Consideration of Size Effects and Stress Localization in Response Determinations Using the DEM

Abstract

In the truss-like Discrete Element Method (DEM) masses are considered lumped at nodal points and linked by means of unidimensional elements with arbitrary constitutive relations. In previous studies of the tensile fracture behavior of concrete cubic samples, it was verified that numerical predictions of fracture of non-homogeneous materials using DEM models are feasible and yield results that are consistent with the experimental evidence so far available. Applications that demand the use of large elements, in which extensive cracking within the elements of the model may be expected, require the consideration of the increase with size of the fractured area, in addition to the effective stress-strain curve for the element. This is a basic requirement in order to achieve mesh objectivity. Note that the degree of damage localization must be known a priori, which is a still unresolved difficulty of the nonlinear fracture analysis of non-homogeneous large structures. Results of the numerical fracture analysis of 2D systems employing the DEM are reported in this contribution and compared with predictions based on the multi-fractal theory proposed by Carpinteri et al according to which a fractal dimension, contained in the interval (1,2), defines the fracture area for a unitary thickness. The assessment of the equivalence and ranges of validity of different approaches to account for size and strain rate effects appear today as one of the most urgent areas of study in the mechanics of materials. The influences of various parameters, such as the mesh size, the strain velocity and the shape of the fracture surface are assessed by means of numerical simulation. Methods employed in the homogenization of heterogeneous materials, in which damage is expected to occur with different level of stress localization, are also examined. Finally, conclusions on the performance of the numerical procedures employed in the reported studies are presented.