Dynamic fracture analysis of concrete or rock plates by means of the discrete element method

The authors apply the so-called Discrete Element Method (DEM) to determine the dynamic response of concrete and rock plates of various sizes that fracture under the action ofstatic and dynamic loading. When, on account of the size of the model, larger elements must be employed, the issue of mesh objectivity must be addressed. In response determinations of structures with initial cracks or high stress gradients, which result in fracture localization, well established procedures lead to results that appear to be mesh independent. However, in elements subjected to approximately uniform stress fields a hitherto unknown problem arises in the analysis of non-homogeneous materials: the need to know a priori the degree of fracturing of the element. This should also affect finite element analysis in cases in which there is no clear fracture localization. In order to provide additional evidence on fracture localization, plates of different sizes subjected to external uni-axial tensile loading under different levels of stress localization are investigated in this paper. The effective stress-strain relationship, ultimate tensile stress and strain, dissipated fracture energy and fracture patterns are determined for plates ranging in size from 0.25 to 15m. Difficulties associated to the prediction of the behavior of large non linear structural systems are discussed in connection with the available results