Viscohyperelastic law for finite deformations: a frequency analysis
 Mathieu Charlebois,
 Hamid Motallebzadeh,
 W. Robert J. Funnell
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Some biological tissues are repeatedly stimulated under cyclic loading, and this stimulation can be combined with large pressures, thus leading to large deformations. For such applications, viscohyperelastic models have been proposed in the literature and used in finiteelement studies. An extensively used quasilinear model (QLVH), which assumes linear evolution equations, is compared with a nonlinear model (NLVH), which assumes a multiplicative split of the deformation gradient. The comparison is made here using sets of simulations covering a large frequency range. Lost and stored energies are computed, and the additional parameter of the NLVH model is set to two values found in the literature (NLVH2 and NLVH30 models). The predicted behaviour is very similar for all models at small strains, with each time constant (and corresponding viscous modulus) being associated with a damping peak and a storedenergy increase. When the strain amplitude is increased, the ratio of lost to stored energy increases for the QLVH model, but decreases for the NLVH models. The NLVH30 model also displays a shift of the peak damping towards higher frequencies. Before reaching a steady state, all models display a decay of energy independent of the frequency, and the additional parameter of the NLVH model permits the modelling of complex types of evolution of the damping. In conclusion, this study compares the behaviour of two viscous hyperelastic laws to allow an informed choice between them.
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 Title
 Viscohyperelastic law for finite deformations: a frequency analysis
 Journal

Biomechanics and Modeling in Mechanobiology
Volume 12, Issue 4 , pp 705715
 Cover Date
 20130801
 DOI
 10.1007/s1023701204352
 Print ISSN
 16177959
 Online ISSN
 16177940
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Middle ear
 Vocal folds
 Viscoelasticity
 Large deformations
 Nonlinearity
 Frequency response
 Authors

 Mathieu Charlebois ^{(1)}
 Hamid Motallebzadeh ^{(1)}
 W. Robert J. Funnell ^{(2)}
 Author Affiliations

 1. BioMedical Engineering Department, Faculty of Medicine, McGill University, 3775 rue University, Montreal, QC, H3A 2B4, Canada
 2. Department of Biomedical Engineering and Otolaryngology – Head & Neck Surgery, Faculty of Medicine, McGill University, 3775 rue University, Montreal, QC, H3A 2B4, Canada