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Visco-hyperelastic law for finite deformations: a frequency analysis
Mathieu Charlebois1, Hamid Motallebzadeh, W Robert J Funnell
1BioMedical Engineering Department, Faculty of Medicine, McGill University, 3775 rue University, Montreal, QC H3A 2B4, Canada. mathieu.charlebois@mcgill.ca
Biomechanics and Modeling in Mechanobiology
|September 12, 2012
Summary
This study compares quasi-linear (QLVH) and nonlinear (NLVH) visco-hyperelastic models for biological tissues under cyclic loading. NLVH models better capture complex damping behaviors at higher strains, offering more accurate simulations for tissue mechanics.
Area of Science:
- Biomechanics
- Materials Science
- Computational Solid Mechanics
Background:
- Biological tissues often undergo cyclic loading and large deformations, necessitating advanced constitutive models.
- Visco-hyperelastic models are crucial for simulating the complex mechanical behavior of soft tissues.
- Existing models like the quasi-linear visco-hyperelastic (QLVH) model have limitations in capturing nonlinear phenomena.
Purpose of the Study:
- To compare the predictive capabilities of a quasi-linear visco-hyperelastic (QLVH) model and a nonlinear visco-hyperelastic (NLVH) model.
- To investigate the influence of strain amplitude and frequency on energy dissipation and storage in these models.
- To evaluate the suitability of NLVH models, particularly NLVH-2 and NLVH-30, for simulating complex damping behaviors in biological tissues.
Main Methods:
- Finite-element simulations were conducted across a wide frequency range.
- The study computed lost and stored energies for both QLVH and NLVH models.
- The NLVH model's additional parameter was set to literature-derived values (2 and 30) for comparative analysis.
Main Results:
- At small strains, both models exhibit similar behavior, with time constants correlating to damping peaks and stored energy increases.
- At increased strain amplitudes, the ratio of lost to stored energy rises for QLVH but declines for NLVH models.
- The NLVH-30 model demonstrates a notable shift in peak damping towards higher frequencies, unlike the QLVH model.
Conclusions:
- Nonlinear visco-hyperelastic (NLVH) models offer superior accuracy in predicting the behavior of biological tissues under large deformations and cyclic loading compared to QLVH models.
- The additional parameter in NLVH models allows for the simulation of complex damping evolutions and frequency-dependent responses.
- This comparative study provides valuable insights for selecting appropriate visco-hyperelastic models in biomechanical and finite-element analyses.
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