{'fraction_non_alphanumeric': 0.018038331454340473, 'fraction_numerical': 0.002254791431792559, 'mean_word_length': 5.388489208633094, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A three‐dimensional discrete element model for heterogeneous solids under mechanical loading

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.