Anisotropic viscodamage–viscoplastic consistency constitutive model with a parabolic cap for rocks with brittle and ductile behaviour

• A novel material model for rocks with brittle and ductile behaviour is presented.
• The model describes the load-induced anisotropy via compliance tensor damage model.
• The visco-damage consistency concept provides a localization limiter.
• The model captures the brittle-to-ductile transition of compact carbonate rocks.
• The model accommodates the strong loading rate sensitivity of rocks by viscosity.

This paper presents a new constitutive model for rocks that exhibit either brittle or ductile behaviour. The model is based on a combination of the viscoplastic consistency model in compression, and an anisotropic viscodamage consistency model in tension. The main novelty of the model is in the damage part formulated in the same manner as the viscoplastic consistency model by Wang. The model accounts for the damage-induced anisotropy by the corresponding evolution of damage compliance tensor. The Drucker–Prager yield function and the Modified Rankine criterion with a tension cut-off and a parabolic cap surface as a compression cut-off are used to indicate the stress states leading to strain softening/hardening and damage. A confining pressure dependent parabolic hardening-linear softening law in compression is calibrated with respect to the degradation index. Thereby, the model is able to capture the brittle-to-ductile transition exhibited by many rocks under high confining pressure. The hardening behaviour of rock under extremely high confined stress states is described by the viscoplastic cap model. The model performance is illustrated at the material point level with various uniaxial and triaxial tests. It is also shown finally that the viscodamage consistency model provides a localization limiter in the softening regime.