Bending, Twisting, Merging and Branching Cracks: A Challenging Set of Problems

In this work, the challenges of the computational evaluation of localized structural failure are discussed and a set of challenging problems for the numerical modeling of quasi-brittle structural failure is presented for the assessment of the performance of models aiming at reproducing the phenomenon. The selected set of challenging problems includes numerical benchmarks and experimental tests reported in the literature, covering several localized structural failure conditions: bending, twisting, merging and branching cracks. The present work focuses on the critical issues when computing localized structural failure faced by present models including: the need to employ a method that produces mesh bias objective results, the requirement to reproduce experimental results in terms of bearing capacity, force–displacement curves, mechanical dissipation, structural size effect, collapse mechanisms with accuracy, the need to perform 3D calculations in a computationally efficient manner to address engineering applications, or the ability to accommodate a broad range of material constitutive behaviors including isotropic and orthotropic crack models with several failure criteria. In the present work, these points are addressed with the use of mixed strain/displacement finite element formulations, which guarantee the local convergence of the computed strains and displacements. This approach is general enough to solve the issues discussed including the spurious mesh bias dependence of computed results in localized structural failure, the aptness to reproduce structural size effect in the computations and the inclusion of orthotropic damage constitutive behavior. To ensure the computational efficiency of the Mixed Finite Element Method, the simulations are performed with adaptive formulation refinement (AFR) and adaptive mesh refinement (AMR) capabilities.