Numerical multiscale solution strategy for fracturing heterogeneous materials

Abstract This paper presents a numerical multiscale modelling strategy for simulating fracturing in materials where the fine-scale heterogeneities are fully resolved, with a particular focus on concrete. 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 preconditioner that is appropriate for fracturing heterogeneous materials. This paper proposes a two-grid strategy for construction of the preconditioner that utilizes scale transition techniques derived for computational homogenization and represents an adaptation of the work of Miehe and Bayreuther [2] and its extension to fracturing heterogeneous materials. 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 two numerical examples.