Comparative Modeling of Quasi Brittle Fracture Using a Truss-Based Discrete Element Method and a Phase Field Formulation

Resumen

This work presents a comparative study between two numerical approaches for modeling fracture in quasi-brittle materials: the truss-based Discrete Element Method (DEM) and the Phase Field Method (PFM), formulated within the Finite Element Method (FEM) framework. In the version of the Discrete Element Method used here (referred to as DEM), the spatial discretization is performed using a regular arrangement of pinned bars with masses concentrated at the nodes. The equivalent cross-sectional area of the diagonal and normal bars allows the representation of an equivalent elastic solid. To capture the nonlinear mechanical behaviour produced for the evolution of the material damage, a bilinear constitutive law is applied to each bar. This formulation enables the definition of a motion equation that must be integrated in time using an explicit scheme, such as the central difference finite difference method. An important feature of the present model is its ability to incorporate material properties as random fields. In contrast, the phase field model introduces a scalar damage field to describe fracture as a continuous transition in the medium, and in this work, it is implemented based on the Principle of Virtual Work. To compare the performance of both methods, three examples are presented. A Single Edge Notch Bending (SENB) performed in epoxy resin, a Notched Plate with Hole (NPWH) also built in cement mortar, and finally a parametric study where the influence of the material parameters of a specimen composed of a substrate, and an interface orthogonal to the crack propagation direction is analyzed. The comparison of the two approaches through these three examples allows the identification of the strengths and weaknesses of each method.