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Modelling of predeformation‐ and frequency‐dependent material behaviour of filled rubber under large predeformations superimposed with harmonic deformations of small amplitudes
Author(s) -
Wollscheid Daniel,
Lion Alexander
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210135
Subject(s) - viscoelasticity , frequency domain , amplitude , compressibility , modulus , harmonic , constitutive equation , natural rubber , dynamic modulus , materials science , mechanics , physics , dynamic mechanical analysis , composite material , mathematical analysis , mathematics , thermodynamics , finite element method , acoustics , optics , polymer
Viscoelastic materials show a significant frequency and predeformation dependent behaviour under loadings consisting of large predeformations superimposed by small harmonic deformations. Based on further material models of Haupt & Lion [1] and Lion, Retka & Rendek [2] we introduce a recently developed constitutive approach of finite viscoelasticity in the frequency domain that is able to describe the frequency and predeformation dependent material behaviour with respect to storage and loss modulus. The constitutive equations are geometrically linearised in the neighbourhood of the predeformation and will be evaluated in the frequency domain. Furthermore a formulation for incompressible material behaviour is introduced and the corresponding dynamic modulus tensors are derived. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)