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A three‐dimensional discrete element model for heterogeneous solids under mechanical loading
Author(s) -
Ockelmann Felix,
Dinkler Dieter
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610102
Subject(s) - spheres , discrete element method , anisotropy , hexagonal crystal system , materials science , porous medium , constitutive equation , porosity , mechanics , strain energy , elastic energy , finite element method , statistical physics , physics , composite material , crystallography , thermodynamics , chemistry , quantum mechanics , astronomy
The Discrete Element Method (DEM) is used to model solids under quasi‐static and dynamic loading. In order to model elastic bodies, a microscopic model must be able to represent the macroscopic properties of the material. An energy‐based approach to determine the model parameters is presented for an unit cell assemblage of 13 particles in the hexagonal close packing of spheres. The stored strain energy in the unit cell is added up and the specific strain energy expression is derived with respect to the macroscopic strains. The resulting stress‐strain relations can be compared to the constitutive equations of the elastic continuum. To avoid cubic anisotropy for Poisson's ratios above zero, an advanced octahedrongap‐filled hexagonal close packing of spheres is presented and validated. This approach for regular lattices can be transferred to heterogeneous materials with the goal of describing porous media such as cement stone. Therefore it is possible to use the presented regular lattices with statistically distributed properties or to investigate irregular distributions of particles. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)