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Streszczenie:
This work presents a new original formulation of the discrete element method (DEM) with deformable cylindrical particles. Uniform stress and strain fields are assumed to be induced in the particles under the action of contact forces. Particle deformation obtained by strain integration is taken into account in the evaluation of interparticle contact forces. The deformability of a particle yields a nonlocal contact model, it leads to the formation of new contacts, it changes the distribution of contact forces in the particle assembly, and it affects the macroscopic response of the particulate material. A numerical algorithm for the deformable DEM (DDEM) has been developed and implemented in the DEM program DEMPack. The new formulation implies only small modifications of the standard DEM algorithm. The DDEM algorithm has been verified on simple examples of an unconfined uniaxial compression of a rectangular specimen discretized with regularly spaced equal bonded particles and a square specimen represented with an irregular configuration of nonuniform-sized bonded particles. The numerical results have been verified by a comparison with equivalent finite elementmethod results and available analytical solutions. The micro-macro relationships for elastic parameters have been obtained. The results have proved to have enhanced the modeling capabilities of the DDEM with respect to the standard DEM.

Słowa kluczowe:
average stress, deformable particles, discrete element method, elastic constants, micro-macro relationships, nonlocal contact model

Streszczenie:
The phenomenon of rock burst occurs when the static stability conditions of the rock mass are violated and the dynamic failure process proceeds starting from the equilibrium state. In view of the difficulties in determining numerically the instability point, an alternative approach is advocated here: after solving the initial static problem the mode and onset of dynamic failure are studied by superposition of dynamic disturbances. In this way quantitative analyses of rock burst phenomena may be handled in a relatively simple manner.

Streszczenie:
A new original formulation of the discrete element method based on the soft contact approach is presented in this work. The standard DEM has heen enhanced by the introduction of the additional (global) deformation mode caused by the stresses in the particles induced by the contact forces. Uniform stresses and strains are assumed for each particle. The stresses are calculated from the contact forces. The strains are obtained using an inverse constitutive relationship. The strains allow us to obtain deformed particle shapes. The deformed shapes (ellipses) are taken into account in contact detection and evaluation of the contact forces. A simple example of a uniaxial compression of a rectangular specimen, discreti.zed with equal sized particles is simulated to verify the DDEM algorithm. The numerical example shows that a particle deformation changes the particle interaction and the distribution of forces in the discrete element assembly. A quantitative study of micro-macro elastic properties proves the enhanced capabilities of the DDEM as compared to standard DEM.

Słowa kluczowe:
Discrete Element Method, Deformable Particles, Nonlocal Contact Model, Poisson's Effect

Streszczenie:
This work presents a new original formulation of the discrete element method based on the soft contact approach. The standard DEM has been enhanced by introduction of the additional (global) deformation mode caused by the stresses in the particles induced by the contact forces. Uniform stresses and strains are assumed for each particle. The stresses are calculated from the contact forces. The strains are obtained using an inverse constitutive relationship. The strains allow us to obtain deformed particle shapes. The deformed shapes (ellipses) are taken into account in contact detection and evaluation of the contact forces. The numerical example shows that a particle deformation changes the particle interaction and the distribution of forces in the discrete element assembly.

Słowa kluczowe:
discrete element method, deformable particles, soft contact