From particle mechanics to micromorphic media. Part I: Homogenisation of discrete interactions towards stress quantities

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:187

Article

Ehlers, Wolfgang¹  Bidier, Sami¹ 

[1] Univ Stuttgart, Inst Appl Mech, Pfaffenwaldring 7, D-70569 Stuttgart, Germany

关键词: Granular media;    Particle mechanics;    Homogenisation;    Micromorphic continua;    Micropolar continua;    Discrete-Element Method;   

DOI  :  10.1016/j.ijsolstr.2018.08.013

来源: Elsevier

【 摘 要 】

The present article concerns a homogenisation strategy that links particle-based interaction forces to stress quantities of kinematically extended microcontinuum theories. The homogenisation procedure is based on the investigation of the balance relations for single, homogeneously deformable particles and for ensembles of particles forming a Representative Elementary Volume, thus exhibiting the relation of particle-based forces and stresses with characteristic micromorphic stress states. The formalism includes the established homogenisation procedure for rigid particle ensembles linking particle-interaction forces to characteristic micropolar stress states as a special case of microcontinua. In order to demonstrate the applicability of the proposed homogenisation technique, a localisation problem of granular media is investigated by use of the Discrete-Element Method and a subsequent homogenisation of the microstructural information. A comparison between the arising micromorphic and micropolar cases is presented. The former is a result of microstructures that include deformable components, while the latter is already resulting from rigid-particle microstructures. In both cases, the averaged extended stress states are predominant in the region of localised zones. (C) 2018 Elsevier Ltd. All rights reserved.

【 授权许可】

Free