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On the direct connection of rheological elements in nonlinear continuum mechanics
Author(s) -
Landgraf Ralf,
Ihlemann Jörn
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210143
Subject(s) - nonlinear system , continuum mechanics , rheology , viscoelasticity , finite element method , connection (principal bundle) , elasticity (physics) , mechanics , phenomenological model , mathematics , classical mechanics , physics , geometry , thermodynamics , statistics , quantum mechanics
The structure of complicated phenomenological material models at finite strains is often exemplified with the help of rheological elements. Thereby, simple material behaviour, i.e. elasticity or viscous and plastic flow, are composes by components. In our approach, we directly apply this concept to obtain material models at finite strains. Towards this end, the thermodynamically consistent material behaviour of single elements is defined first. Subsequently, the elements are connected by evaluation of stress equilibria equations formulated on interconnecting configurations. The basic equations of this concept are presented using the example of nonlinear viscoelasticity of Maxwell type. The model results from a series connection of an elastic and a viscous element, whereas both are formulated in a thermodynamically consistent way within the framework on nonlinear continuum mechanics. Furthermore, an approach of numerical implementation using the stress equilibria is suggested. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)