Effect of characteristic length on nonlocal prediction of damage and fracture in concrete

The paper deals with a new nonlocal integral-type model for simulation of an anisotropic, localised damage and for prediction of combined failure modes in a plane-notched concrete specimen. The nonlocal incremental-type model of the elastic-brittle-damage material is an extension of the relevant local model originated by Murakami and Kamiya (1997), modified later to the incremental form by Kuna-Ciskał and Skrzypek (2004). In order to avoid the mesh-dependence and ensure stability and convergence, two localisation limiters are examined: the concept of Nonlocal Averaging (NA) and the additional Cut-off Algorithm (CA), applied to damage conjugate thermodynamic forces. The elastic-brittle damage constitutive equations are formulated in an incremental and nonlocal fashion, by the use of a damage dissipation potential defined in the space of averaged regularised damage variables instead of the corresponding local ones. The Gauss distribution function is taken as the weight function for the definition of a nonlocal continuum. In order to assess how much the new nonlocal model is capable of describing localised strain and damage fields, an example of the plane double-notched specimen of Nooru-Mohammed (1992) is examined. Much emphasis is put to proper choice of the characteristic length of the nonlocal continuum. Convergence of the mesh size is proved for both, the damage incubation period and fracture, when a single localisation limiter (NA) is active.