Numerical multiscale solution strategy for fracturing of concrete

This paper presents a numerical multiscale modelling strategy for simulating fracturing of concrete where the fine-scale heterogeneities are fully resolved. The fine-scale is modelled using a hybrid-Trefftz stress formulation for modelling propagating cohesive cracks. The very large system of algebraic equations that emerges from detailed resolution of the fine-scale structure requires an efficient iterative solver with a precon- ditioner that is appropriate for fracturing heterogeneous materials. This paper presents a two-grid strategy for construction of the preconditioner that utilizes scale transition techniques derived for computational homog- enization and represents an adaptation and extension of the work of Miehe and Bayreuther (IJNME, 2007). For the coarse scale, this paper investigates both classical C 0 -continuous displacement-based finite elements as well as C 1 -continuous elements. The preconditioned GMRES Krylov iterative solver with dynamic convergence tolerance is integrated with a constrained Newton method with local arc-length control and line searches. The convergence properties and performance of the parallel implementation of the proposed solution strategy is illustrated on a numerical examples.