Single objective optimization for modeling elastoplastic damage of rock

Abstract

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 $O\left(n^2\right)$. 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 in finite element simulation of a projectile penetrating into limestone.