On Scale Effects and Mesh Independence in Dynamic Fracture Analysis by Means of the Discrete Element Method

摘要

Numerical predictions of the failure load of large structures, accounting for size effects, require the adoption of appropriate constitutive relations. These relations depend on the size of the elements and on the correlation lengths of the random fields that describe material properties. Previously, the authors proposed expressions for the tensile stress-strain relation of concrete, whose parameters are related to standard properties of the material, such as Young's modulus or its specific Fracture Energy and to size. Simulations conducted for a typical concrete showed that as size increases, the effective stress-strain diagram becomes increasingly linear, with a sudden rupture, while at the same time the CVs of the relevant parameters decrease to negligible values, situation that renders Linear Elastic Fracture Mechanics (LEFM) applicable. However, it was later observed that a hither to unknown problem arises in the analysis of non-homogeneous materials, leading to lack of mesh objectivity: the need to know a priori the degree of fracturing. This should also affect finite element analysis, requiring a careful evaluation of the energy dissipated by fracture or other mechanisms in the course of the loading process. In the paper a tentative criterion is proposed to account for the effect in non-linear dynamic fracture analysis.