Mathematical Physics - Volume II - Numerical Methods

Chapter 6. Introduction to Computational Mechanics of Discontinua

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conglomerate is described on the basis of the motion of these individual elements and specification of the constitutive rules or contact forces among them. Like other methods of CMD, DEM provides a detailed temporal evolution of the system by solving Newton’s equations of motion of individual discrete elements (6.1), including the complex damage mechanisms that naturally arise from such simulations. This chapter outlines only the traditional DEM; the review of more advanced DEM models is beyond the scope of this short introduction. The same goes for advanced topics and specifics of DEM technique such as packing and grain shape, flow laws, capillary effects, high deformation loadings, which are available, for example, in the review paper by Donze and co-authors [10] and references cited therein. It is common to classify DEMmodels based on the load transfer mechanisms illustrated in Figure 6.18.

Figure 6.18: (a) A group of particles or grains (with a cluster of three highlighted) with prominent interacting lines forming an associated network. Based on the load transfer mechanism used in the model, DEM are divided into models with: (b) Central interactions (these models represent the generalization of the α model of Chapter 6.4.2); (c) Central and angular interactions (generalization of the α − β model of Chapter 6.4.3); (d) Central, shear and bending interactions (generalization of the beam lattices described in Chapter 6.4.4; this is a typical DEM, which can be called a “local inhomogeneous micropolar continuum” [3]); and (e) Central, shear, bending and angular interactions. (Adopted from [3].)

The DEM problem-solving methodology is based on the MD formalism, which includes explicit finite difference schemes in which the computational cycle involves