Modeling cohesive crack growth via a truly-mixed formulation

Abstract

An alternative approach for cohesive crack growth in elastic media is proposed. Standard methods move from displacement-based formulations that are enriched to handle discontinuities in the inherently continuous displacement field. The herein adopted formulation is conversely based on a truly-mixed discretization that has stresses as main regular variables, while discontinuous displacements play the role of Lagrangian multipliers. The approach directly handles the analysis of propagating cohesive cracks in elastic media through the appropriate inclusion of interface energy terms that enrich the formulation when a crack is growing. Notably, no edge element is introduced but simply the inherent discontinuity of the displacement field is taken advantage of. Furthermore, the continuity of traction vectors is imposed in an exact fashion within the formulation and not as an additional weak constraint, as classically done. The work has the main aim of investigating the features of the approach through numerical simulations that refer to well-known experimental results on concrete specimens. The capability of modeling size effect is firstly tested in case of a pure mode I growth. The accuracy of truly-mixed stress interpolation is also exploited to recover crack path and to handle energy dissipation in mixed mode simulations.