A statistical DEM approach for modelling heterogeneous brittle materials

Abstract

By utilizing numerical models and simulation, insights about the fracture process of brittle heterogeneous materials can be gained without the need for expensive, difficult, or even impossible, experiments. Brittle and heterogeneous materials like rocks usually exhibit a large spread of experimental data and there is a need for a stochastic model that can mimic this behaviour. In this work, a new numerical approach, based on the Bonded Discrete Element Method, for modelling of heterogeneous brittle materials is proposed and evaluated. The material properties are introduced into the model via two main inputs. Firstly, the grains are constructed as ellipsoidal subsets of spherical discrete elements. The sizes and shapes of these ellipsoidal subsets are randomized, which introduces a grain shape heterogeneity Secondly, the micromechanical parameters of the constituent particles of the grains are given by the Weibull distribution. The model was applied to the Brazilian Disc Test, where the crack initiation, propagation, coalescence and branching could be investigated for different sets of grain cement strengths and sample heterogeneities. The crack initiation and propagation was found to be highly dependent on the level of heterogeneity and cement strength. Specifically, the amount of cracks initiating from the loading contact was found to be more prevalent for cases with higher cement strength and lower heterogeneity, while a more severe zigzag shaped crack pattern was found for the cases with lower cement strength and higher heterogeneity. Generally, the proposed model was found to be able to capture typical phenomena associated with brittle heterogeneous materials, e.g. the unpredictability of the strength in tension and crack properties.

Micromechanics-based variational phase-field modeling of Brazilian splitting tests

“…These steps are taken at each iteration to obtain the stress tensor σ and the corresponding consistent tangent C ep to be used in equation (30).…”

“…Numerical approaches in fracture mechanics can be broadly classified into two categories: discrete and continuum methods [25]. Discrete approaches, such as the Flat-Joint Method (FJM), Discrete Element Method (DEM), non-ordinary state-based peridynamics, and Discontinuous Deformation Analysis (DDA), have been used by researchers [1,4,[26][27][28][29][30][31] to model the fracture in a Brazilian splitting test. These methods provide an insight into the (quasi-)brittle fracture behavior of the material.…”

Dynamic Compressive and Tensile Characterisation of Igneous Rocks Using Split-Hopkinson Pressure Bar and Digital Image Correlation

“…Hence, a so-called rectangular sensing region (RSR) was defined, large enough to avoid local effects, such as voids and microcracks or singular grains, but small enough to capture the nearly constant indirect tensile strain region close to the centre of the disc. Furthermore, it is crucial that the region covers the point of crack initiation, which does not always coincide with the centre of the disc [3,15]. To this end, five tests of each rock were conducted with the high-speed camera set to 381,000 fps in order to capture the full surface of the disc, see Figure 5.…”

“…By utilizing numerical simulations, insights can be gained regarding the hard rock drilling process that otherwise would be difficult to obtain. A recently developed statistical model by Wessling et al [3], based on the discrete element method, has been shown to capture typical rock fracture behaviour. However, in order for this model to be accurate, precise information regarding the dynamic properties of the rock material is crucial.…”