Abstract
In this paper two discrete element methods (DEM) are discussed. The free hexagon element method is considered a powerful discrete element method, which is broadly used in mechanics of granular media. It substitutes the methods for solving continuum problems. The great disadvantage of classical DEM, such as the particle flow code (material properties are characterized by spring stiffness), is that they have to be fed with material properties provided from laboratory tests (Young's modulus, Poisson's ratio, etc.). The problem consists in the fact that the material properties of continuum methods (FEM, BEM) are not mutually consistent with DEM. This is why we utilize the principal idea of DEM, but cover the continuum by hexagonal elastic, or elastic-plastic, elements. In order to complete the study, another one DEM is discussed. The second method starts with the classical particle flow code (PFC - which uses dynamic equilibrium), but applies static equilibrium. The second method is called the static particle flow code (SPFC). The numerical experience and comparison numerical with experimental results from scaled models are discussed in forthcoming paper by both authors.
Highlights
The principal problem of classical numerical methods, such as finite element methods, boundary element methods, etc., consists in “too stiff ” models, or too complicated simulations of the real states when no a priori knowledge of crack initiation is available. This is why discrete element methods have been introduced to replace fracture mechanics problems by contact problems, which are in many respects more transparent, and which lead us to the same results
In the early 1970s Cundall, [2], and others, [3], introduced discrete elements starting with dynamic equilibrium
Two new discrete element methods have been introduced in this paper
Summary
The principal problem of classical numerical methods, such as finite element methods, boundary element methods, etc., consists in “too stiff ” models, or too complicated simulations of the real states when no a priori knowledge of crack initiation is available This is why discrete element methods have been introduced to replace fracture mechanics problems by contact problems, which are in many respects more transparent, and which lead us to the same results. Brick-like elements were used (professional computer program UDEC), and later circular elements in 2D and spherical elements in 3D (PFC – particle flow code – both computer systems issued by ITASCA) simulated the continuum behavior of structures The application of such methods took place mainly in geotechnics, where soil is a typical grain material with the above-mentioned shape, [11]. Applications in several fields of practical problems are discussed in a forthcoming paper by the authors [13]
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