This contribution is on algebraic multigrid (AMG) based preconditioning methods for the iterative solution of linear systems of equations arising in numerical simulations of failure of quasi-brittle materials using generalized continuum approaches and indirect displacement control. The problem under consideration involves three coupled fields: displacements, microrotations, and non-local damage. It is a multi-physics problem, exhibiting block-structured matrices which allow us to develop tailored AMG-based block preconditioning strategies. When modeling failure of quasi-brittle materials, either due to brittle cracking or due to the sudden formation of shear bands, structural snap-back behavior is frequently encountered. Hence, this unstable structural response cannot be simulated using direct displacement control or load control techniques. However, it can be treated with the indirect displacement control approach. However, the indirect displacement control introduces further complexity by adding an additional unknown and a constraint equation, causing the arising large linear systems to be of saddle point type with an extra zero diagonal entry in the row of the constraint equation. These augmented systems can be treated in two ways. The first way is to use a segregated Schur complement-based approach, involving two preconditioned iterative solutions of linear systems without the constraint equation per solution of the augmented system. The second way is to pursue a monolithic iterative linear solution of the augmented system using a tailored saddle-point preconditioner. In this context, we propose a problem-adapted Schur complement preconditioner for the augmented system, which is an extended version of a block preconditioner that was previously developed in the context of displacement controlled problems. We present numerical results for simulations of borehole breakout that clearly show the superiority of the proposed monolithic iterative linear solution strategy, given that it decreases the computational effort per solution of the augmented linear system by more than 50%.