From particle mechanics to microcontinuum theories

From particle mechanics to microcontinuum theories Microcontinuum theories enable the consideration of particle‐based microstructures within a continuum mechanical framework. Several classes of microcontinua, such as the micromorphic, the micropolar, the microstrain or the microstrech formulation, have been successfully applied to engineering applications, although a clear physical determination and interpretation of the kinematical extensions and the resulting higher‐order stresses within the formulation is frequently missing. In this regard, the present contribution focuses on establishing the physical link between discrete contact forces, stresses and deformation of particle‐based microstructures and the characteristic stress states of microcontinuum theories. Representative Elementary Volumes (REVs) are therefore constructed on the mesoscale as ensembles of deformable particles from the mircoscale. Establishing the REV balance relations justifies the common generalisation of the angular momentum balance commonly applied in microcontinuum theories. It furthermore leads to the identification of the continuum stresses based on micro‐quantities and enables the application of homogenisation techniques by exploitation of the equilibrium conditions of a REV. In order to investigate the hereby established link from the micro‐ to the macroscale, granular materials are simulated using the Discrete‐Element Method (DEM). In particular, localisation phenomena in granulates, e. g. in biaxial compression tests or during ground‐failure processes are studied. This implies the formulation of the contact between particles in an appropriate constitutive manner in accordance to the envisaged granular material behaviour, e. g. whether loose material, such as sand, or bonded multi‐component material, such as polyurethan‐sand compounds for metal casting applications are of interest. With the full solution of a particle‐based initial‐boundary‐value problem, the homogenisation formalism is applied and enables the study of the extended continuum field quantities, essentially demonstrating the applicability of microcontinuum theories in the field of granular material. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings in Applied Mathematics & Mechanics Wiley

From particle mechanics to microcontinuum theories

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Publisher
Wiley
Copyright
Copyright © 2017 Wiley Subscription Services
ISSN
1617-7061
eISSN
1617-7061
D.O.I.
10.1002/pamm.201710259
Publisher site
See Article on Publisher Site

Abstract

Microcontinuum theories enable the consideration of particle‐based microstructures within a continuum mechanical framework. Several classes of microcontinua, such as the micromorphic, the micropolar, the microstrain or the microstrech formulation, have been successfully applied to engineering applications, although a clear physical determination and interpretation of the kinematical extensions and the resulting higher‐order stresses within the formulation is frequently missing. In this regard, the present contribution focuses on establishing the physical link between discrete contact forces, stresses and deformation of particle‐based microstructures and the characteristic stress states of microcontinuum theories. Representative Elementary Volumes (REVs) are therefore constructed on the mesoscale as ensembles of deformable particles from the mircoscale. Establishing the REV balance relations justifies the common generalisation of the angular momentum balance commonly applied in microcontinuum theories. It furthermore leads to the identification of the continuum stresses based on micro‐quantities and enables the application of homogenisation techniques by exploitation of the equilibrium conditions of a REV. In order to investigate the hereby established link from the micro‐ to the macroscale, granular materials are simulated using the Discrete‐Element Method (DEM). In particular, localisation phenomena in granulates, e. g. in biaxial compression tests or during ground‐failure processes are studied. This implies the formulation of the contact between particles in an appropriate constitutive manner in accordance to the envisaged granular material behaviour, e. g. whether loose material, such as sand, or bonded multi‐component material, such as polyurethan‐sand compounds for metal casting applications are of interest. With the full solution of a particle‐based initial‐boundary‐value problem, the homogenisation formalism is applied and enables the study of the extended continuum field quantities, essentially demonstrating the applicability of microcontinuum theories in the field of granular material. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Journal

Proceedings in Applied Mathematics & MechanicsWiley

Published: Jan 1, 2017

References

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