A unified objective optimization framework is developed for damage-coupled multisurface plasticity in the context of normal-dissipative media. The framework is shown to be advantageous in rock and soil mechanics applications to overcome difficulty associated with non-smoothness of the elastic domain due to the use of multiple intersecting yield-surfaces. The basic approach is one of mathematical programming, where the evolution of internal variables over a finite time step incrementally minimizes a suitable convex functional of the internal-energy and dissipative terms. A variant of the Broyden-Fletcher-Goldfarb-Shanno algorithm (BFGS) is employed to obviate the need for matrix inversion while constricting order of operations to O(n2). To demonstrate the effectiveness of the novel multi-surface model in modeling strength and damage behavior over a range of confining pressures, we provide validation against existing triaxial compression data for Tavel limestone. Model robustness and utility in damage-based element deletion is further demonstrated infinite element simulation of a projectile penetrating into limestone.

A novel unified hardening/softening model is presented, addressing challenges in the constitutive modelling of rocks' strain-hardening and strain-softening behaviours with brittle-ductile transition. The model highlights the impact of confining pressure on failure mode transition when capturing variations in initial yield, peak, and residual strength. The yield criterion and hardening/softening law are developed by a strength-mapping method, where the peak strength is considered the upper bound. The strength-mapping method relies on a mapping index formulated by plastic shear strains. The mapping index is then incorporated into the fractional plastic flow rule, leading to the proposed constitutive model with 9 easy-to-calibrate parameters. The model predictions have been validated by 4 series of rock samples on triaxial tests, where the brittle-ductile transitions have been well captured. The results indicate that it is reliable to capture the rocks' complicated mechanical responses, particularly the brittle-ductile transition, with our proposed strength-mapping method and fractional plastic flow rule.