applications to take shear failure mechanism and the subsequent development of mode-II shear bands or faults into account. Many existing codes incorporate non-associated Drucker-Prager or Mohr-Coulomb plasticity models to simulate this behavior. Yet, when effective mean stress becomes extensional, for example when fluid pressure becomes large, the dominant failure mode changes to a mode-I (opening) mode, which initiates plastic volumetric deformation. It is rather difficult to represent both failure modes in numerical models in a self-consistent manner, while also accounting for the nonlinear visco-elastic host rock rheology, which varies from being nearly incompressible in the mantle to being compressible in surface-near regions. Here, we present a simple plasticity model that is designed to overcome these difficulties. We employ a combination of a linearized Drucker-Prager shear failure envelope with a circular tensile cap function in way that ensures continuity and smoothness of both yield surface and flow potential in the entire stress space. A Perzyna-type viscoplastic regularization ensures that the resulting localization zones are mesh-insensitive. To deal with the near incompressibility condition, a mixed two-field finite element formulation is employed. The local nonlinear iterations at the integration-point level are used to determine the stress increments. The global Newton-Raphson iterations are applied to solve the discretized momentum and continuity residual equations. The presented plasticity model is implemented in an open-source 2D unstructured finite element code GeoTech2D. The results of several typical test cases that range from crustal scale deformation to the propagation of fluid-induced tensile failure zones demonstrate rapid convergence. The robustness of the solution scheme is enhanced by the adaptive time stepping algorithm.