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Alternative Definitions of Micro–to–Macro Transitions in Particle Aggregates of Granular Materials
Author(s) -
Dettmar Joachim,
Miehe Christian
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310404
Subject(s) - macro , granular material , aggregate (composite) , stiffness , displacement (psychology) , boundary (topology) , macro level , statistical physics , mechanics , mathematics , computer science , materials science , structural engineering , physics , mathematical analysis , engineering , nanotechnology , composite material , psychology , psychotherapist , programming language , economic system , economics
An alternative approach to the modelling of the overall macroscopic response of granular materials is presented based on micro–macro transitions. A homogenized macro–continuum is considered with locally attached granular microstructures. The new developments include a consistent transfer of micro–macro transitions from continuous to particle microstructures with a new overall macro–stress definition. Secondly, a new class of boundary conditions for displacements/ rotations on prescribed boundary–frame particles is presented that yields upper and lower bounds with regard to the aggregate stiffness. Thirdly, a unified implementation of the displacement/ rotation boundary constraints by a penalty method is developed that proves to be a convenient computational tool in explicit codes.