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Theory and Implementation of Time‐Dependent Fibre Reorientation in Transversely Isotropic Materials
Author(s) -
Himpel Grieta,
Menzel Andreas,
Kuhl Ellen,
Steinmann Paul
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610046
Subject(s) - transverse isotropy , piezoelectricity , isotropy , orientation (vector space) , principal axis theorem , finite element method , elasticity (physics) , context (archaeology) , constant (computer programming) , physics , classical mechanics , materials science , geometry , mechanics , computer science , mathematics , structural engineering , acoustics , optics , composite material , engineering , geology , paleontology , programming language
Abstract Transversely isotropic materials are commonly described by one characteristic direction in the material configuration, which commonly is assumed to be constant. However, for some applications it makes sense to consider a reorientation of the characteristic direction, as for instance the orientation of biological materials adapts to the mechanical loading, see e.g. Kuhl et al. [4]. Other examples are piezoelectric materials, which reorient due to electric or mechanical loading, as described in Smith [7], and liquid crystals changing their orientation on account of electric or magnetic fields, see Ericksen [1]. Furthermore simulations with a reorientation of the characteristic direction can be used in the context of optimisation of composites. In this contribution we restrict ourselves to the modelling of hyper‐elasticity and assume a time dependent reorientation of the characteristic direction with respect to the principal strain directions, see for instance Menzel [5]. Thereby we concentrate on the numerical implementation into a finite element code. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)