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Modelling of Mass Changes in Anisotropic Materials
Author(s) -
Himpel Grieta,
Kuhl Ellen,
Menzel Andreas,
Steinmann Paul
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510126
Subject(s) - ansatz , isotropy , anisotropy , transverse isotropy , coupling (piping) , kinematics , weighting , constitutive equation , deformation (meteorology) , statistical physics , function (biology) , mechanics , classical mechanics , physics , materials science , finite element method , thermodynamics , composite material , mathematical physics , optics , evolutionary biology , biology , acoustics
For the modelling of biomaterials with changing mass one can distinguish between a coupling of mass changes and deformations at the constitutive level, see e.g. [3], and a coupling at the kinematic level, see e.g. [4]. The constitutive coupling is typically realised by weighting the free energy function with the relative density. Such an ansatz enables the simulation of density changes and is generally used to model hard tissues. The kinematic coupling is characterised by a multiplicative split of the deformation gradient into an elastic part and a growth part. Such an ansatz enables the simulation of mass changes as changes in density and volume and is appropriate to model soft tissues. In this contribution the agreements and disagreements of both approaches should be presented by means of a transversely isotropic material and studied by numerical examples. For a more detailed description of the discussed topic, the reader is also referred to [2]. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)