Abstract
This paper presents a nonlinear and quasilinear viscoelasticity model for the behavior of soft fibrous tissues that incorporates the effects of matrix and fiber-level viscoelasticity. Both models treat the tissue as a composite of N fiber families in an isotropic matrix. For the nonlinear model, the anisotropic contribution of the fibers to the constitutive behavior of the tissue is developed by first defining the stress response and viscous flow response of the fiber families, then averaging by the fiber orientation. Similarly, the anisotropic contribution of the quasilinear model is developed from a hereditary integral formulation for the stress response of the fiber families. The stress relaxation response of the nonlinear and quasilinear models are compared for different applied strains. As expect, the time-dependent response of the two formulations are nearly identical for small strain, but they exhibit significant differences at large strain.
Keywords
- Relaxation Curve
- Free Energy Density
- Kirchhoff Stress
- Characteristic Relaxation Time
- Viscous Deformation
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Nguyen, T.D. (2010). A Comparison of a Nonlinear and Quasilinear Viscoelastic Anisotropic Model for Fibrous Tissues. In: Garikipati, K., Arruda, E. (eds) IUTAM Symposium on Cellular, Molecular and Tissue Mechanics. IUTAM Bookseries, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3348-2_2
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DOI: https://doi.org/10.1007/978-90-481-3348-2_2
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