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Micromorphic and micropolar continua: A comparative study based on homogenisation of particle simulations
Author(s) -
Bidier Sami,
Ehlers Wolfgang
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800390
Subject(s) - granular material , materials science , boundary value problem , homogenization (climate) , microstructure , context (archaeology) , deformation (meteorology) , discrete element method , mechanics , finite element method , stress (linguistics) , particle (ecology) , statistical physics , classical mechanics , mathematics , composite material , physics , mathematical analysis , thermodynamics , geology , biodiversity , ecology , paleontology , linguistics , philosophy , oceanography , biology
Extended continuum‐mechanical theories, such as the micromorphic, the micropolar or the microstrain continuum, are suitable formulations when additional characteristic microstructural deformation modes should be included into macroscopic modelling techniques. This is especially the case when the microscopic view of the considered material reveals a granular or particulate structure. Then, by means of a particle‐centre‐based homogenisation technique, it is possible to link the microstructural information that can be gained, for example, from Discrete‐Element (DE) simulations, to the extended deformation and stress states of the above mentioned extended continua. In this context the present contribution focuses on two main aspects: at first, different granular microstructures, in particular bonded and unbonded granular systems, are investigated using a discrete‐element formulation with the emphasis on the evolution of strain localisation phenomena. Secondly, the obtained results of these initial‐boundary‐value problems are homogenised towards micropolar and micromorphic stress measures. Depending on the microstructural characteristics, the activation and evolution of the extended stress states are compared and evaluated with special emphasis on the size of the chosen homogenisation domain.