Theory and numerics of geometrically non-linear open system mechanics

Kuhl, E. and Steinmann, P. (2003) Theory and numerics of geometrically non-linear open system mechanics. International Journal for Numerical Methods in Engineering, 58(11), pp. 1593-1615. (doi: 10.1002/nme.827)

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Abstract

he present contribution aims at deriving a general theoretical and numerical framework for open system thermodynamics. The balance equations for open systems differ from the classical balance equations by additional terms arising from possible local changes in mass. In contrast to existing formulations, these changes not only originate from additional mass sources or sinks but also from a possible in- or outflux of matter. Constitutive equations for the mass source and the mass flux are discussed for the particular model problem of bone remodelling in hard tissue mechanics. Particular emphasis is dedicated to the spatial discretization of the coupled system of the balance of mass and momentum. To this end we suggest a geometrically non-linear monolithic finite element based solution technique introducing the density and the deformation map as primary unknowns. It is supplemented by the consistent linearization of the governing equations. The resulting algorithm is validated qualitatively for classical examples from structural mechanics as well as for biomechanical applications with particular focus on the functional adaption of bones. It turns out that, owing to the additional incorporation of the mass flux, the proposed model is able to simulate size effects typically encountered in microstructural materials such as open-pored cellular solids, e.g. bones.

Item Type:Articles
Additional Information:Funding Information: German Science Foundation DFG. Grant Number: KU‐1313.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Steinmann, Professor Paul
Authors: Kuhl, E., and Steinmann, P.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:International Journal for Numerical Methods in Engineering
Publisher:Wiley
ISSN:0029-5981
ISSN (Online):1097-0207
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