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Direct connection of rheological elements at large strains: Application to multiplicative viscoplasticity
Author(s) -
Kießling Robert,
Landgraf Ralf,
Ihlemann Jörn
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510147
Subject(s) - viscoplasticity , rheology , connection (principal bundle) , multiplicative function , nonlinear system , mathematics , physics , mathematical analysis , finite element method , geometry , thermodynamics , constitutive equation , quantum mechanics
Abstract In the field of nonlinear continuum mechanics, rheological models are often used to exemplify the structure of complex material models at large strains. For this purpose, different rheological elements are combined in series and parallel connections. Ihlemann [1] developed an innovative concept, which enables the direct connection of rheological elements within the framework of multiplicative decomposition of the deformation gradient. In the contribution at hand, this approach is applied to multiplicative viscoplasticity. Towards this end, the relations for parallel and series connections are introduced and several individual material models, i.e. the rheological elements, are defined. By analytical and numerical evaluation of the connection relations, a viscoplastic material model from the literature is reproduced. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)