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On the physically motivated choice of internal variables describing martensitic phase transformations
Author(s) -
ObersteBrandenburg Claus
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510133
Subject(s) - scalar (mathematics) , phase (matter) , phenomenological model , statistical physics , constitutive equation , phase boundary , martensite , materials science , phase transition , variable (mathematics) , thermodynamics , microstructure , mechanics , mathematics , physics , mathematical analysis , geometry , metallurgy , statistics , quantum mechanics , finite element method
Phenomenological models which describe phase transformation in solids often employ a single scalar variable, the mass (or volume) fraction of one of the phases involved. However, the orientation of the applied stress has a major influence on the microstructure developing during the phase transition and thus the overall mechanical behavior. Therefore, additional internal variables of higher order have to be introduced in order to capture this aspect. The choice of these internal variables is often based on purely phenomenological considerations. In contrast to this, based on local observations at the phase boundary, a thermodynamically dual pair of second order tensors is introduced here. Constitutive relations for shape menory alloys in the pseudoelastic and pseudoplastic range are proposed. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)