Numerical multiscale solution strategy for fracturing heterogeneous materials

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. (c) 2009 Elsevier B.V. All rights reserved.