Strain localization criteria for viscoplastic geomaterials

This work presents a viscoplastic localization criterion to detect quasi-instantaneous (i.e., load-induced) and delayed (creep-induced) strain localization in rate-dependent solids. The study is based on the theory of controllability and a viscoplastic description of the mechanical response. Analytical precursors of unstable states are defined through systems of ordinary differential equations (OEDs). The use of the proposed criteria is illustrated at the material point level through a set of strain localization analyses simulating active strain localization of a porous rock. In addition, full-field finite element simulations of compression tests conducted under various pressures are reported to demonstrate the role of local unstable viscoplasticity in the spontaneous propagation of deformation bands under stationary boundary conditions. The study shows that the viscoplastic localization criterion maintains a negative sign as long as the behavior is unstable, that is, the rate of deformation is accelerating. The sign switch coincides with the transition to decelerating deformation. The analyses revealed that pulses of overstress always emerge in correspondence with the growth of unstable behavior, and the peak matches the transition to stable behavior. The local responses recovered from full-field analyses were consistent with those observed in analyses at material point level and the predictions of the presented theory.

Automated summary

This work presents a viscoplastic localization criterion based on the theory of controllability and a viscoplastic description of the mechanical response to detect strain localization in rate-dependent solids. The proposed criteria are illustrated through strain localization analyses of a porous rock and finite element simulations of compression tests. The study shows that the viscoplastic localization criterion maintains a negative sign during unstable behavior and switches to positive during decelerating deformation. The analysis also reveals the emergence of overstress pulses during unstable behavior, matching the transition to stable behavior.