Mathematical Physics - Volume II - Numerical Methods

Chapter 6. Introduction to Computational Mechanics of Discontinua

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Potyondy and Cundall [128] devised the bonded-particle model to simulate rock massifs and other heterogeneous, brittle systems of intermittent sub-structure. In the original variant, the model consisted of a densely packed group of rigid circular/spherical grains of different sizes interconnected at contact points by additional parallel bonds that represent the cohesive action of the cement (Figure 6.20). The rigid discrete elements interact only through soft contacts (i.e., small overlaps are allowed) that possess limited normal and shear stiffness. The model is fully dynamic. It is able to describe complex phenomena of rock damage evolution such as nucleation, growth, branching and merging of microcracks resulting in the damage-induced anisotropy, hysteresis, dilatation, postcritical softening, strength-increasing with lateral confinement. At the beginning of 2000s when this modeling approach commenced, the DEM modeling of discontinuous media was still in its infancy compared to the mechanics of the continuum. Therefore, the authors paid great attention to the systematic development of an appropriate modeling methodology that included not only careful virtual experimentation and qualitative comparison of results with physically observed mechanisms on micro- and macro-scale but also quantitative comparison with experimentally measured properties.

Figure 6.20: Bonded-particle model for simulation of heterogeneous materials composed of cemented grains. Schematics of (a) the behavior of grains in contact (the non-cohesive bond), and (b) cement behavior (the parallel bond). If the cement (which provides the parallel bond) is not present, then only the grain behavior remains and the slip model with rolling (outlined in Chapter 6.5.3) is recovered. In general, the model is defined by the density of the particles, their shape and the size distribution, their packing, and the meso-properties of the grains and the cement. Potyondy and Cundall [128] used circular / spherical elements corresponding to the PFC 2D / PFC 3D programs (Itasca Consulting Group). Note the striking similarity with the epoxy-cemented glass beads of Figure 6.1a. It cannot be overemphasized that, unlike some other computational methods in CMD, the term "particle" in this context means a discrete element that occupies a finite part of space (the term “grain” will be also used interchangeably). The radii of the circular discrete elements (particles, grains) are drawn from a uniform distribution bounded by R min and R max and dense packaging was obtained by following the appropriate material generation procedure. The rigid particles can independently translate and rotate and interact via soft